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- Committer: Bazaar Package Importer
- Author(s): Christoph Berg
- Date: 2010-04-20 23:27:57 UTC
- mfrom: (1.1.4 upstream)
- Revision ID: james.westby@ubuntu.com-20100420232757-rzez7nr9st6ymeje
Tags: 2.0.0+ddd105-1
* New dds upstream version (only bumping version).
* Add SolveBoard.3 manpage.
* Add SolveBoard.3 manpage.
- files added:
- DDS_alg_descr-revE4.rtf
- debian/source
- files removed:
- DDS_alg_descr-revE3.rtf
- files modified:
- dds.cpp
added
removed
DDS_alg_descr-revE4.rtf
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\listoverridecount0\ls17}}{\info{\title Bo Haglund}{\author Bo Haglund}{\operator Bo Haglund}{\creatim\yr2008\mo9\dy7\hr11\min21}{\revtim\yr2010\mo4\dy10\hr9\min55}{\version17}{\edmins115}{\nofpages23}{\nofwords6036}{\nofchars-32766}{\*\company }
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\par }\pard \s16\ri360\nowidctlpar\tqc\tx4536\tqr\tx9072\adjustright {
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\par }}{\*\pnseclvl1\pnucrm\pnstart1\pnindent720\pnhang{\pntxta .}}{\*\pnseclvl2\pnucltr\pnstart1\pnindent720\pnhang{\pntxta .}}{\*\pnseclvl3\pndec\pnstart1\pnindent720\pnhang{\pntxta .}}{\*\pnseclvl4\pnlcltr\pnstart1\pnindent720\pnhang{\pntxta )}}
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{\*\pnseclvl5\pndec\pnstart1\pnindent720\pnhang{\pntxtb (}{\pntxta )}}{\*\pnseclvl6\pnlcltr\pnstart1\pnindent720\pnhang{\pntxtb (}{\pntxta )}}{\*\pnseclvl7\pnlcrm\pnstart1\pnindent720\pnhang{\pntxtb (}{\pntxta )}}{\*\pnseclvl8
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\pnlcltr\pnstart1\pnindent720\pnhang{\pntxtb (}{\pntxta )}}{\*\pnseclvl9\pnlcrm\pnstart1\pnindent720\pnhang{\pntxtb (}{\pntxta )}}\pard\plain \s1\keepn\nowidctlpar\outlinelevel0\adjustright \lang2057 {\lang1053 Bo Haglund
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\par }\pard\plain \nowidctlpar\adjustright \lang2057 {Rev. E4}{\lang1053 , 2010-04-09}{
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\par }\pard\plain \s1\keepn\nowidctlpar\outlinelevel0\adjustright \lang2057 {\b\fs28\lang1053
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\par
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\par Search Algorithms for a Bridge Double Dummy Solver
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\par }\pard\plain \nowidctlpar\adjustright \lang2057 {\lang1053
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\par This description is intended for anyone interested in the inner workings of a bridge double dummy solver (DDS). It describes my solver implemented in the Win32 environment as a DLL.
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\par
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\par }{DDS algorithm descriptions already exist, see reference list at the end. However, to my knowledge, no document exists that gives an in depth description of all algorithms covered in this document.}{\lang1053
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\par
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\par
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\par
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\par
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\par {\listtext\pard\plain\b \hich\af0\dbch\af0\loch\f0 1.\tab}}\pard \nowidctlpar\jclisttab\tx0\ls16\adjustright {\b\lang1053 The basic search algorithm
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\par }\pard \nowidctlpar\adjustright {\lang1053
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\par The search is based on the zero window search [Pearl 1980].
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\par Pseudo code for its application on DD solver search is given.
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\par Cards searched are described as \'94moves\'94 in contrast to cards that are really played.\page
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\par int Search(posPoint, target, depth) \{
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\par if (depth==0) \{
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\par tricks=Evaluate;
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\par if (tricks >= target)
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\par value=TRUE;
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\par else
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\par value=FALSE;
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\par return value;
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\par \}
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\par else \{
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\par GenerateMoves;
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\par if (player_side_to_move) \{
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\par value=FALSE; moveExists=TRUE;
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\par while (moveExists) \{
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\par Make;
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\par value=Search(posPoint, target, depth-1);
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\par Undo;
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\par if (value==TRUE)
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\par \tab goto searchExit;\tab /* Cutoff, current move recorded as \'94best move\'94 */
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\par moveExists=NextMove;
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\par \}
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\par \}\tab /* Opponents to move */
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\par else \{\tab
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\par value=TRUE; moveExists=TRUE;
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\par while (moveExists) \{
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\par Make;
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\par value=Search(posPoint, target, depth-1);
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\par Undo;
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\par if (value==FALSE)
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\par \tab goto searchExit;\tab /* Cutoff, current move recorded as \'94best move\'94 */
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\par moveExists=NextMove;
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\par \}
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\par \}
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\par \}
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\par
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\par searchExit:
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\par return value;
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\par \}
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\par
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\par
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\par }{The Search parameters are:
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\par {\pntext\pard\plain\f3\lang2057 \loch\af3\dbch\af0\hich\f3 \'b7\tab}}\pard \fi-360\li360\nowidctlpar\jclisttab\tx360{\*\pn \pnlvlblt\ilvl0\ls5\pnrnot0\pnf3\pnstart1\pnindent360\pnhang{\pntxtb \'b7}}\ls5\adjustright {\b posPoint - }{
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a pointer to a structure containing state information for the position (deal) to be searched, e.g. leading hand, hand-to-play, cards yet to play etc.
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\par {\pntext\pard\plain\f3\lang2057 \loch\af3\dbch\af0\hich\f3 \'b7\tab}}\pard \fi-360\li360\nowidctlpar\jclisttab\tx360{\*\pn \pnlvlblt\ilvl0\ls5\pnrnot0\pnf3\pnstart1\pnindent360\pnhang{\pntxtb \'b7}}\ls5\adjustright {\b target}{
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- the number of tricks the player must take.
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\par {\pntext\pard\plain\f3\lang2057 \loch\af3\dbch\af0\hich\f3 \'b7\tab}}\pard \fi-360\li360\nowidctlpar\jclisttab\tx360{\*\pn \pnlvlblt\ilvl0\ls5\pnrnot0\pnf3\pnstart1\pnindent360\pnhang{\pntxtb \'b7}}\ls5\adjustright {\b depth}{ - the current search depth.
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\par }\pard \nowidctlpar\adjustright {
128
\par Search returns TRUE if the target is reached, otherwise FALSE.
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\par }{\lang1053
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\par When Search is called, depth is set to the number of cards left to play minus 4.
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\par GenerateMoves generates a list of alternative moves (=cards) that can be played in the initial position whose state da
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ta is pointed to by posPoint. For cards that are equivalent (e.g. AK) only the card with highest rank is generated. Card equivalence is reanalyzed after each trick.
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\par }{E.g. if the hand-to-play has AQ in a suit where K was played in a previous trick, then A and Q become equivalents.}{\lang1053
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\par
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\par If the side of the player has the move, Search tries to find a move that meets the target, i.e that evaluates to TRUE. If such a move is found, search returns TRUE, and saves the move as \'94best\'94.
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\par If the other side has the move, Search tries to find a move that defies meeting the target, i.e. that evaluates to FALSE. If such a move is found, search returns FALSE, and saves the move as \'94best\'94.
137
\par
138
\par Each move in the generated move list is handled by first calling Make, which removes the ca
139
rd from the position state information. Search is then recursively called with a position state that now has excluded the played card, depth has been decremented by one. For each new recursive call to Search, a card is removed from the position state info
140
r
141
mation and depth is decremented. This goes on until depth equals 0 in which case only one trick remains. The outcome of this trick is calculated by Evaluate. If the total number of tricks won by the side of the player then reaches target, Search returns T
142
RUE, otherwise FALSE. This result propagates upwards as Search returns for each level, Undo is called which reinstalls the searched card on this level.\line Finally, Search returns for the top level.
143
\par
144
\par This basic search algorithm is not powerful enough to terminate the search of a typical 52 cards deal in a reasonable time. To accomplish this, a number of search algorithm enhancements are required, which will be described in the following chapters.
145
146
\par \page
147
\par The described search algorithm only tells if a predefined target can be reached. It does not tell how many tricks that the side of the player can get. This is accomplished by repeated calls to Search:
148
\par
149
\par g = guessed number of tricks for side of the player
150
\par iniDepth = number of cards to play minus 4
151
\par upperbound = 13;
152
\par lowerbound = 0;
153
\par do \{
154
\par if (g==lowerbound)
155
\par tricks=g+1;
156
\par else
157
\par tricks=g;
158
\par if ((Search(posPoint, tricks, iniDepth)==FALSE) \{
159
\par upperbound=tricks-1;
160
\par g=upperbound;
161
\par \}
162
\par else \{
163
\par lowerbound=tricks;
164
\par g=lowerbound;
165
\par \}
166
\par \}
167
\par while (lowerbound < upperbound);
168
\par g=maximum tricks to be won by side of player.}{\b\lang1053
169
\par
170
\par
171
\par
172
\par {\listtext\pard\plain\s3 \b \hich\af0\dbch\af0\loch\f0 2.\tab}}\pard\plain \s3\keepn\nowidctlpar\jclisttab\tx0\ls16\outlinelevel2\adjustright \b\lang1053 {Overview of the search algorithms used in the DD solver
173
\par }\pard\plain \nowidctlpar\adjustright \lang2057 {\b\lang1053
174
\par }{\lang1053 The additional functions in the pseudo code for supporting the search speed enhancements are given in }{\i\lang1053 italics}{\lang1053 .
175
\par \page
176
\par int Search(posPoint, target, depth) \{
177
\par if (no_move_yet_in_trick) \{}{\cf1\lang1053
178
\par }{\lang1053 }{\i\lang1053 TargetTooLowOrHigh;
179
\par }{\lang1053 if (target_already_obtained)
180
\par }\pard\plain \s16\nowidctlpar\adjustright \lang2057 {\lang1053 return TRUE;
181
\par }\pard\plain \nowidctlpar\adjustright \lang2057 {\lang1053 else if (target_can_no_longer_be_obtained)
182
\par return FALSE;}{\i\lang1053
183
\par QuickTricks;
184
\par LaterTricks;
185
\par }{\lang1053 if (cutoff_for_player_side)
186
\par return TRUE;
187
\par else if (cutoff_for_opponent_side)
188
\par return FALSE;}{\i\lang1053 \line RetrieveTTresult;
189
\par }\pard\plain \s16\nowidctlpar\adjustright \lang2057 {\lang1053 if (transposition_table_entry_match) \{
190
\par }\pard\plain \nowidctlpar\adjustright \lang2057 {\i\lang1053 }{\lang1053 if (target_reached)
191
\par return TRUE;
192
\par else
193
\par return FALSE;
194
\par \}}{\i\lang1053
195
\par }\pard\plain \s16\nowidctlpar\adjustright \lang2057 {\lang1053 \}
196
\par }\pard\plain \nowidctlpar\adjustright \lang2057 {\lang1053
197
\par if (depth==0) \{
198
\par }{\i\lang1053 evalRes=Evaluate;
199
\par }{\lang1053 if (evalRes.tricks >= target)
200
\par value=TRUE;
201
\par else
202
\par value=FALSE;
203
\par return value;
204
\par \}
205
\par else \{
206
\par GenerateMoves;
207
\par }{\i\lang1053 MoveOrdering;
208
\par CheckMovesForCutoff; }{\lang1053 /* For pseudo-code, see chapter 6 */}{\i\lang1053
209
\par }{\lang1053 if (player_side_to_move) \{
210
\par value=FALSE; moveExists=TRUE;
211
\par while (moveExists) \{
212
\par Make;
213
\par value=Search(posPoint, target, depth-1);\tab
214
\par Undo;
215
\par if (value==TRUE) \{
216
\par \tab }{\i\lang1053 MergeMoveData;}{\lang1053 }{\i\lang1053
217
\par }{\lang1053 \tab goto searchExit;\tab /* Cutoff, current move recorded as \'94best move\'94 */
218
\par \}
219
\par }{\i\lang1053 MergeAllMovesData;
220
\par }{\lang1053 moveExists=}{\i\lang1053 NextMove}{\lang1053 ;
221
\par \}
222
\par \}\tab /* Opponents to move */
223
\par else \{\tab
224
\par value=TRUE; moveExists=TRUE;
225
\par while (moveExists) \{
226
\par Make;
227
\par value=Search(posPoint, target, depth-1);\tab
228
\par Undo;
229
\par if (value==FALSE) \{
230
\par \tab }{\i\lang1053 MergeMoveData;}{\lang1053
231
\par \tab goto searchExit;\tab /* Cutoff, current move recorded as \'94best move\'94 */
232
\par \}
233
\par }{\i\lang1053 MergeAllMovesData;}{\lang1053
234
\par moveExists=}{\i\lang1053 NextMove}{\lang1053 ;
235
\par \}
236
\par \}
237
\par \}
238
\par searchExit:
239
\par }{\i\lang1053 AddNewTTentry;
240
\par }{\lang1053 return value;
241
\par \}
242
\par
243
\par
244
\par }{\i\lang1053 TargetTooLowOrHigh }{\lang1053 checks the target value against the number of tricks currently won by side }{\cf1\lang1053 of the player}{\lang1053 and against number of tricks left to play.
245
\par It is executed at the beginning of each trick, before any card has been played.
246
\par }{If number of currently won tricks }{\cf1 by player\rquote s side}{ equals or exceeds target, Search returns TRUE.\line If number of currently won tricks }{\cf1 by player\rquote s side}{ plus tricks left to play is less than target Search returns FALSE.
247
248
\par Since possible winning cards for the remaining tricks are irrelevant, no winning cards are backed up at cutoff termination.}{\lang1053
249
\par }\pard\plain \s16\nowidctlpar\adjustright \lang2057 {\lang1053
250
\par }\pard\plain \nowidctlpar\adjustright \lang2057 {\i\lang1053 TargetTooLowOrHigh }{\lang1053 search enhancement is described e.g. in [Chang].
251
\par
252
\par }\pard\plain \s1\keepn\nowidctlpar\outlinelevel0\adjustright \lang2057 {\i QuickTricks}{ determines if the side to move can take one or more sure tricks. }{\lang1053
253
E.g. if the hand to move has an Ace in an NT contract, at least one sure trick can be taken.
254
\par }\pard\plain \nowidctlpar\adjustright \lang2057 {\lang1053 It is executed at the beginning of each trick, before any card has been played. A simple quick trick is also executed after the leading card of the trick is played.}{
255
\par }\pard\plain \s1\keepn\nowidctlpar\outlinelevel0\adjustright \lang2057 {\lang1053 Assuming that the sure tricks are won by the side to move, then the conditions for search cutoff in }{\i\lang1053 TargetTooLowOrHigh}{\lang1053
256
are again tested to produce further search cutoffs.
257
\par The detailed conditions for determination of sure tricks are described in Chapter 3.
258
\par }\pard\plain \nowidctlpar\adjustright \lang2057 {When quicktricks win by rank, they are backed up at cutoff termination.
259
\par }\pard\plain \s1\keepn\nowidctlpar\outlinelevel0\adjustright \lang2057 {\lang1053
260
\par The idea of }{\i\lang1053 QuickTricks }{\lang1053 is described e.g. in [Chang].
261
\par }\pard\plain \nowidctlpar\adjustright \lang2057 {
262
\par }{\i LaterTricks}{ determines if the opponents of the side to move can take one or more tricks at their turn or later in the play. It is also executed at the beginning of each trick and uses similar criteria for search cutoff as }{\i Quicktricks}{.
263
264
\par When quicktricks win by rank, they are backed up at cutoff termination.\line For a detailed description, see Chapter 4.
265
\par }\pard\plain \s1\keepn\nowidctlpar\outlinelevel0\adjustright \lang2057 {\lang1053
266
\par }{\i\lang1053 RetrieveTTresult }{\lang1053 scans the set of positions in the transposition table to see if there is a match against the current position.
267
\par It is executed at the beginning of each trick, before any card has been played. After detection of a transposition table entry match, the winning ranks necessary in the remaining cards are backed up. \line For details, see Chapter 7.
268
\par }\pard\plain \nowidctlpar\adjustright \lang2057 {\fs20\lang1053
269
\par }{\i Evaluate }{returns evalResult which updates the position state information. evalResult contains:
270
\par {\listtext\pard\plain\f3\lang2057 \loch\af3\dbch\af0\hich\f3 \'b7\tab}}\pard \fi-360\li780\nowidctlpar\jclisttab\tx780\ls6\adjustright {\b evalResult.tricks}{, the number of tricks won by the side of the player, and
271
\par {\listtext\pard\plain\f3\lang2057 \loch\af3\dbch\af0\hich\f3 \'b7\tab}}{\b evalResult.winRank}{ which includes the card in the last trick that won by rank.
272
\par }\pard \nowidctlpar\adjustright {E.g. if the last trick includes the spades A, Q, 9 and 3, evalResult.winRank returns spade A. But
273
\par if the last trick was won without a win by rank as for spade 5 (leading and winning card), heart A, heart Q, heart 5, no winning rank is returned. }{\lang1053
274
\par
275
\par }{Keeping record of cards that win by ranks and subsequently using this information to ignore ranks for other cards is discussed in the Partition Search concept invented by Matthew Ginsberg and described in his paper [Ginsberg]. }{\lang1053
276
\par
277
\par }{\i MoveOrdering. }{The alternative cards created by MoveGenerate are sorted, with the cards most likely to terminate the search fastest being sorted first in the move list.The allocation of card weights are described in detail in Chapter 5.}{\lang1053
278
279
\par
280
\par }{\i\lang1053 CheckMovesForCutoff }{\lang1053 checks if any of the moves just generated will lead to a position that can be found in the transposition table. If so, an immediate S
281
earch return can be done, saving unnecessary search effort. This is further described in Chapter 6.
282
\par
283
\par To my knowledge this is not described anywhere for usage in a DDS. It is described in [Plaat et al.] and named Enhanced Transposition Cutoffs.
284
\par
285
\par At move search cutoff,}{\i\lang1053 MergeMoveData }{\lang1053
286
collects the union of the backed up accumulated winning ranks and the rank of the made move, assuming it did win by rank. The state data of the position is updated with the collected information.
287
\par
288
\par }{\i\lang1053 MergeAllMovesData }{\lang1053 collects the un
289
ion of the backed up accumulated winning ranks, the previous accumulated winning ranks of the alternative moves generated on this depth, and the rank of the made move, assuming it did win by rank. When all alternative moves have been searched without a cu
290
toff, the state data of the position is updated with the collected information.
291
\par
292
\par The information from }{\i\lang1053 MergeMoveData}{\lang1053 and }{\i\lang1053 MergeAllMovesData}{\lang1053 is later stored in the transposition table and determines which ranks that are essential when }{\i\lang1053 RetrieveTTresult}{\lang1053 scans th
293
e set of positions in the transposition table. A match of ranks with the current position is only needed for winning ranks. See Chapter 7.}{\strike\cf6\lang1053
294
\par }{\lang1053
295
\par }{\i\lang1053 AddNewTTentry }{\lang1053 adds the evaluated position as a new entry in the transposition table. See Chapter 7.
296
\par
297
\par }{\i\lang1053 NextMove }{\lang1053 filters out all \'94small\'94 cards except one per hand/suit combination. A \'94small\'94 card is a backed up card that is shown to never win by rank. The rest of the \'94small\'94
298
card moves for the hand/suit combination are never searched, leading to a smaller search tree.\line This search enhancement was suggested by Hans Kuijf [Kuijf].
299
\par
300
\par
301
\par
302
\par {\listtext\pard\plain\b \hich\af0\dbch\af0\loch\f0 3.\tab}}\pard \nowidctlpar\jclisttab\tx0\ls16\adjustright {\b\lang1053 The Quick Tricks cutoff algorithm
303
\par }\pard \nowidctlpar\adjustright {\b\lang1053
304
\par }{\lang1053 The number of tricks that can immediately be taken by the side to play the leading card of the trick consists of:
305
\par {\pntext\pard\plain\hich\af0\dbch\af0\loch\f0 a)\tab}}\pard \fi-360\li360\nowidctlpar\tx360{\*\pn \pnlvlbody\ilvl0\ls3\pnrnot0\pnlcltr\pnstart1\pnindent360 {\pntxta )}}\ls3\adjustright {\lang1053 The number of tricks that can be taken
306
by the hand-to-play, and
307
\par {\pntext\pard\plain\hich\af0\dbch\af0\loch\f0 b)\tab}}\pard \fi-360\li360\nowidctlpar\tx360{\*\pn \pnlvlbody\ilvl0\ls3\pnrnot0\pnlcltr\pnstart1\pnindent360 {\pntxta )}}\ls3\adjustright {\lang1053
308
The number of tricks that can be taken by the partner of the hand-to-play
309
\par }\pard \nowidctlpar\adjustright {\lang1053 At return by }{\i\lang1053 QuickTricks}{\lang1053 , the position state information is updated with the winning ranks found.
310
\par
311
\par }{Of course, in order to add b), there must be an entry from the hand-to-play to the partner\rquote s hand.
312
\par
313
\par For each \'94s\'94 (suit) the following is calculated:}{\lang1053
314
\par
315
\par If the hand-to-play is the only hand having cards in s, and the opponents have no trumps (when s is not trumps), the number of quick tricks for s is the suit length of the hand-to-play.
316
\par
317
\par If the opponents have no trumps, a check is made to see if quick tricks equal to the maximum of the trumps length for leading hand and the partner causes a search cutoff.
318
\par
319
\par If the hand-to-play has a card in a suit where the partner has a winning rank, and partner is the only hand having cards in s:
320
\par The number of quick tricks for s is the suit length of partner.
321
\par
322
\par Else:
323
\par If the winning rank is in hand-to-play, and the opponents can
324
not ruff, the number of quick tricks is incremented by one. Further, if the second best rank is also in hand-to-play, and the opponents cannot still ruff, the quick tricks is again incremented by one.
325
\par
326
\par Else:
327
\par If the winning rank is in partner and partner has winning rank as entry, the same applies for the partner as for the hand-to-play described above.
328
\par
329
\par }{If it is a trump contract, the first suit to be investigated is the trump suit. Then if there are trump suit quick tricks for the side to play, those are cashed and quick tricks incremented accordingly.
330
\par \line When the other suits are investigated for quick tricks, only the remaining opponent trump cards need to be considered.\line }{\lang1053
331
\par }{The quick tricks are then summarized from each suit, and the total calculated}{\lang1053 .
332
\par
333
\par A simple Quick Tricks algorithm is also executed after the leading card of the trick has been played:
334
\par
335
\par A quick trick is gained either if the hand-to-play or the partner can win the current trick with the card having the highest rank of the suit played, or if hand-to-play or the partner can win the trick by ruffing.
336
\par
337
\par The idea to also execute Quick Tricks after the leading card has been played was given by Hans Kuijf [Kuijf].
338
\par
339
\par
340
\par
341
\par {\listtext\pard\plain\b \hich\af0\dbch\af0\loch\f0 4.\tab}}\pard \nowidctlpar\jclisttab\tx0\ls16\adjustright {\b\lang1053 The Later Tricks cutoff algorithm}{\lang1053
342
\par }\pard \nowidctlpar\adjustright {\lang1053
343
\par Check for search cutoff if the opponents to the trick leading hand have at least a sure trick later.
344
\par
345
\par }{\b\lang1053 If not trump contract:\line
346
\par {\pntext\pard\plain\hich\af0\dbch\af0\loch\f0 1)\tab}}\pard \fi-360\li360\nowidctlpar\jclisttab\tx360{\*\pn \pnlvlbody\ilvl0\ls17\pnrnot0\pndec\pnstart1\pnindent360\pnhang{\pntxta )}}\ls17\adjustright {\lang1053
347
The opponents have at least a sure trick if for all suits where the trick leading hand has a card, the side of the leading hand does not have the highest rank.\line
348
More than one sure trick can be taken by the opponents if they possess the winning rank for more than one suit, or\line
349
\par {\pntext\pard\plain\hich\af0\dbch\af0\loch\f0 2)\tab}}\pard \fi-360\li360\nowidctlpar\jclisttab\tx360{\*\pn \pnlvlbody\ilvl0\ls17\pnrnot0\pndec\pnstart1\pnindent360\pnhang{\pntxta )}}\ls17\adjustright {\lang1053
350
Assume that all suits where the side of the trick leading hand has the winning rank give maximum possible number of tricks, i.e. that the sure trick number is the sum of the\line maximum lengths of these suits.\line
351
If this still cannot cause a cutoff for the trick leading side, allocate one sure trick for the opponents side.
352
\par }\pard \nowidctlpar\adjustright {\lang1053
353
\par }{\b\lang1053 If trump contract:
354
\par }{\lang1053
355
\par Quick tricks for the opponents of the leading hand are added when the opponents have one or more winning trumps. This idea was given by Pedja Stanojevic [Stanojevic].\line \line
356
1) If the opponent side have all the trumps, the number of sure tricks is the maximum suit length\line length, or\line
357
\par 2) If the opponent side has the highest trump, they have 1 sure trick. If they also have the second\line highest trump, they have 2 sure tricks, or\line \line 3) If the opponent side has the second highest trump plus at least one tr
358
ump more behind the \line hand with the highest trump, the opponent side has 1 sure trick.
359
\par \page
360
\par {\listtext\pard\plain\s3 \b \hich\af0\dbch\af0\loch\f0 5.\tab}}\pard\plain \s3\keepn\nowidctlpar\jclisttab\tx0\ls16\outlinelevel2\adjustright \b\lang1053 {The Move Ordering algorithm
361
\par }\pard\plain \nowidctlpar\adjustright \lang2057 {\b\lang1053
362
\par }{\lang1053 The weight of a card in the move list is affected by the suit and the rank of the card and by the other cards in the same trick.
363
\par The weights of the cards in the move list are used to sort them, }{with the cards having the highest weight being sorted first in the list}{\lang1053 .
364
\par
365
\par If the hand-to-play is trick leading hand or void in the suit played by leading hand, the card with the highest weight
366
for each present suit will get a high additional bonus weight. After list resorting, those cards will occupy the first positions in the move list.
367
\par
368
\par Two "best moves" are maintained for each searched depth, one for an alpha-beta cutoff and one at a Transpos
369
ition Table entry match. At an alpha-beta cutoff, the move causing the cutoff overwrites the present "best move" for the current depth. When a Transposition Table entry is created, the current best move is stored in that entry if:
370
\par The target is met and the leading hand belongs to the player\rquote s side, or target is not met and the leading hand belongs to the other side. Otherwise the best move is not stored in the Transposition Table entry.
371
\par At a Transposition Table entry match, }{its stored best move will be best move for the current search depth.}{\lang1053
372
\par
373
\par By \'94card move\'94 in the following pseudo code is meant the card by the hand-to-play that is getting a weight in the move list. }{\cf1\lang1053 The \'94card rank\'94 is a value in the range 2-14, corresponding to the card ranks 2 to the Ace.
374
\par
375
\par }{\lang1053 For the determination of the weight, it is calculated whether or not the current card move is a card that wins the current trick for the side of the hand-to-play, assuming that both sides play their optimum cards.
376
\par
377
\par If the hand-to-play is void in the trick lead suit, the suit selected for the discard gets the following\line bonus:
378
\par
379
\par suitAdd = ((suit length) * 64)/36;
380
\par
381
\par If the suit length is 2, and the hand-to-play has the next highest rank of the suit, the bonus \line (suitAdd) is subtracted by 2. }{\cf1\lang1053
382
\par }{\fs20\lang1053
383
\par
384
\par }\pard\plain \s2\keepn\nowidctlpar\outlinelevel1\adjustright \lang2057 {\ul\lang1053 Hand-to-play is trick leading hand
385
\par }\pard\plain \nowidctlpar\adjustright \lang2057 {\lang1053
386
\par The contribution of the suit to the weight:
387
\par
388
\par }\pard\plain \s16\nowidctlpar\adjustright \lang2057 {\lang1053 suitWeightDelta = suitBonus \endash ((countLH+countRH) * 32)/15
389
\par }\pard\plain \nowidctlpar\adjustright \lang2057 {\lang1053
390
\par suitBonus has the initial value 0, changed if conditions below apply:
391
\par
392
\par If trump contract, and the suit is not trump, then there is a (negative) suitBonus change of \endash 10 if
393
\par {\pntext\pard\plain\f3 \loch\af3\dbch\af0\hich\f3 \'b7\tab}}\pard \fi-360\li360\nowidctlpar\tx360{\*\pn \pnlvlblt\ilvl0\ls2\pnrnot0\pnf3\pnindent360 {\pntxtb \'b7}}\ls2\adjustright {\lang1053 LHO is void and LHO has trump card(s), or
394
\par {\pntext\pard\plain\f3 \loch\af3\dbch\af0\hich\f3 \'b7\tab}}\pard \fi-360\li360\nowidctlpar\tx360{\*\pn \pnlvlblt\ilvl0\ls2\pnrnot0\pnf3\pnindent360 {\pntxtb \'b7}}\ls2\adjustright {\lang1053 RHO is void and RHO has trump card(s)
395
\par }\pard \nowidctlpar\tx360\adjustright {\lang1053 \line If RHO has either the highest rank of the suit played by hand-to-play or the next highest rank,
396
\par then there is a suitBonus change of \endash 18.
397
\par
398
\par If it is a trump contract, the suit is not trump, own hand has a singleton, own hand has at least one trump, partner has the highest rank in the suit and at least a suit length of 2, then there is a suitBonus change of +16.
399
\par }\pard \nowidctlpar\adjustright {\lang1053
400
\par countLH = (suit length of LHO) * 4, if LHO is not void in the suit,
401
\par countLH = (depth + 4), if LHO is void in the suit
402
\par
403
\par countRH = (suit length of RHO) * 4, if RHO is not void in the suit,
404
\par countRH = (depth + 4), if RHO is void in the suit
405
\par
406
\par Suits are thus favoured where the opponents have as few move alternatives as possible.
407
\par
408
\par
409
\par if (trick winning card move) \{
410
\par if (one of the opponents has a singleton highest rank in the suit)
411
\par weight = suitWeightDelta + 40 \endash (rank of card move)
412
\par else if (hand-to-play has highest rank in suit) \{
413
\par if (partner has second highest rank in suit)
414
\par weight = suitWeightDelta + 50 \endash (rank of card move)
415
\par else if (the card move is the card with highest rank in the suit)
416
\par weight = suitWeightDelta + 31
417
\par else
418
\par weight = suitWeightDelta + 19 \endash (rank of card move)
419
\par \}
420
\par else if (partner has highest rank in suit) \{
421
\par if (hand-to-play has second highest rank in suit)
422
\par weight = suitWeightDelta + 50 \endash (rank of card move)
423
\par else
424
\par weight = suitWeightDelta + 35 \endash (rank of card move)
425
\par \}
426
\par else if (hand-to-play has second highest rank together with equivalent card(s) in suit)
427
\par weight = suitWeightDelta + 40
428
\par else
429
\par weight = suitWeightDelta + 30 \endash (rank of card move)
430
\par if (the card move is \'94best move\'94 as obtained at alpha-beta cutoff)
431
\par weight = weight + 52;
432
\par if (the card move is \'94best move\'94 as obtained from a Transposition Table entry match)
433
\par weight = weight + 11;
434
\par \}
435
\par else \{\tab /* Not a trick winning move */
436
\par if (either LHO or RHO has singleton in suit which has highest rank)
437
\par weight = suitWeightDelta + 29 \endash (rank of card move)
438
\par else if (hand-to-play has highest rank in suit) \{
439
\par if (partner has second highest rank in suit)
440
\par weight = suitWeightDelta + 44 \endash (rank of card move)
441
\par else if (the card move is the card with highest rank in the suit)
442
\par weight = suitWeightDelta + 25
443
\par else
444
\par weight = suitWeightDelta + 13 \endash (rank of card move)
445
\par \}
446
\par else if (partner has highest rank in suit) \{
447
\par if (hand-to-play has second highest rank in suit)
448
\par weight = suitWeightDelta + 44 \endash (rank of card move)
449
\par else
450
\par weight = suitWeightDelta + 29 \endash (rank of card move)
451
\par \}
452
\par else if (hand-to-play has second highest rank together with equivalent card(s) in suit)
453
\par weight = suitWeightDelta + 29
454
\par else
455
\par weight = suitWeightDelta + 13 \endash (rank of card move)
456
\par if (the card move is \'94best move\'94 as obtained at alpha-beta cutoff)
457
\par weight = weight + 20;
458
\par if (the card move is \'94best move\'94 as obtained from a Transposition Table entry match)
459
\par weight = weight + 9;
460
\par \}
461
\par
462
\par
463
\par }{\ul\lang1053 Hand-to-play is left hand opponent (LHO) to leading hand
464
\par }{\lang1053
465
\par if (trick winning card move) \{
466
\par if (hand-to-play void in the suit played by the leading hand) \{
467
\par if (trump contract and trump is equal to card move suit)
468
\par }{\cf1\lang1053 weight = 30 - (rank of card move) + suitAdd
469
\par else
470
\par weight = 60 - (rank of card move) + suitAdd
471
\par \}
472
\par else if (lowest card for partner to leading hand is higher than LHO played card)
473
\par weight = 45 - (rank of card move)
474
\par else if (RHO has a card in the leading suit that is higher than the trick leading card\line but lower than the highest rank of the leading hand)
475
\par weight = 60 - (rank of card move)
476
\par else if (LHO played card is higher than card played by the leading hand) \{
477
\par if (played card by LHO is lower than any card for RHO in the same suit)
478
\par weight = 75 - (rank of card move)
479
\par else if (played card by LHO is higher than any card in the same suit for the leading hand)
480
\par weight = 70 - (rank of card move)
481
\par else \{
482
\par }{\lang1053 if (LHO move card has at least one equivalent card) \{
483
\par }{\cf1\lang1053 weight = 60 - (rank of card move)}{\lang1053
484
\par else
485
\par }{\cf1\lang1053 weight = 45 - (rank of card move)
486
\par \}
487
\par \}
488
\par else if (RHO is not void in the suit played by the leading hand) \{
489
\par }{\lang1053 if (LHO move card has at least one equivalent card) }{\cf1\lang1053 }{\lang1053 }{\cf1\lang1053
490
\par weight = 50 - (rank of card move)
491
\par else
492
\par weight = 45 - (rank of card move)
493
\par \}
494
\par else
495
\par weight = 45 - (rank of card move)
496
\par \}
497
\par else \{\tab /* card move is not trick winning */
498
\par }{\lang1053 if (hand-to-play void in the suit played by the leading hand) \{
499
\par if (trump contract and trump is equal to card move suit)}{\cf1\lang1053
500
\par }{\lang1053 }{\cf1\lang1053 weight = 15 - (rank of card move) + suitAdd
501
\par else
502
\par weight = - (rank of card move) + suitAdd
503
\par \}
504
\par else if (lowest card for partner to leading hand or for RHO in the suit played is higher \line than played card for LHO)
505
\par weight = - (rank of card move)
506
\par else if (LHO played card is higher than card played by the leading hand) \{
507
\par }{\lang1053 if (LHO move card has at least one equivalent card)
508
\par }{\cf1\lang1053 weight = 20 - (rank of card move)
509
\par else}{\lang1053
510
\par }{\cf1\lang1053 weight = 10 - (rank of card move)
511
\par \} }{\lang1053
512
\par else
513
\par }{\cf1\lang1053 weight = - (rank of card move)
514
\par \} }{\lang1053 }{\cf1\lang1053 }{\lang1053 }{\cf1\lang1053
515
\par }{\lang1053
516
\par
517
\par
518
\par }\pard\plain \s2\keepn\nowidctlpar\outlinelevel1\adjustright \lang2057 {\ul\lang1053 Hand-to-play is partner to trick leading hand
519
\par }\pard\plain \nowidctlpar\adjustright \lang2057 {\lang1053
520
\par if (trick winning card move) \{
521
\par if (hand-to-play void in the suit played by the leading hand) \{
522
\par if (card played by the leading hand is highest so far) \{
523
\par if (card by hand-to-play is trump and the suit played by the leading hand is not trump)
524
\par }{\cf1\lang1053 weight = 30 - (rank of card move) + suitAdd
525
\par else
526
\par weight = 60 - (rank of card move) + suitAdd
527
\par \}
528
\par else if (hand-to-play is on top by ruffing)
529
\par weight = 70 - (rank of card move) + suitAdd
530
\par else if (hand-to-play discards a trump but still loses)
531
\par weight = 15 - (rank of card move) + suitAdd
532
\par else }{\lang1053
533
\par }{\cf1\lang1053 weight = 30 - (rank of card move) + suitAdd
534
\par \}
535
\par else }{\lang1053
536
\par }{\cf1\lang1053 weight = 60 - (rank of card move)
537
\par \}
538
\par else \{ /* card move is not trick winning */
539
\par }{\lang1053 if (hand-to-play void in the suit played by the leading hand) \{
540
\par }{\cf1\lang1053 if (hand-to-play is on top by ruffing)
541
\par weight = 40 - (rank of card move) + suitAdd
542
\par else if (hand-to-play underruffs */
543
\par weight = -15 - (rank of card move) + suitAdd
544
\par else
545
\par weight = - (rank of card move) + suitAdd
546
\par \}
547
\par else \{
548
\par if (the card by hand-to-play is highest so far) \{
549
\par if (rank of played card is second highest in the suit)
550
\par weight = 25
551
\par else }{\lang1053 if (hand-to-play card has at least one equivalent card)
552
\par }{\cf1\lang1053 weight = 20 - (rank of card move)
553
\par else
554
\par weight = 10 - (rank of card move)
555
\par \}
556
\par else
557
\par weight = -10 - (rank of card move)
558
\par \}
559
\par \}}{\lang1053
560
\par
561
\par }{\ul\lang1053 Hand-to-play is right hand opponent (RHO) to leading hand
562
\par
563
\par }{\lang1053 if (hand-to-play is void in leading suit) \{
564
\par if (LHO has current highest rank of the trick) \{
565
\par if (card move ruffs)
566
\par weight = 14- (rank of card move) + suitAdd
567
\par else
568
\par weight = 30- (rank of card move) + suitAdd
569
\par }{\fs20\lang1053 \}
570
\par }{\lang1053 else if (hand-to-play ruffs and wins)
571
\par }{\fs20\lang1053 }{\lang1053 weight = 30- (rank of card move) + suitAdd
572
\par else if (card move suit is trump, but not winning)
573
\par weight = - (rank of card move)
574
\par else
575
\par weight = 14- (rank of card move) + suitAdd
576
\par \}
577
\par else if (LHO has current winning move) \{
578
\par if (RHO ruffs LHO\rquote s winner)
579
\par weight = 24 - (rank of card move)
580
\par else
581
\par weight = 30- (rank of card move)
582
\par \}
583
\par else if (card move superior to present winning move not by LHO) \{ }{\fs20\lang1053
584
\par }{\lang1053 weight = 30- (rank of card move)
585
\par else \{
586
\par if (card move ruffs but still losing)
587
\par weight = - (rank of card move)
588
\par else
589
\par weight = 14- (rank of card move)
590
\par \}}{\fs20\lang1053
591
\par }{\lang1053
592
\par }\pard \fi1304\nowidctlpar\adjustright {\lang1053
593
\par \page
594
\par {\listtext\pard\plain\b \hich\af0\dbch\af0\loch\f0 6.\tab}}\pard \nowidctlpar\jclisttab\tx0\ls16\adjustright {\b\lang1053 Algorithm to try early cutoff for generated moves
595
\par }\pard \nowidctlpar\adjustright {\b\lang1053
596
\par }\pard\plain \s1\keepn\nowidctlpar\outlinelevel0\adjustright \lang2057 {\lang1053 After generating moves at the end of a trick, they are each checked to see if one of them will lead to a position that already is stored in the Transposition Table.
597
\par Due to the processing overhead, this check is only made if the depth is 33 or more (i.e there are at least 33 cards in the position).
598
\par }\pard\plain \nowidctlpar\adjustright \lang2057 {\lang1053 Pseudo code:
599
\par }\pard\plain \s1\keepn\nowidctlpar\outlinelevel0\adjustright \lang2057 {\lang1053
600
\par moveExists = TRUE;
601
\par }\pard\plain \nowidctlpar\adjustright \lang2057 {\lang1053 while (moveExists) \{
602
\par Make;
603
\par depth = depth \endash 1;
604
\par RetrieveTTresult;
605
\par if (hit in the transposition table) \{
606
\par Search returnsTRUE if value of the position is TRUE and player side to move, or
607
\par FALSE if value of the position is FALSE and opponents side to move.
608
\par Else: Increment weight of move with 100.
609
\par \}
610
\par depth = depth +1;
611
\par Undo;
612
\par moveExists = NextMove;
613
\par \}
614
\par
615
\par The performance improvement for this enhancement is less than for the other enhancements. The number of generated nodes is roughly decreased by 10% and the search time is slighly decreased.
616
\par
617
\par
618
\par
619
\par {\listtext\pard\plain\b \hich\af0\dbch\af0\loch\f0 7.\tab}}\pard \nowidctlpar\jclisttab\tx0\ls16\adjustright {\b\lang1053 Storage and retrieval of position state data in the Transposition Table
620
\par }\pard\plain \s16\nowidctlpar\tx360\adjustright \lang2057 {\lang1053 }{\b\lang1053 \line }{\cf1\lang1053
621
Positions stored in the Transposition Table always consist of completed tricks. Positions stored start at depth=4, then 8,12, and so on. The information stored is information on won cards, th
622
e suit lengths of the hands, the hand to play the leading card in the position and upper and lower bounds for the number of future tricks to be taken by the side of the player.
623
\par
624
\par Starting from issue 1.1.8, each \'94winning cards node\'94 contain all winning cards for one suit after an idea by Jo\'ebl Bradmetz. This new solution is faster.}{\b\cf1 \line }{\b\cf1\lang1053
625
\par }\pard\plain \nowidctlpar\adjustright \lang2057 {\b\lang1053 7.1 Transposition Table storing winning card ranks
626
\par }\pard \nowidctlpar\tx360\adjustright {\b\lang1053
627
\par }{\lang1053 For the outcome of played tricks, only card ranks that are winning due to their ranks matter:
628
\par Assume that the last two tricks of a deal without trumps looks like the following:
629
\par Trick 12: Leading hand North plays heart A, East, South and West follow by hearts Q, 9 and 7 respectively.
630
\par Trick 13: North then leads spade A, the other hands plays diamonds J, 8,3 in that order.
631
\par
632
\par In trick 12, heart A wins by rank. In trick 13, spade A wins but not by rank.
633
\par The sequence of cards could have been the following without changing the outcome:
634
\par Trick 12: heart A, heart x, heart x, heart x
635
\par Trick 13: spade x, diamond x, diamond x, diamond x
636
\par where x is any rank below lowest winning rank.
637
\par
638
\par The cards that win by rank are recorded during the search and backed up similarly to the search value. If a card wins by rank and there are equivalent cards, e.g. only spade A is searched from a sequence o
639
f AKQ, then also the other cards K and Q must be recorded as having won by rank.
640
\par
641
\par The cards winning by rank are stored in the Transposition Table as relative ranks, however any rank larger than the lowest winning rank in the suit are also stored as \'94winning ranks\'94
642
. Using relative ranks rather than absolute ranks considerably increases the number of positions that match this Transposition Table entry:\line As an example, assume that there are only 4 cards left in a suit, A, Q, 9, 7 where each hand has one card in
643
the suit. Then any combination of ranks, e.g. 8, 6, 3, 2 that preserves the relative order of ranks between hands will cause a match.
644
\par
645
\par In the state position information absolute ranks are used, it is only in the Transposition Table where the ranks are stored as relatives.
646
\par
647
\par }\pard \fi-420\li420\nowidctlpar\tx420\adjustright {\b
648
\par }\pard \nowidctlpar\adjustright {\b 7.2 Backing up the winning ranks
649
\par }\pard \nowidctlpar\tx420\adjustright {\b
650
\par }{At the search termination, either at the last trick or at a cutoff, the cards that have won by rank are backed up in the search tree together with the search value.
651
\par As this information propagates upwards, it is aggregated with backed up information from other tree branches.
652
\par At a search cutoff, }{\i\lang1053 MergeMoveData }{\lang1053 merges the information (V is a union):
653
\par }{
654
\par }\pard \fi-420\li420\nowidctlpar\tx420\adjustright {(winning ranks of all suits for current depth) = (winning ranks of all suits for depth - 1) V (possible winning rank for the current move causing the cutoff)
655
\par
656
\par For each new move not causing cutoff, }{\i\lang1053 MergeAllMovesData }{\lang1053 merges:
657
\par
658
\par }{(winning ranks of all suits for current depth) = (winning ranks of all suits for current depth) V (winning ranks of all suits for depth - 1) V (possible winning rank for the current move)
659
\par }\pard \nowidctlpar\tx420\adjustright {
660
\par }\pard \fi-420\li420\nowidctlpar\tx420\adjustright {\b
661
\par 7.3\tab }{\b\lang1053 Checking the current position for a Transposition Table entry match
662
\par
663
\par }\pard \nowidctlpar\tx420\adjustright {\cf1\lang1053 The "Transposition Table" has a tree structure rather than a table, consisting of 2 interconnected trees.
664
\par For deciding if there is a match, input is the position state data, including the cards left to play and the current leading hand.
665
\par There are \'94root pointers\'94 per number of tricks left and per leading hand which each points to the root of a tree of \'94suit lengths combination\'94
666
nodes. Each such node includes a 64-bit code that uniquely defines one combination of suit lengths for the hands. Th
667
e nodes are ordered such that the value of the 64-bit code in a parent node is higher than the 64-bit code of its left child but lower than the 64-bit code of its right child. So to find the node with the suit lengths combination for the actual position,
668
a binary search is made. The basic binary search algorithm is described in [Knuth].
669
\par Each \'94suit length combination node\'94 points to the root of a tree consisting of \'94winning cards nodes\'94, ie. cards that win by rank. (So the Transposition Table is really a number of trees, a forest.)
670
\par When a position is checked for a possible Transposition Table match, a tree branch is selected consisting of 4 subsequent \'94winning cards nodes\'94, each \'94winning cards node\'94 includes an aggregate of all winning cards for one suit. Th
671
is branch is followed as long as the \'94winning cards\'94 also can be found in the current position. (Note that the ranks of the \'94winning card nodes\'94
672
are relative, so the ranks of the current position must first be translated from absolute to relative ranks.) When the \'94winning cards node\'94 no longer matches with the current position and there is no other alternative \'94winning cards node\'94
673
that fits, then the search backs up and tries an alternative \'94winning cards node\'94 on a higher level.
674
\par \line When the last of the 4 subsequent \'94winning cards nodes\'94 containing clubs is reached, it points to a \'94set of positions node\'94. Its stored upper and lower value bounds are checked against the number of tricks won so far by the player
675
\rquote s side and the target value. The following conditions are then checked, assuming that it is the North/South side that is the player\rquote s side:
676
\par
677
\par If the sum of the stored lower value bound and the number of tricks won so far for the player\rquote s side is equal or larger than target, then target can be reached for the player\rquote
678
s side in the current position. Search on this depth is terminated and TRUE is returned.
679
\par
680
\par If the sum of the stored upper value bound and the number of tricks won so far for the player\rquote s side is less than target, then reaching target can be prevented by the opponents to the player\rquote
681
s side in the current position. Search on this depth is terminated and FALSE is returned.
682
\par
683
\par If instead it is East/West that is the player\rquote s side, the following conditions apply:
684
\par
685
\par If the sum of number of tricks remaining and the number of tricks won so far for the player\rquote s side minus the upper value bound is equal or larger than target, then target can be reached for the player\rquote
686
s side in the current position. Search on this depth is terminated and TRUE is returned.
687
\par
688
\par If the sum of number of tricks remaining and the number of tricks won so far for the player\rquote s side minus the lower value bound is less than target, then reaching target can be prevented by the opponents to the player\rquote
689
s side in the current position. Search on this depth is terminated and FALSE is returned.
690
\par
691
\par For all other cases, the search continues for the current depth.
692
\par
693
\par For example, take the previous example with 2 tricks remaining with spade rank order 1 at North. (Rank order 1 is highest rank.) The hearts have
694
rank orders 1 at North, 2 at East, 3 at South and 4 at West. The diamond rank orders are orders 1 at East, 2 at South and 3 at West. North is leading hand.
695
\par The \'94root pointer\'94 is now defined by the number of tricks remaining (=2) and North as leading hand.
696
\par The \'94root pointer\'94 points to the root node of its \'94suit lengths combination\'94
697
tree. The 64-bit integer coded from the suit lengths for all suits and hands is now searched within the tree. When the node is found with matching 64-bit suit lengths code, this node will point to the root of its \'94winning card\'94 tree.
698
\par This pointer points to a "winning cards node" containing spade rank order 1 at North which fits with the current position. This \'94winning cards node\'94
699
points to another "winning cards node" containing hearts rank orders 1 at North and 2 at East which also fits the current position. Next \'94winning cards node\'94
700
pointed to contains diamonds order 1 at South, which does not match the current position. However, there is an alternative \'94winning cards node\'94 that has diamonds order 1 at East, which fits. (If there had been no alternative \'94winning cards node
701
\'94 which fitted, the search had backed up to the previous \'94winning cards node\'94 to see if there was an alternative \'94winning cards node\'94 on this level which also fitted.) The next \'94winning cards node\'94
702
pointed to is for clubs. This node is empty, which fits the current position which have no clubs.
703
\par This \'94winning cards node\'94 points to a "set of positions node\'94 which have upper and lower value bounds defined. The conditions for these bounds are assumed to be fulfilled causing search termination on this depth, as described earlier.
704
\par
705
\par The usage of upper and lower value bounds in transposition tables is described in [Chang] and [Kupferschmid, Helmert].}{\b\lang1053
706
\par }\pard \nowidctlpar\adjustright {\b\lang1053
707
\par
708
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200029002a002a00250015001b002a001c0015001700290025001500050000002e0100000000050000001402000000000500000014020c06b20e050000002e010100000011000000320a0c06b20e04000400000000002a10cc0d6e6578742900260029001700050000002e01000000000500000014020000000005000000
863
020101000000050000000201010000000500000014026b06f609050000002e010100000017000000320a6b06f60908000400000000002a10cc0d7375697420696e2020002900170017001500180029001500050000002e0100000000050000001402000000000500000014026b06d80a050000002e010100000013000000
864
320a6b06d80a05000400000000002a10cc0d74686973200018002900170020001500050000002e0100000000050000001402000000000500000014026b06650b050000002e010100000013000000320a6b06650b05000400000000002a10cc0d74726565200017001c00250025001500050000002e010000000005000000
865
1402000000000500000014026b06f70b050000002e01010000002c000000320a6b06f70b16000400000000002a10cc0d6272616e636820616e6420746f206120736574206f662a001c0025002900260029001500250029002a00150017002a0015002500150020002500170015002a001b00050000002e01000000000500
866
00001402000000000500000002010100000005000000020101000000050000001402cb06f609050000002e01010000001a000000320acb06f6090a000400000000002a10cc0d706f736974696f6e73202a002a0020001700170017002a00290020001600050000002e010000000005000000140200000000050000001402
867
cb06380b050000002e010100000013000000320acb06380b05000400000000002a10cc0d6e6f6465200029002a002a0025001500050000002e010000000005000000140200000000050000001402cb06ef0b050000002e01010000001f000000320acb06ef0b0d000400000000002a10cc0d696620697420697320746865
868
200017001b0015001700170015001700200015001800290025001600050000002e010000000005000000140200000000050000001402cb06410d050000002e010100000017000000320acb06410d08000400000000002a10cc0d77696e6e696e67203b0018002900290018002a0029001500050000002e01000000000500
869
0000140200000000050000001402cb06660e050000002e010100000013000000320acb06660e05000400000000002a10cc0d636172647300250025001c002a002000050000002e01000000000500000014020000000005000000020101000000050000000201010000000500000014022d07f609050000002e0101000000
870
26000000320a2d07f60912000400000000002a10cc0d6e6f646520666f7220746865206c6173742029002a002a00250015001b002a001c001500170029002500150017002500200017001500050000002e0100000000050000001402000000000500000014022d07250c050000002e010100000014000000320a2d07250c
871
06000400000000002a10cc0d737569742e2e210029001700170015001500050000002e01000000000500000014020000000005000000020101000000040000002701ffff07000000fc020000ffffff000000040000002d01030008000000fa0200000600000000000002040000002d010500070000001b04830138025600
872
9300040000002d01040004000000f0010300040000002d01020004000000f0010500030000001e000700000016046101f9017700d20005000000020101000000040000002d010100050000000902000000000500000014027800d200050000002e010100000011000000320a7800d20004000400000000002a10cc0d526f
873
6f7437002a002a001700050000002e01000000000500000014020902640e0500000002010100000005000000020101000000050000001402da00d200050000002e010100000016000000320ada00d20007000400000000002a10cc0d706f696e746572002a002a0017002900170025001c00050000002e01000000000500
874
000014020000000005000000020101000000040000002701ffff07000000fc020000ffffff000000040000002d01030008000000fa0200000600000000000002040000002d010500070000001b048301340656005304040000002d01040004000000f0010300040000002d01020004000000f0010500030000001e000700
875
000016046101f5057700920405000000020101000000040000002d0101000500000009020000000005000000140278009204050000002e010100000011000000320a7800920404000400000000002a10cc0d526f6f7437002a002a001700050000002e01000000000500000014020902640e050000000201010000000500
876
0000020101000000050000001402da009204050000002e010100000016000000320ada00920407000400000000002a10cc0d706f696e746572002a002a0017002900170025001c00050000002e01000000000500000014020000000005000000020101000000040000002701ffff1000000026060f001600ffffffff0000
877
ab020000ca000000e0030000d300000008000000fa0205000100000000000000040000002d01030007000000fc020000000000000000040000002d010500050000000601020000002800000024031200b002cb00af02cb00ae02cc00ad02cd00ac02ce00ac02ce00ad02cf00ae02d000af02d100af02d100af02d100b002
878
d000b102cf00b202ce00b202ce00b102cd00b002cc00b002cb002800000024031200bb02cb00ba02cb00b902cc00b802cd00b802ce00b802cf00b802d000b902d100ba02d100bb02d100bb02d100bc02d000bd02cf00be02ce00be02ce00bd02cd00bc02cc00bc02cb002800000024031200c702cb00c602cb00c502cc00
879
c402cd00c402ce00c402cf00c402d000c502d100c602d100c702d100c702d100c802d000c902cf00ca02ce00ca02ce00c902cd00c802cc00c802cb002800000024031200d302cb00d202cb00d102cc00d002cd00d002ce00d002cf00d002d000d102d100d202d100d302d100d302d100d402d000d502cf00d602ce00d602
880
ce00d502cd00d402cc00d402cb002800000024031200df02cb00de02cb00dd02cc00dc02cd00dc02ce00dc02cf00dc02d000dd02d100de02d100df02d100df02d100e002d000e102cf00e202ce00e202ce00e102cd00e002cc00e002cb002800000024031200eb02cb00ea02cb00e902cc00e802cd00e802ce00e802cf00
881
e802d000e902d100ea02d100eb02d100eb02d100ec02d000ed02cf00ee02ce00ee02ce00ed02cd00ec02cc00ec02cb002800000024031200f702cb00f602cb00f502cc00f402cd00f402ce00f402cf00f402d000f502d100f602d100f702d100f702d100f802d000f902cf00fa02ce00fa02ce00f902cd00f802cc00f802
882
cb0028000000240312000303cb000203cb000103cc000003cd000003ce000003cf000003d0000103d1000203d1000303d1000303d1000403d0000503cf000603ce000603ce000503cd000403cc000403cb0028000000240312000f03cb000e03cb000d03cc000c03cd000c03ce000c03cf000c03d0000d03d1000e03d100
883
0f03d1000f03d1001003d0001103cf001203ce001203ce001103cd001003cc001003cb0028000000240312001b03cb001a03cb001903cc001803cd001803ce001803cf001803d0001903d1001a03d1001b03d1001b03d1001c03d0001d03cf001e03ce001e03ce001d03cd001c03cc001c03cb0028000000240312002703
884
cb002603cb002503cc002403cd002403ce002403cf002403d0002503d1002603d1002703d1002703d1002803d0002903cf002a03ce002a03ce002903cd002803cc002803cb0028000000240312003303cb003203cb003103cc003003cd003003ce003003cf003003d0003103d1003203d1003303d1003303d1003403d000
885
3503cf003603ce003603ce003503cd003403cc003403cb0028000000240312003f03cb003e03cb003d03cc003c03cd003c03ce003c03cf003c03d0003d03d1003e03d1003f03d1003f03d1004003d0004103cf004203ce004203ce004103cd004003cc004003cb0028000000240312004b03cb004a03cb004903cc004803
886
cd004803ce004803cf004803d0004903d1004a03d1004b03d1004b03d1004c03d0004d03cf004e03ce004e03ce004d03cd004c03cc004c03cb0028000000240312005703cb005603cb005503cc005403cd005403ce005403cf005403d0005503d1005603d1005703d1005703d1005803d0005903cf005a03ce005a03ce00
887
5903cd005803cc005803cb0028000000240312006303cb006203cb006103cc006003cd006003ce006003cf006003d0006103d1006203d1006303d1006303d1006403d0006503cf006603ce006603ce006503cd006403cc006403cb0028000000240312006f03cb006e03cb006d03cc006c03cd006c03ce006c03cf006c03
888
d0006d03d1006e03d1006f03d1006f03d1007003d0007103cf007203ce007203ce007103cd007003cc007003cb0028000000240312007b03cb007a03cb007903cc007803cd007803ce007803cf007803d0007903d1007a03d1007b03d1007b03d1007c03d0007d03cf007e03ce007e03ce007d03cd007c03cc007c03cb00
889
28000000240312008703cb008603cb008503cc008403cd008403ce008403cf008403d0008503d1008603d1008703d1008703d1008803d0008903cf008a03ce008a03ce008903cd008803cc008803cb0028000000240312009303cb009203cb009103cc009003cd009003ce009003cf009003d0009103d1009203d1009303
890
d1009303d1009403d0009503cf009603ce009603ce009503cd009403cc009403cb0028000000240312009f03cb009e03cb009d03cc009c03cd009c03ce009c03cf009c03d0009d03d1009e03d1009f03d1009f03d100a003d000a103cf00a203ce00a203ce00a103cd00a003cc00a003cb002800000024031200ab03cb00
891
aa03cb00a903cc00a803cd00a803ce00a803cf00a803d000a903d100aa03d100ab03d100ab03d100ac03d000ad03cf00ae03ce00ae03ce00ad03cd00ac03cc00ac03cb002800000024031200b703cb00b603cb00b503cc00b403cd00b403ce00b403cf00b403d000b503d100b603d100b703d100b703d100b803d000b903
892
cf00ba03ce00ba03ce00b903cd00b803cc00b803cb002800000024031200c303cb00c203cb00c103cc00c003cd00c003ce00c003cf00c003d000c103d100c203d100c303d100c303d100c403d000c503cf00c603ce00c603ce00c503cd00c403cc00c403cb002800000024031200cf03cb00ce03cb00cd03cc00cc03cd00
893
cc03ce00cc03cf00cc03d000cd03d100ce03d100cf03d100cf03d100d003d000d103cf00d203ce00d203ce00d103cd00d003cc00d003cb0005000000060101000000040000002d010200040000002d01040004000000f00105000800000026060f000600ffffffff010007000000fc020000ffffff000000040000002d01
894
050008000000fa0200000600000000000002040000002d010600070000001b04bb05fc01ca04cf00040000002d01040004000000f0010500040000002d01020004000000f0010600030000001e000700000016049905bd01eb040e0105000000020101000000040000002d01010005000000090200000000050000001402
895
ee040e01050000002e010100000010000000320aee040e0103000400000000002a10cc0d57696e034f0017002900050000002e01000000000500000014020902640e05000000020101000000040000002701ffff07000000fc020000ffffff000000040000002d01050008000000fa020000060000000000000204000000
896
2d010600070000001b04bb050805ca04db03040000002d01040004000000f0010500040000002d01020004000000f0010600030000001e000700000016049905c904eb041a0405000000020101000000040000002d01010005000000090200000000050000001402ee041a04050000002e010100000010000000320aee04
897
1a0403000400000000002a10cc0d57696e034f0017002900050000002e01000000000500000014020902640e05000000020101000000040000002701ffff07000000fc020000ffffff000000040000002d01050008000000fa0200000600000000000002040000002d010600070000001b041308fc012207cf0004000000
898
2d01040004000000f0010500040000002d01020004000000f0010600030000001e00070000001604f107bd0143070e0105000000020101000000040000002d0101000500000009020000000005000000140246070e01050000002e010100000010000000320a46070e0103000400000000002a10cc0d57696e034f001700
899
2900050000002e01000000000500000014020902640e05000000020101000000040000002701ffff07000000fc020000ffffff000000040000002d01050008000000fa0200000600000000000002040000002d010600070000001b04130808052207db03040000002d01040004000000f0010500040000002d0102000400
900
0000f0010600030000001e00070000001604f107c90443071a0405000000020101000000040000002d0101000500000009020000000005000000140246071a04050000002e010100000010000000320a46071a0403000400000000002a10cc0d57696e034f0017002900050000002e01000000000500000014020902640e
901
05000000020101000000040000002701ffff07000000fc020000ffffff000000040000002d01050008000000fa0200000600000000000002040000002d010600070000001b046b0afc017a09cf00040000002d01040004000000f0010500040000002d01020004000000f0010600030000001e00070000001604490abd01
902
9b090e0105000000020101000000040000002d010100050000000902000000000500000014029e090e01050000002e010100000010000000320a9e090e0103000400000000002a10cc0d57696e034f0017002900050000002e01000000000500000014020902640e05000000020101000000040000002701ffff07000000
903
fc020000ffffff000000040000002d01050008000000fa0200000600000000000002040000002d010600070000001b046b0a08057a09db03040000002d01040004000000f0010500040000002d01020004000000f0010600030000001e00070000001604490ac9049b091a0405000000020101000000040000002d010100
904
050000000902000000000500000014029e091a04050000002e010100000010000000320a9e091a0403000400000000002a10cc0d57696e034f0017002900050000002e01000000000500000014020902640e05000000020101000000040000002701ffff07000000fc020000ffffff000000040000002d01050008000000
905
fa0200000600000000000002040000002d010600070000001b04130814082207e706040000002d01040004000000f0010500040000002d01020004000000f0010600030000001e00070000001604f107d5074307260705000000020101000000040000002d01010005000000090200000000050000001402460726070500
906
00002e010100000010000000320a4607260703000400000000002a10cc0d57696e034f0017002900050000002e01000000000500000014020902640e05000000020101000000040000002701ffff07000000fc020000ffffff000000040000002d01050008000000fa0200000600000000000002040000002d0106000700
907
00001b046b0a14087a09e706040000002d01040004000000f0010500040000002d01020004000000f0010600030000001e00070000001604490ad5079b09260705000000020101000000040000002d010100050000000902000000000500000014029e092607050000002e010100000010000000320a9e09260703000400
908
000000002a10cc0d57696e034f0017002900050000002e01000000000500000014020902640e05000000020101000000040000002701ffff07000000fc020000ffffff000000040000002d01050008000000fa0200000600000000000002040000002d010600070000001b040f0cfc011e0bcf00040000002d0104000400
909
0000f0010500040000002d01020004000000f0010600030000001e00070000001604ed0bbd013f0b0e0105000000020101000000040000002d01010005000000090200000000050000001402420b0e01050000002e010100000010000000320a420b0e0103000400000000002a10cc0d534f50032e003c002f0005000000
910
2e01000000000500000014020902640e05000000020101000000040000002701ffff07000000fc020000ffffff000000040000002d01050008000000fa0200000600000000000002040000002d010600070000001b040f0c08051e0bdb03040000002d01040004000000f0010500040000002d01020004000000f0010600
911
030000001e00070000001604ed0bc9043f0b1a0405000000020101000000040000002d01010005000000090200000000050000001402420b1a04050000002e010100000010000000320a420b1a0403000400000000002a10cc0d534f50032e003c002f00050000002e01000000000500000014020902640e050000000201
912
01000000040000002701ffff07000000fc020000ffffff000000040000002d01050008000000fa0200000600000000000002040000002d010600070000001b040f0c14081e0be706040000002d01040004000000f0010500040000002d01020004000000f0010600030000001e00070000001604ed0bd5073f0b26070500
913
0000020101000000040000002d01010005000000090200000000050000001402420b2607050000002e010100000010000000320a420b260703000400000000002a10cc0d534f50032e003c002f00050000002e01000000000500000014020902640e05000000020101000000040000002701ffff07000000fc020000ffff
914
ff000000040000002d01050008000000fa0200000600000000000002040000002d010600070000001b040f0c940f6a0af309040000002d01040004000000f0010500040000002d01020004000000f0010600030000001e00070000001604ed0b550f8b0a320a05000000020101000000040000002d010100050000000902
915
000000000500000014028c0a320a050000002e010100000026000000320a8c0a320a12000400000000002a10cc0d536574206f6620706f736974696f6e7320282e002500170015002a001b0015002a002a0020001700170017002a002a00200015001c00050000002e01000000000500000014020902640e050000001402
916
8c0a690c050000002e010100000013000000320a8c0a690c05000400000000002a10cc0d534f502920002e003c002f001c001500050000002e0100000000050000001402000000000500000014028c0a330d050000002e010100000013000000320a8c0a330d05000400000000002a10cc0d6e6f6465730029002a002a00
917
25002000050000002e0100000000050000001402000000000500000002010100000005000000020101000000050000001402ec0a320a050000002e010100000031000000320aec0a320a19000400000000002a10cc0d636f6e7461696e696e672074686520706f736974696f6e73200025002a0029001700250017002900
918
18002a002900150017002900250015002a002a0020001700180017002a00290020001600050000002e010000000005000000140200000000050000001402ec0a630d050000002e010100000019000000320aec0a630d09000400000000002a10cc0d757070657220616e642029002a002a0025001c001500250029002a00
919
050000002e01000000000500000014020000000005000000020101000000050000000201010000000500000014024c0b320a050000002e010100000014000000320a4c0b320a06000400000000002a10cc0d6c6f7765722017002b003a0025001c001500050000002e010000000005000000140200000000050000001402
920
4c0b040b050000002e010100000014000000320a4c0b040b06000400000000002a10cc0d76616c756520290025001800290025001500050000002e0100000000050000001402000000000500000014024c0bcd0b050000002e010100000014000000320a4c0bcd0b06000400000000002a10cc0d626f756e642e2a002a00
921
2a0029002a001500050000002e010000000005000000140200000000050000000201010000000500000002010100000005000000020101000000040000002701ffff1000000026060f001600ffffffff0000f70100007e010000b40200007702000008000000fa0200000600000000000000040000002d01050007000000
922
fc020100000000000000040000002d0106000800000025030200fb0182018a024002040000002d01030004000000f001050007000000fc020000000000000000040000002d0105000a000000240303006e025202af027202a2022b02040000002d010200040000002d01040004000000f00105000800000026060f000600
923
ffffffff01001000000026060f001600ffffffff0000f70100001e050000e00300006805000008000000fa0200000600000000000000040000002d010500040000002d0106000800000025030200fb0142059c034205040000002d01030004000000f001050007000000fc020000000000000000040000002d0105000a00
924
0000240303009a036305db0342059a032205040000002d010200040000002d01040004000000f00105000800000026060f000600ffffffff01001000000026060f001600ffffffff000022010000b60500006c0100002707000008000000fa0200000600000000000000040000002d010500040000002d01060008000000
925
250302004701ba054701e306040000002d01030004000000f001050007000000fc020000000000000000040000002d0105000a000000240303002601e106470122076701e106040000002d010200040000002d01040004000000f00105000800000026060f000600ffffffff01001000000026060f001600ffffffff0000
926
f701000076070000e0030000c007000008000000fa0200000600000000000000040000002d010500040000002d0106000800000025030200fb019a079c039a07040000002d01030004000000f001050007000000fc020000000000000000040000002d0105000a000000240303009a03bb07db039a079a037a0704000000
927
2d010200040000002d01040004000000f00105000800000026060f000600ffffffff01001000000026060f001600ffffffff00000305000076070000ec060000c007000008000000fa0200000600000000000000040000002d010500040000002d010600080000002503020007059a07a8069a07040000002d0103000400
928
0000f001050007000000fc020000000000000000040000002d0105000a00000024030300a606bb07e7069a07a6067a07040000002d010200040000002d01040004000000f00105000800000026060f000600ffffffff01001000000026060f001600ffffffff0000220100000e0800006c0100007f09000008000000fa02
929
00000600000000000000040000002d010500040000002d01060008000000250302004701120847013b09040000002d01030004000000f001050007000000fc020000000000000000040000002d0105000a000000240303002601390947017a0967013909040000002d010200040000002d01040004000000f00105000800
930
000026060f000600ffffffff01001000000026060f001600ffffffff00002e0400000e080000780400007f09000008000000fa0200000600000000000000040000002d010500040000002d01060008000000250302005304120853043b09040000002d01030004000000f001050007000000fc0200000000000000000400
931
00002d0105000a000000240303003204390953047a0973043909040000002d010200040000002d01040004000000f00105000800000026060f000600ffffffff01001000000026060f001600ffffffff00003a0700000e080000840700007f09000008000000fa0200000600000000000000040000002d01050004000000
932
2d01060008000000250302005f0712085f073b09040000002d01030004000000f001050007000000fc020000000000000000040000002d0105000a000000240303003e0739095f077a097f073909040000002d010200040000002d01040004000000f00105000800000026060f000600ffffffff01001000000026060f00
933
1600ffffffff000022010000660a00006c010000230b000008000000fa0200000600000000000000040000002d010500040000002d010600080000002503020047016a0a4701df0a040000002d01030004000000f001050007000000fc020000000000000000040000002d0105000a000000240303002601dd0a47011e0b
934
6701dd0a040000002d010200040000002d01040004000000f00105000800000026060f000600ffffffff0100040000002d010600040000002d010300070000001b04bb056403ca043702040000002d010400040000002d010200030000001e000700000016049c052803e804730205000000020101000000040000002d01
935
010005000000090200000000050000001402eb047302050000002e010100000011000000320aeb04730204000400000000002a10cc0d416c742e3b00170017001500050000002e01000000000500000014020902640e05000000020101000000040000002701ffff040000002d010600040000002d010300070000001b04
936
1308640322073702040000002d010400040000002d010200030000001e00070000001604f40728034007730205000000020101000000040000002d0101000500000009020000000005000000140243077302050000002e010100000011000000320a4307730204000400000000002a10cc0d416c742e3b00170017001500
937
050000002e01000000000500000014020902640e05000000020101000000040000002701ffff040000002d010600040000002d010300070000001b041308700622074305040000002d010400040000002d010200030000001e00070000001604f407340640077f0505000000020101000000040000002d01010005000000
938
09020000000005000000140243077f05050000002e010100000011000000320a43077f0504000400000000002a10cc0d416c742e3b00170017001500050000002e01000000000500000014020902640e05000000020101000000040000002701ffff040000002d010600040000002d010300070000001b04e7067402f605
939
4701040000002d010400040000002d010200030000001e00070000001604c80638021406830105000000020101000000040000002d0101000500000009020000000005000000140217068301050000002e010100000011000000320a1706830104000400000000002a10cc0d4e6578743c00250029001700050000002e01
940
000000000500000014020902640e05000000020101000000040000002701ffff040000002d010600040000002d010300070000001b043f0974024e084701040000002d010400040000002d010200030000001e00070000001604200938026c08830105000000020101000000040000002d01010005000000090200000000
941
0500000014026f088301050000002e010100000011000000320a6f08830104000400000000002a10cc0d4e6578743c00250029001700050000002e01000000000500000014020902640e05000000020101000000040000002701ffff040000002d010600040000002d010300070000001b043f0980054e08530404000000
942
2d010400040000002d010200030000001e00070000001604200944056c088f0405000000020101000000040000002d010100050000000902000000000500000014026f088f04050000002e010100000011000000320a6f088f0404000400000000002a10cc0d4e6578743c00250029001700050000002e01000000000500
943
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1106
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1112
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1117
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1119
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1120
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1121
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1122
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1123
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1124
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1125
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1126
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1127
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1128
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1129
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1130
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1131
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1132
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1133
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1134
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1135
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1136
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1137
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1138
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1139
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1140
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1141
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1142
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1143
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1144
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1145
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1146
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1147
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1148
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1149
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1150
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1151
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1152
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1153
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1154
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1155
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1156
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1157
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1158
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1159
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1160
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1161
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1162
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1163
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1164
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1165
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1166
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1167
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1168
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1169
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1170
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1171
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1172
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1173
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1174
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1175
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1176
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1177
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1178
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1179
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1180
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1181
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1182
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1183
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1323
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1325
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1326
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1327
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1328
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1329
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1330
2800000024031200c303cb00c203cb00c103cc00c003cd00c003ce00c003cf00c003d000c103d100c203d100c303d100c303d100c403d000c503cf00c603ce00
1331
c603ce00c503cd00c403cc00c403cb002800000024031200cf03cb00ce03cb00cd03cc00cc03cd00cc03ce00cc03cf00cc03d000cd03d100ce03d100cf03d100
1332
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1333
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1335
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1336
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1337
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1338
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1339
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1340
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1341
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1342
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1343
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1344
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1345
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1346
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1347
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1348
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1349
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1350
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1351
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1352
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1353
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1354
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1355
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1356
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1357
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1358
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1359
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1360
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1361
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1362
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1363
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1364
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1365
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1366
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1367
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1368
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1369
020101000000040000002701ffff07000000fc020000ffffff000000040000002d01050008000000fa0200000600000000000002040000002d01060007000000
1370
1b040f0c14081e0be706040000002d01040004000000f0010500040000002d01020004000000f0010600030000001e00070000001604ed0bd5073f0b26070500
1371
0000020101000000040000002d01010005000000090200000000050000001402420b2607050000002e010100000010000000320a420b26070300040000000000
1372
2a10cc0d534f50032e003c002f00050000002e01000000000500000014020902640e05000000020101000000040000002701ffff07000000fc020000ffffff00
1373
0000040000002d01050008000000fa0200000600000000000002040000002d010600070000001b040f0c940f6a0af309040000002d01040004000000f0010500
1374
040000002d01020004000000f0010600030000001e00070000001604ed0b550f8b0a320a05000000020101000000040000002d01010005000000090200000000
1375
0500000014028c0a320a050000002e010100000026000000320a8c0a320a12000400000000002a10cc0d536574206f6620706f736974696f6e7320282e002500
1376
170015002a001b0015002a002a0020001700170017002a002a00200015001c00050000002e01000000000500000014020902640e0500000014028c0a690c0500
1377
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1378
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1379
2e0100000000050000001402000000000500000002010100000005000000020101000000050000001402ec0a320a050000002e010100000031000000320aec0a
1380
320a19000400000000002a10cc0d636f6e7461696e696e672074686520706f736974696f6e73200025002a002900170025001700290018002a00290015001700
1381
2900250015002a002a0020001700180017002a00290020001600050000002e010000000005000000140200000000050000001402ec0a630d050000002e010100
1382
000019000000320aec0a630d09000400000000002a10cc0d757070657220616e642029002a002a0025001c001500250029002a00050000002e01000000000500
1383
000014020000000005000000020101000000050000000201010000000500000014024c0b320a050000002e010100000014000000320a4c0b320a060004000000
1384
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1385
14000000320a4c0b040b06000400000000002a10cc0d76616c756520290025001800290025001500050000002e01000000000500000014020000000005000000
1386
14024c0bcd0b050000002e010100000014000000320a4c0bcd0b06000400000000002a10cc0d626f756e642e2a002a002a0029002a001500050000002e010000
1387
000005000000140200000000050000000201010000000500000002010100000005000000020101000000040000002701ffff1000000026060f001600ffffffff
1388
0000f70100007e010000b40200007702000008000000fa0200000600000000000000040000002d01050007000000fc020100000000000000040000002d010600
1389
0800000025030200fb0182018a024002040000002d01030004000000f001050007000000fc020000000000000000040000002d0105000a000000240303006e02
1390
5202af027202a2022b02040000002d010200040000002d01040004000000f00105000800000026060f000600ffffffff01001000000026060f001600ffffffff
1391
0000f70100001e050000e00300006805000008000000fa0200000600000000000000040000002d010500040000002d0106000800000025030200fb0142059c03
1392
4205040000002d01030004000000f001050007000000fc020000000000000000040000002d0105000a000000240303009a036305db0342059a03220504000000
1393
2d010200040000002d01040004000000f00105000800000026060f000600ffffffff01001000000026060f001600ffffffff000022010000b60500006c010000
1394
2707000008000000fa0200000600000000000000040000002d010500040000002d01060008000000250302004701ba054701e306040000002d01030004000000
1395
f001050007000000fc020000000000000000040000002d0105000a000000240303002601e106470122076701e106040000002d010200040000002d0104000400
1396
0000f00105000800000026060f000600ffffffff01001000000026060f001600ffffffff0000f701000076070000e0030000c007000008000000fa0200000600
1397
000000000000040000002d010500040000002d0106000800000025030200fb019a079c039a07040000002d01030004000000f001050007000000fc0200000000
1398
00000000040000002d0105000a000000240303009a03bb07db039a079a037a07040000002d010200040000002d01040004000000f00105000800000026060f00
1399
0600ffffffff01001000000026060f001600ffffffff00000305000076070000ec060000c007000008000000fa0200000600000000000000040000002d010500
1400
040000002d010600080000002503020007059a07a8069a07040000002d01030004000000f001050007000000fc020000000000000000040000002d0105000a00
1401
000024030300a606bb07e7069a07a6067a07040000002d010200040000002d01040004000000f00105000800000026060f000600ffffffff0100100000002606
1402
0f001600ffffffff0000220100000e0800006c0100007f09000008000000fa0200000600000000000000040000002d010500040000002d010600080000002503
1403
02004701120847013b09040000002d01030004000000f001050007000000fc020000000000000000040000002d0105000a000000240303002601390947017a09
1404
67013909040000002d010200040000002d01040004000000f00105000800000026060f000600ffffffff01001000000026060f001600ffffffff00002e040000
1405
0e080000780400007f09000008000000fa0200000600000000000000040000002d010500040000002d01060008000000250302005304120853043b0904000000
1406
2d01030004000000f001050007000000fc020000000000000000040000002d0105000a000000240303003204390953047a0973043909040000002d0102000400
1407
00002d01040004000000f00105000800000026060f000600ffffffff01001000000026060f001600ffffffff00003a0700000e080000840700007f0900000800
1408
0000fa0200000600000000000000040000002d010500040000002d01060008000000250302005f0712085f073b09040000002d01030004000000f00105000700
1409
0000fc020000000000000000040000002d0105000a000000240303003e0739095f077a097f073909040000002d010200040000002d01040004000000f0010500
1410
0800000026060f000600ffffffff01001000000026060f001600ffffffff000022010000660a00006c010000230b000008000000fa0200000600000000000000
1411
040000002d010500040000002d010600080000002503020047016a0a4701df0a040000002d01030004000000f001050007000000fc0200000000000000000400
1412
00002d0105000a000000240303002601dd0a47011e0b6701dd0a040000002d010200040000002d01040004000000f00105000800000026060f000600ffffffff
1413
0100040000002d010600040000002d010300070000001b04bb056403ca043702040000002d010400040000002d010200030000001e000700000016049c052803
1414
e804730205000000020101000000040000002d01010005000000090200000000050000001402eb047302050000002e010100000011000000320aeb0473020400
1415
0400000000002a10cc0d416c742e3b00170017001500050000002e01000000000500000014020902640e05000000020101000000040000002701ffff04000000
1416
2d010600040000002d010300070000001b041308640322073702040000002d010400040000002d010200030000001e00070000001604f4072803400773020500
1417
0000020101000000040000002d0101000500000009020000000005000000140243077302050000002e010100000011000000320a430773020400040000000000
1418
2a10cc0d416c742e3b00170017001500050000002e01000000000500000014020902640e05000000020101000000040000002701ffff040000002d0106000400
1419
00002d010300070000001b041308700622074305040000002d010400040000002d010200030000001e00070000001604f407340640077f050500000002010100
1420
0000040000002d0101000500000009020000000005000000140243077f05050000002e010100000011000000320a43077f0504000400000000002a10cc0d416c
1421
742e3b00170017001500050000002e01000000000500000014020902640e05000000020101000000040000002701ffff040000002d010600040000002d010300
1422
070000001b04e7067402f6054701040000002d010400040000002d010200030000001e00070000001604c8063802140683010500000002010100000004000000
1423
2d0101000500000009020000000005000000140217068301050000002e010100000011000000320a1706830104000400000000002a10cc0d4e6578743c002500
1424
29001700050000002e01000000000500000014020902640e05000000020101000000040000002701ffff040000002d010600040000002d010300070000001b04
1425
3f0974024e084701040000002d010400040000002d010200030000001e00070000001604200938026c08830105000000020101000000040000002d0101000500
1426
00000902000000000500000014026f088301050000002e010100000011000000320a6f08830104000400000000002a10cc0d4e6578743c002500290017000500
1427
00002e01000000000500000014020902640e05000000020101000000040000002701ffff040000002d010600040000002d010300070000001b043f0980054e08
1428
5304040000002d010400040000002d010200030000001e00070000001604200944056c088f0405000000020101000000040000002d0101000500000009020000
1429
00000500000014026f088f04050000002e010100000011000000320a6f088f0404000400000000002a10cc0d4e6578743c00250029001700050000002e010000
1430
00000500000014020902640e05000000020101000000040000002701ffff040000002d010600040000002d010300070000001b043f098c084e085f0704000000
1431
2d010400040000002d010200030000001e00070000001604200950086c089b0705000000020101000000040000002d0101000500000009020000000005000000
1432
14026f089b07050000002e010100000011000000320a6f089b0704000400000000002a10cc0d4e6578743c00250029001700050000002e010000000005000000
1433
14020902640e05000000020101000000040000002701ffff1000000026060f001600ffffffff00002e040000660a000078040000230b000008000000fa020000
1434
0600000000000000040000002d010500040000002d010600080000002503020053046a0a5304df0a040000002d01030004000000f001050007000000fc020000
1435
000000000000040000002d0105000a000000240303003204dd0a53041e0b7304dd0a040000002d010200040000002d01040004000000f0010500080000002606
1436
0f000600ffffffff01001000000026060f001600ffffffff00003a070000660a000084070000230b000008000000fa0200000600000000000000040000002d01
1437
0500040000002d01060008000000250302005f076a0a5f07df0a040000002d01030004000000f001050007000000fc020000000000000000040000002d010500
1438
0a000000240303003e07dd0a5f071e0b7f07dd0a040000002d010200040000002d01040004000000f00105000800000026060f000600ffffffff010007000000
1439
fc020000ffffff000000040000002d01050008000000fa0200000600000000000002040000002d010700070000001b049f03340672020b01040000002d010400
1440
04000000f0010500040000002d01020004000000f0010700030000001e000700000016047d03f50593024a0105000000020101000000040000002d0101000500
1441
000009020000000005000000140294024a01050000002e010100000017000000320a94024a0108000400000000002a10cc0d54726565206f662034001c002500
1442
240015002a001b001500050000002e01000000000500000014020902640e05000000140294025202050000002e010100000014000000320a9402520206000400
1443
000000002a10cc0d6e6f6465732029002a002a00250020001500050000002e01000000000500000014020000000005000000140294022903050000002e010100
1444
00001f000000320a940229030d000400000000002a10cc0d656163682073746f72696e67200025002500250029001500200017002a001c0017002a0029001500
1445
050000002e0100000000050000001402000000000500000014029402d204050000002e010100000011000000320a9402d20404000400000000002a10cc0d6f6e
1446
65202a00290025001500050000002e01000000000500000014020000000005000000140294025f05050000002e010100000011000000320a94025f0504000400
1447
000000002a10cc0d737569742100290017001700050000002e010000000005000000140200000000050000000201010000000500000002010100000005000000
1448
1402f6024a01050000002e010100000028000000320af6024a0113000400000000002a10cc0d6c656e6774687320636f6d62696e6174696f6e03170025002900
1449
2a0017002a002000150025002b003f002a00180029002500170017002a002900050000002e010000000005000000140200000000050000000201010000000400
1450
00002701ffff1000000026060f001600ffffffff0000430100009a03000078020000cf04000008000000fa0200000600000000000000040000002d0105000400
1451
00002d010600080000002503020073029e0373019e04040000002d01030004000000f001050007000000fc020000000000000000040000002d0105000a000000
1452
240303005e0185044701ca048c01b304040000002d010200040000002d01040004000000f00105000800000026060f000600ffffffff0100040000002d0100000300000000000000000000000000000000000000000000000000}}}}}{\lang1053
1453
\par The \'94suit lengths combination\'94 node includes:
1454
\par {\pntext\pard\plain\f3 \loch\af3\dbch\af0\hich\f3 \'b7\tab}}\pard \fi-360\li360\nowidctlpar\jclisttab\tx360{\*\pn \pnlvlblt\ilvl0\ls14\pnrnot0\pnf3\pnstart1\pnindent360\pnhang{\pntxtb \'b7}}\ls14\adjustright {\lang1053
1455
The suit lengths combination as a 64-bit integer.
1456
\par {\pntext\pard\plain\f3 \loch\af3\dbch\af0\hich\f3 \'b7\tab}}\pard \fi-360\li360\nowidctlpar\jclisttab\tx360{\*\pn \pnlvlblt\ilvl0\ls14\pnrnot0\pnf3\pnstart1\pnindent360\pnhang{\pntxtb \'b7}}\ls14\adjustright {\lang1053 A pointer to the top \'94
1457
winning cards node\'94.
1458
\par {\pntext\pard\plain\f3 \loch\af3\dbch\af0\hich\f3 \'b7\tab}}\pard \fi-360\li360\nowidctlpar\jclisttab\tx360{\*\pn \pnlvlblt\ilvl0\ls14\pnrnot0\pnf3\pnstart1\pnindent360\pnhang{\pntxtb \'b7}}\ls14\adjustright {\lang1053 A pointer to next left \'94
1459
suit lengths combination node\'94 in the binary tree.
1460
\par {\pntext\pard\plain\f3 \loch\af3\dbch\af0\hich\f3 \'b7\tab}}\pard \fi-360\li360\nowidctlpar\jclisttab\tx360{\*\pn \pnlvlblt\ilvl0\ls14\pnrnot0\pnf3\pnstart1\pnindent360\pnhang{\pntxtb \'b7}}\ls14\adjustright {\lang1053 A pointer to next right \'94
1461
suit lengths combination node\'94 in the binary tree.
1462
\par }\pard \nowidctlpar\adjustright {\lang1053
1463
\par
1464
\par The \'94winning cards node\'94 includes:
1465
\par {\pntext\pard\plain\f3 \loch\af3\dbch\af0\hich\f3 \'b7\tab}}\pard \fi-720\li720\nowidctlpar{\*\pn \pnlvlblt\ilvl0\ls4\pnrnot0\pnf3 {\pntxtb \'b7}}\ls4\adjustright {\lang1053 The hands of the relative ranks for each winning card of the actual suit.
1466
\par {\pntext\pard\plain\f3 \loch\af3\dbch\af0\hich\f3 \'b7\tab}}\pard \fi-720\li720\nowidctlpar{\*\pn \pnlvlblt\ilvl0\ls4\pnrnot0\pnf3 {\pntxtb \'b7}}\ls4\adjustright {\lang1053
1467
A pointer to the next winning cards node required to achieve a Transposition Table match for this branch of the tree.
1468
\par {\pntext\pard\plain\f3 \loch\af3\dbch\af0\hich\f3 \'b7\tab}}\pard \fi-720\li720\nowidctlpar{\*\pn \pnlvlblt\ilvl0\ls4\pnrnot0\pnf3 {\pntxtb \'b7}}\ls4\adjustright {\lang1053 A pointer to the previous winning cards node.
1469
\par {\pntext\pard\plain\f3 \loch\af3\dbch\af0\hich\f3 \'b7\tab}}\pard \fi-720\li720\nowidctlpar{\*\pn \pnlvlblt\ilvl0\ls4\pnrnot0\pnf3 {\pntxtb \'b7}}\ls4\adjustright {\lang1053 A pointer to the next alternative winning cards n
1470
ode that leads to a Transposition Table match in an alternative tree branch.
1471
\par {\pntext\pard\plain\f3 \loch\af3\dbch\af0\hich\f3 \'b7\tab}}\pard \fi-360\li360\nowidctlpar\jclisttab\tx360{\*\pn \pnlvlblt\ilvl0\ls10\pnrnot0\pnf3\pnstart1\pnindent360\pnhang{\pntxtb \'b7}}\ls10\adjustright {\lang1053
1472
A pointer to the "set of positions node".
1473
\par }\pard \nowidctlpar\adjustright {\lang1053
1474
\par
1475
\par The "set of positions node\'94 includes:
1476
\par {\pntext\pard\plain\f3 \loch\af3\dbch\af0\hich\f3 \'b7\tab}}\pard \fi-720\li720\nowidctlpar{\*\pn \pnlvlblt\ilvl0\ls4\pnrnot0\pnf3 {\pntxtb \'b7}}\ls4\adjustright {\lang1053
1477
An upper and a lower bound for the winning tricks of the North/South side. These values\line are used to determine whether or not a search cutoff can be done.
1478
\par {\pntext\pard\plain\f3 \loch\af3\dbch\af0\hich\f3 \'b7\tab}}\pard \fi-720\li720\nowidctlpar{\*\pn \pnlvlblt\ilvl0\ls4\pnrnot0\pnf3 {\pntxtb \'b7}}\ls4\adjustright {\lang1053 The lowest winning rank per suit, expressed as relative rank.
1479
\par {\pntext\pard\plain\f3 \loch\af3\dbch\af0\hich\f3 \'b7\tab}}\pard \fi-720\li720\nowidctlpar{\*\pn \pnlvlblt\ilvl0\ls4\pnrnot0\pnf3 {\pntxtb \'b7}}\ls4\adjustright {\lang1053 The suit and rank for the currently best move.
1480
\par }\pard \nowidctlpar\adjustright {\lang1053
1481
\par
1482
\par }\pard \nowidctlpar\tx420\adjustright {\cf1\lang1053
1483
After a Transposition Table match, the current position may later be part of a position that will be stored in the Transposition Table. Therefore, the stored winning ranks in the Transposition Table must be included in the state information of the current
1484
position. However, the winning ranks cannot be taken as is, because they are stored as relative ranks which now must be converted to absolute ranks in the current position.
1485
\par This is done using the lowest winning relative rank for each suit that is stored in the \'94set of positions\'94 node that gave the Transposition Table match:
1486
\par The aggregated set of (absolute) ranks for each suit in the current position is filtered using the stored information on the lowest winning relative rank. The winning ranks for each suit
1487
is then the aggregated set with only the number of highest ranks implied by the stored lowest winning relative rank in the \'94set of positions\'94 node.
1488
\par E.g. if the aggregated rank set for spades is A J 9 4 2 and lowest winning relative rank is order=2, then winning ranks are A J.
1489
\par }\pard \nowidctlpar\adjustright {\lang1053
1490
\par
1491
\par }\pard \nowidctlpar\tx420\adjustright {\b\cf1\lang1053 7.4 Building a new entry in the Transposition Table}{\cf1\lang1053
1492
\par
1493
\par When the value of the current position is known and it is the end of a trick (except the last), position state information is collected for storage in the Transposition Table.
1494
\par The ranks of the backed up winning cards are converted from absolute to relative.
1495
\par For each suit, it is determined which winning rank that is lowest. The relative ranks then stored in the new Transposition Table entry are all ranks above and including the lowest rank, filling out any \'94holes\'94
1496
in the ranks that might have been present.
1497
\par The trees of the Transposition Table are searched starting from the \'94root pointer\'94 and additional nodes are inserted corresponding to the current position.
1498
\par First, the suit lengths of the current position are used to find a \'94suit lengths combination node\'94 or to create a new such node if it does not exist already.
1499
\par The next step is to search for a \'94winning card node\'94 that has the \'94suit length combination node\'94 as parent. This \'94winning card node\'94 has then winning cards for spades.
1500
\par If no such node yet exists, \'94winning card nodes\'94, one for each suit, are created using the winning cards of the current position. Each such node includes all winning cards for one of the suits. Then, a \'94set of positions\'94
1501
node is created. This node is pointed to from the last created \'94winning card node\'94 created for the winning cards of clubs.
1502
\par Otherwise, if there already exists a matching \'94winning card node\'94 with the \'94suit length combination node\'94 as parent, it is checked whether or not the \'94winning card nodes\'94
1503
in a subsequent tree branch already created for hearts, diamonds and clubs also are matched with the current position.
1504
\par If such a sequence of nodes can be found, the upper or lower bound in the connected \'94set of positions node\'94 may be updated to allow for an increased number of cutoffs:
1505
\par
1506
\par If the current position upper value bound is less than the stored upper value bound, the stored value is updated with the current position value.
1507
\par If the current position lower value bound is larger than the stored lower value bound, the stored value is updated with the current position value.
1508
\par
1509
\par In case a matching \'94winning card node\'94 cannot be found, a new \'94winning card node\'94 is created and linked to the last matching node. E.g. if existing \'94winning card nodes\'94
1510
for spades and hearts match the current position, but no node match for diamonds, then a \'94winning cards node\'94 for diamonds is created and linked to the previous \'94winning cards node\'94 for hearts. Then a clubs \'94winning cards node\'94 and a
1511
\'94set of positions node\'94 are created.
1512
\par
1513
\par
1514
\par }\pard \nowidctlpar\adjustright {\b\lang1053
1515
\par
1516
\par
1517
\par References
1518
\par }{\lang1053
1519
\par James Dow Allen:
1520
\par Source code for a simple DDS.
1521
\par }{\field\fldedit{\*\fldinst {\lang1053 HYPERLINK \\l "_Hlk134153111" }{\fs20\lang1053 {\*\datafield
1522
08d0c9ea79f9bace118c8200aa004ba90b02000000080000000e0000005f0048006c006b00310033003400310035003300310031003100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
1523
00000000000000}}}{\fldrslt {\cs15\ul\cf2 http://freepages.genealogy.rootsweb.com/~jamesdow/Tech/dbldum.htm}}}{\lang1053
1524
\par
1525
\par Matthias Brill:
1526
\par DDS algorithms description (in German) and DDS source code.
1527
\par }{\field\fldedit{\*\fldinst {\lang1053 HYPERLINK \\l "_Hlk134153080" }{\fs20\lang1053 {\*\datafield
1528
08d0c9ea79f9bace118c8200aa004ba90b02000000080000000e0000005f0048006c006b00310033003400310035003300300038003000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
1529
00000000000000}}}{\fldrslt {\ul\cf2 http://linux.softpedia.com/get/Science-and-Engineering/Artificial-Intelligence/cddsolve-20055.shtml}{\lang1053 }}}{\lang1053
1530
\par
1531
\par Ming-Sheng Chang:
1532
\par DDS algorithms description.
1533
\par {\*\bkmkstart _Hlt193293965}}{\field\fldedit{\*\fldinst {\lang1053 HYPERLINK "\\\\l "_Hlk132979785" "}{\fs20\lang1053 {\*\datafield
1534
00d0c9ea79f9bace118c8200aa004ba90b02000000010000000303000000000000c0000000000000460000040000005c6c2000ffffadde000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
1535
000000000000000000000000000000000000000000000000000000000000000000000000}}}{\fldrslt {cs.nyu.edu/web/Research/TechReports/TR1996-725/TR1996-725.ps.gz
1536
\par }}}\pard\plain \nowidctlpar\adjustright \lang2057 {\lang1053 {\*\bkmkend _Hlt193293965}
1537
\par
1538
\par Ed Colley:
1539
\par DDS source code and DDS executable.
1540
\par }{\field\flddirty{\*\fldinst {\lang1053 HYPERLINK "\\\\l "_Hlk133040134" "}{\fs20\lang1053 {\*\datafield
1541
00d0c9ea79f9bace118c8200aa004ba90b02000000010000000303000000000000c0000000000000460000040000005c6c2000ffffadde000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
1542
000000000000000000000000000000000000000000000000000000000000000000000000}}}{\fldrslt {\ul\cf2\lang1053 http://freefinesse.sourceforge.net/}}}{\lang1053
1543
\par
1544
\par Matthew L. Ginsberg:
1545
\par DDS algorithms description.
1546
\par }{\field\fldedit{\*\fldinst {\lang1053 HYPERLINK \\l "_Hlk134152954" }{\fs20\lang1053 {\*\datafield
1547
08d0c9ea79f9bace118c8200aa004ba90b02000000080000000e0000005f0048006c006b00310033003400310035003200390035003400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
1548
00000000000000}}}{\fldrslt {\cs15\ul\cf2 http://www.cs.cmu.edu/afs/cs/project/jair/pub/volume14/ginsberg01a.pdf}}}{\lang1053
1549
\par
1550
\par Dan Hirschberg:
1551
\par DDS algorithms description and DDS executable (MS DOS, cannot run in XP?)
1552
\par }{\field\flddirty{\*\fldinst {\lang1053 HYPERLINK "\\\\l "_Hlk132979763" "}{\fs20\lang1053 {\*\datafield
1553
00d0c9ea79f9bace118c8200aa004ba90b02000000010000000303000000000000c0000000000000460000040000005c6c2000ffffadde000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
1554
000000000000000000000000000000000000000000000000000000000000000000000000}}}{\fldrslt {\ul\cf2\lang1053 http://www.ics.uci.edu/~dan/bridge/index.html
1555
\par }}}\pard\plain \nowidctlpar\adjustright \lang2057 {\lang1053
1556
\par Alexey Slovesnov:
1557
\par DDS source code and DDS executable.
1558
\par
1559
\par Judea Pearl: Asymptotic properties of minimax trees and game search precedures.\line Artificial Intelligence 14(2):113-138. [Pearl 1980]
1560
\par
1561
\par Aske Plaat, Jonathan Schaeffer, Wim Pijls and Arie de Bruin: Exploiting graph properties of game trees. In }{\i\lang1053 Proceedings of the Thirteenth National Conference on Artificial Intelligence}{\lang1053 , pages 234-239, 1996 [Plaat et al.]
1562
\par
1563
\par Hans Kuijf, personal communication.
1564
\par
1565
\par Pedja Stanojevic, personal communication.
1566
\par
1567
\par Knuth: The art of computer programming, Vol. 3, Searching and Sorting, chapter 6.2.2, Algorithm T.
1568
\par
1569
\par Sebastian Kupferschmid, Malte Helmert: A Skat Player Based on Monte Carlo Simulation.
1570
\par
1571
\par Jo\'ebl Bradmetz, personal communication.
1572
\par http://jibe-bridge.perso.cegetel.net/
1573
\par }}
b'\\ No newline at end of file'
Loggerhead is a web-based interface for Breezy
Version: 2.0.1