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Premise: I know that such a game would be better solved by MCTS, however, from a theoretical point of view, would it be possible to apply minimax to a bayesian multiplayer game where the order of playing is determined by result of the previous turn?

Game description:

  • Players: {A,B,C,D} (A and C are the maximizing team while B and D are the minimizing team)
  • Bayesian to set for example players' cards.
  • Turn 1: A->B->C->D
  • Turn 2(the order depends of the actual epilogue of Turn 1): C->D->A->B
  • Turn 3: B->C->D->A
  • ...
  • Turn N: game ends.

My feeling is that wouldn't be possible because after Turn 1 finished, in minimax standard definition, I must be able to start the next turn from a known player, while chance should be only applied to game's payoffs. Any opinion would be helpful.

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Minmax for multiplayer games shouldn't be dependent on the turn order of the other players, it depends on how well you are doing verses all of the other players.

At any terminal node, your evaluation considers some function of your standing verses the rest of your opponents collective standing; who is going to move next isn't relevant.

That said, multiplayer games have lots of imponderables when developing evaluation functions; there isn't any "correct" framework for dealing with coalition and kingmaker scenarios, and the practical aspects of limited depth search make horizon effects particularly severe.

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  • I usually cast my evaluation function as something which considers the state of only one player. In two player games, the evaluation of a position is e(player1)-e(player2). In multiplayer games, evaluation is e(player1)-max(e(player2),e(player3)). Propagation back up the tree requires recalculating the evaluation for the new node, rather than just negating as would be appropriate for a 2 player game.
    – ddyer
    Dec 27, 2013 at 6:37

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