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en passant, repetition, 50 move state, ... see FEN, EPD ). - So when A and B changed sides, B would still have the same possible moves as A had before. "Same options when changing sides" is the essential concept when combining impartial games. For example combining three games, and at each turn a player first chooses the board where he will do the next move (no matter whether it is white's or black's turn there). - Contrary, consider an "asymmetric chess", where player A captures by pawn only to the left and player B only to the right. Then, when changing sides, B would have different options to move on, compared to A before. - So moving different colored pieces in different(!) positions does not disqualify chess from the class of impartial games. Instead it is the possibility of draw. Positions in impartial games must be either winning or losing positions. - 20:30, 12 April 2020 (UTC)
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tic-tac-toe do not fit the definition because they permit draws (and eliminating draws would have resulted in a radically different game), but go can be easily made into one if we adopt the superko rule (a player cannot make a move that would have resulted in a position being repeated - this can be simulated by adding the whole history to the game state, expanding the number of game states by a factor of no more than 2^N), and a tiebreaker that if both players have the same score, the one who moved first loses. -
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Agreed. Also wondered about that go/chess example. And it's still misleading phrasing in the article, seven years later. Your "redefinition" adopts closer to real chess. A position there consists of a diagram of the pieces, a remark like "white to play" and optional infos about state ( as castling,
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Is there a formal definition of an impartial game? The article says that chess is not impartial because only the white player can move the white pieces, and vice versa. But what if I redefine the position by adding a binary flag indicating whose player's turn it is? I.e., any move when the flag is
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is a position after the first move, etc.; a player loses if he cannot make a move. Note that gameplay is always finite: the standard set theory does not permit an infinite sequence of sets, where A∈B, B∈C, C∈D, etc.; in particular, a set cannot be a member of itself.) That means that chess and
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Most likely someone misunderstood what impartial game means, thought it meant that all sides are equally balanced, and stuck the claim about
Diplomacy there. I have not played diplomacy, but if it has symmetrical payoffs for any given position, it's a very different game than I thought!
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is misleading. Go, even without a no-suicide rule, fails to be impartial for the same reason as chess does, because one player places black stones and the other white. I've rewritten the prior sentence to include both games.
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is also not impartial, although it is closer than chess, because of the "no suicides" rule
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Follow-up: An author has defined a "short impartial game" as: A finite set G = {H
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Ought that to be "partisan game", or is this an unusual usage? --
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Dude, it's
Knowledge. Find some, and put them in the list. --
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