Partially Observable Endgames

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Presented at Board Game Studies, Brugge, 2011.
@inproceedings{teytaud:inria-00625794,
hal_id = {inria-00625794},
url = {http://hal.inria.fr/inria-00625794},
title = {{Lemmas on Partial Observation, with Application to Phantom Games}},
author = {Teytaud, Fabien and Teytaud, Olivier},
abstract = {{Solving games is usual in the fully observable case. The partially observable case is much more difficult; whenever the number of strategies is finite (which is not necessarily the case, even when the state space is finite), the main tool for the exact solving is the construction of the full matrix game and its solving by linear programming. We here propose tools for approximating the value of partially observable games. The lemmas are relatively general, and we apply them for deriving rigorous bounds on the Nash equilibrium of phantom-tic-tac-toe and phantom-Go.}},
language = {Anglais},
affiliation = {Laboratoire de Recherche en Informatique - LRI , TAO - INRIA Saclay - Ile de France},
booktitle = {{Computational Intelligence and Games}},
address = {Seoul, Cor{\'e}e, R{\'e}publique Populaire D{\'e}mocratique De},
audience = {internationale },
year = {2011},
month = Sep,
pdf = {http://hal.inria.fr/inria-00625794/PDF/phantomatari.pdf},
}

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Partially Observable Endgames

  1. 1. Difficult Endgame Analysis Fabien Teytaud, Olivier Teytaud
  2. 2. Outline Fast state of the art Computer-Games Endgame analysis in board games Endgame analysis in partially observable games Our results Discussion
  3. 3. Computer games [Le damier de lopéra]
  4. 4. How strong computers are ? In Chess ? In Go ? In Backgammon ? In poker ? ...
  5. 5. Endgame analysis in boardgames In Chess :  Nalimov tables  Five pieces or fewer has been completly analyzed  Six pieces has been completly analyzed except trivial positions  Just few 7 pieces positions have been analyzed  Perfect play
  6. 6. Endgame analysis in boardgames [Søren Riis in Bielefeld 2010]
  7. 7. Endgame analysis in boardgames [Søren Riis in Bielefeld 2010]
  8. 8. Endgame analysis in partiallyobservable games New challenge ?
  9. 9. Endgame analysis in partiallyobservable games What is phantom games ?
  10. 10. Endgame analysis in partiallyobservable games What are phantom games ?  No information about the moves of the opponent.  Some examples :  In Chess :  Kriegspiel  Dark Chess  In Go :  Phantom Go
  11. 11. Endgame analysis in partiallyobservable games What is phantom games ?  No information about the moves of the opponent.  Some examples :  In Chess :  Kriegspiel  Dark Chess  In Go :  Phantom Go
  12. 12. Endgame analysis in partiallyobservable games What is phantom games ? Example of a Dark Chess position
  13. 13. Endgame analysis in partiallyobservable games What are phantom games ? Example of a Dark Chess position [Wikipedia]
  14. 14. Algorithms Retrograde propagation no more possible Worst case analysis :  Findsperfect strategy against an opponent who sees the board  Does not evaluate properly real positions (example in next slide)
  15. 15. A Phantom-Go example Lets take this position :  Black to play  Position is done so that White wins if and only if he saves all his groups
  16. 16. A Phantom-Go example
  17. 17. Analysis in standard Go ? Easy win for White. Each time black attacks a group then White responds in the same group and make two eyes
  18. 18. Analysis in standard Go ?
  19. 19. Analysis in standard Go ?
  20. 20. Analysis in standard Go ?
  21. 21. Analysis in standard Go ?
  22. 22. Analysis in standard Go ?
  23. 23. But in Phantom-Go ? White does not know which group is under attack Then, White can win only by playing in the exactly in the right order Probably that this happens : 1/8 ! Which algorithm for this case ?  D.Auger :D. Auger. Multiple tree for partially observable Monte-Carlo Tree Search. EvoGames, LNCS, Springer  Adapted to Dark Chess : no observation until game over
  24. 24. Dark Chess examples Small board sizes  3x3  4x4  8x8? Only King vs King final
  25. 25. Dark Chess examples
  26. 26. Dark Chess results
  27. 27. Dark Chess results
  28. 28. Dark Chess results
  29. 29. Dark Chess results
  30. 30. Conclusion Usual methods are approximations of perfect play We propose an (asymptotically) exact algorithm  If finite horizon  But general case undecidable (Teytaud, 2010) Tractable in some cases First ever real endgame analysis in PO games
  31. 31. Dark Chess results

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