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Cool Math Games (branded as Coolmath Games) [a] is an online web portal that hosts HTML and Flash web browser games targeted at children and young adults. Cool Math Games is operated by Coolmath LLC and first went online in 1997 with the slogan: "Where logic & thinking meets fun & games.".
Zermelo's theorem can be applied to all finite-stage two-player games with complete information and alternating moves. The game must satisfy the following criteria: there are two players in the game; the game is of perfect information; the board game is finite; the two players can take alternate turns; and there is no chance element present.
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Nim is an impartial game for two players, and subject to the normal play condition, which means that a player who cannot move loses. In the 1930s, the Sprague–Grundy theorem showed that all impartial games are equivalent to heaps in Nim, thus showing that major unifications are possible in games considered at a combinatorial level, in which ...
A variant first described by Claude Shannon provides an argument about the game-theoretic value of chess: he proposes allowing the move of “pass”. In this variant, it is provable with a strategy stealing argument that the first player has at least a draw thus: if the first player has a winning move in the initial position, let him play it, else pass.
Play free chess online against the computer or challenge another player to a multiplayer board game. With rated play, chat, tutorials, and opponents of all levels!
Sushi Go! - The Pick and Pass Card Game. In this fun (and highly adorable) card game, players compete to collect sushi, sashimi, and other foods worth varying amounts of points.
Consider the sum of the two games. The claim that G 1 and G 2 have the same Sprague-Grundy value is equivalent to the claim that the sum of the two games has Sprague-Grundy value 0. In other words, we are to show that the sum G 1 + G 2 is a P-position. A player is guaranteed to win if they are the second player to move in G 1 + G 2.