Constructing Pin Endgame Databases for the Backgammon Variant Plakoto

Transcription

1 Constructing Pin Endgame Databases for the Backgammon Variant Plakoto Nikolaos Papahristou and Ioannis Refanidis University of Macedonia Department of Applied Informatics AI Group Thessaloniki, Greece 14th International Conference Advances in Computer Games 2015

2 Motivation Previous research: Palamedes: Bot that plays several backgammon variants on expert level. This paper: Endgame databases for the Plakoto variant Evaluation of existing AI using the endgame DBs. Nikolaos Papahristou, Ioannis Refanidis, 14 th ACG, 2015 Constructing Pin DBs for the Backgammon Variant Plakoto 2/16

3 Outline 1. Introduction 2. Plakoto Rules and positions of interest 3. Endgame DB algorithm and AI evaluation 4. Conclusion Nikolaos Papahristou, Ioannis Refanidis, 14 th ACG, 2015 Constructing Pin DBs for the Backgammon Variant Plakoto 3/16

4 Backgammon games 2-player, turn-taking, zero-sum, stochastic board game Each player has 15 checkers or men Checkers move at specific direction Checkers move according to dice rolls Goal of players move all checkers to home quadrant and then remove first their checkers from board Double game: when one player removes all its checkers and opponent hasn t remove any of its own Nikolaos Papahristou, Ioannis Refanidis, 14 th ACG, 2015 Constructing Pin DBs for the Backgammon Variant Plakoto 4/16

5 Palamedes project Initial goal: AI for most popular variants in Greece (Portes, Plakoto, Fevga). Expanded in other variants (Narde, Takhteh, Hypergammon etc) Free download: Windows version: Android: amedes Nikolaos Papahristou, Ioannis Refanidis, 14 th ACG, 2015 Constructing Pin DBs for the Backgammon Variant Plakoto 5/16

6 Current state of backgammon endgame DBs Endgame DBs in standard backgammon cover bearoff and race positions. Two kind of DBs: One-sided Only store positions of the player to move. Pros: Small size Cons: Not 100% accurate for move selection Two-sided Store the full board position Pros: Full game theoretic value -> accurate move selection Cons: Large size Nikolaos Papahristou, Ioannis Refanidis, 14 th ACG, 2015 Constructing Pin DBs for the Backgammon Variant Plakoto 6/16

7 Plakoto Rules Usual backgammon rules apply except: No hitting. Lone checkers can be pinned by opponent Pinned checkers cannot move Initial Position Typical middle-game position Nikolaos Papahristou, Ioannis Refanidis, 14 th ACG, 2015 Constructing Pin DBs for the Backgammon Variant Plakoto 7/16

8 Importance of Pins A made point can be constructed with only one checker (pin). Players can nullify bad luck when they roll small rolls and/or the opponent rolls big rolls. The side that has pinned without getting pinned usually gets a few rolls ahead in the bearoff race. Nikolaos Papahristou, Ioannis Refanidis, 14 th ACG, 2015 Constructing Pin DBs for the Backgammon Variant Plakoto 8/16

9 Pin Endgames Positions of interest The side to move has pinned one checker inside her bearoff quadrant (points 2-6). The opponent has pinned the moving player once. No more further pins are possible (also called race ). Nikolaos Papahristou, Ioannis Refanidis, 14 th ACG, 2015 Constructing Pin DBs for the Backgammon Variant Plakoto 9/16

10 Algorithm Retrograde style Start from end and go backwards Main idea: find the distance to unpin Storage in DB in pairs (position, distance to unpin) Position -> int32 (perfect hash) Distance -> double Actual play DB is activated only when position before roll has the desired characteristics Find distances of all afterstates and select the move which results in position with the max distance value Nikolaos Papahristou, Ioannis Refanidis, 14 th ACG, 2015 Constructing Pin DBs for the Backgammon Variant Plakoto 10/16

11 Algorithm pseudo code Init P // last point where checkers reside Init pin // point where the pin is placed Position = createstartposition(pin) while Position lastpos(p) saveindb(hash(position), finddistance(position)) increment(position) function finddistance(position) avgdistance = 0 for every roll d // There are 21 possible rolls afterstates = findmoves(position, d) distances = readdistancesfromdb(afterstates) distance = max(distances) if d is double roll else avgdistance += distance avgdistance += 2 * distance return avgdistance / 36 Nikolaos Papahristou, Ioannis Refanidis, 14 th ACG, 2015 Constructing Pin DBs for the Backgammon Variant Plakoto 11/16

12 Number of endgame positions C + P 1 P + C 1! R = = C C! P 1! R: Number of positions C: Number of checkers (=13 in our case) P: Number of points that checkers reside Examples: P = 6, R = > 67KB P = 12, R = > 19MB This paper: 5 DBs (2-6 pin points): 12,480,720 Total 2-sided pos: 3.4x10 15 Nikolaos Papahristou, Ioannis Refanidis, 14 th ACG, 2015 Constructing Pin DBs for the Backgammon Variant Plakoto 12/16

13 Potential problems One sided -> best move is not 100% guaranteed. Type of positions with potential problems: Red player is way ahead in the unpinning race Red player to move 31. Possible moves: a) 23-24, b) Green player very close to unpin Best move according to DB is may be the actual best move due to better bearoff placement However, rollouts did not give statistical significant result. Nikolaos Papahristou, Ioannis Refanidis, 14 th ACG, 2015 Constructing Pin DBs for the Backgammon Variant Plakoto 13/16

14 NN evaluation in plakoto endgames Experiment to check if NN selects the same move as the DB. All one-sided positions and all rolls Positions encountered in self play DB activated in 1% of total moves Comparison Method Correct moves by the NN (%) All positions 15% Self-play positions 64% Nikolaos Papahristou, Ioannis Refanidis, 14 th ACG, 2015 Constructing Pin DBs for the Backgammon Variant Plakoto 14/16

15 Conclusions Future Work Conclusions Initial exploration of pin endgames. Small DB size but large number of positions covered. 1-sided DBs means no absolute certainty for move selection but no problems found yet. Pin DBs enhance move selection of the Palamedes program. Future Work More pin databases DBs with pin points outside the bearoff quadrant DBs with more than one pinned point Experiment with lower precision in the value. Explore compression potential. Nikolaos Papahristou, Ioannis Refanidis, 14 th ACG, 2015 Constructing Pin DBs for the Backgammon Variant Plakoto 15/16

16 Thank you for your attention!