Talk:Impartial game

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Ought that to be "partisan game", or is this an unusual usage? --Brion 01:53 Sep 2, 2002 (PDT)

The sentence

Go is also not impartial, although it is closer than chess, because of the "no suicides" rule

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. 02:51, 15 April 2007 (UTC)

More Games[edit]

The list of impartial games should be longer. 13:17, 25 January 2006 (UTC)

Dude, it's Wikipedia. Find some, and put them in the list. --Einstein9073 20:06, 2 March 2006 (UTC)

I've extended the list from 2 to 5. 03:09, 15 April 2007 (UTC)


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! —Preceding unsigned comment added by (talk) 09:40, 1 November 2007 (UTC)

Impartial games[edit]

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 "white" switches it to "black", and vice versa; if the black player ever reached a position where the flag is "white", he could move the white pieces, but the rules never allow the black player to reach such a position. (Or is it the case that if the game states can be split into two sets, one only reachable by the first player and the other only reachable by the second, the game is by definition not impartial?) - Mike Rosoft (talk) 16:57, 13 April 2013 (UTC)

  • Follow-up: An author has defined a "short impartial game" as: A finite set G = {H1, H2, ..., Hn}, where each of Hi is a short impartial game. [1] (I.e., the set G is the initial position, each of Hi 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 [by the axiom of regularity] 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 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. - Mike Rosoft (talk) 06:46, 14 April 2013 (UTC)