In combinatorial game theory, the strategy-stealing argument is a general argument that shows, for many two-player games, that the second player cannot...

the game. A standard strategy stealing argument from combinatorial game theory shows that in no m,n,k-game can there be a strategy that assures that the...

position whose Grundy value is zero, whenever this is possible. A strategy-stealing argument shows that the Grundy value is nonzero for every poset that has...

(). This can be a non-constructive proof (possibly involving a strategy-stealing argument) that need not actually determine any details of the perfect play...

a standard strategy-stealing argument, one can thus conclude that if two players alternate, then the first player has a winning strategy when H is sufficiently...

with finitely many strategies, there exists a value V and a mixed strategy for each player, such that (a) Given Player 2's strategy, the best payoff possible...

the level of rational argument, but begin by denouncing all argument; they may forbid their followers to listen to rational argument, because it is deceptive...

impossible for Player 2 to form an I-tromino before Player 1 does: the strategy-stealing argument applies.) Harary defines the unqualified terms "winner" and "loser":...

An evolutionarily stable strategy (ESS) is a strategy (or set of strategies) that is impermeable when adopted by a population in adaptation to a specific...

always be a winning strategy for player X. There will never be a winning strategy for player O because of the Strategy-stealing argument since an nd game...

situation. A player's strategy determines the action the player will take at any stage of the game. However, the idea of a strategy is often confused or...

(White), a second player win (Black), or a forced draw. Solved game Strategy-stealing argument Zugzwang Determinacy Combinatorial game theory First-move advantage...

probabilities are either 1 or 0, the strategy is called deterministic. An example of a deterministic strategy is the tit-for-tat strategy written as P = { 1 , 0 ,...

situation where no player could gain by changing their own strategy (holding all other players' strategies fixed). The idea of Nash equilibrium dates back to...

Nine men's morris is a strategy board game for two players, dating back to at least the Roman Empire. The game is also known as nine-man morris, mill,...

often played by young children who may not have discovered the optimal strategy. Because of the simplicity of tic-tac-toe, it is often used as a pedagogical...

In game theory, a strategy A dominates another strategy B if A will always produce a better result than B, regardless of how any other player plays. Some...

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...

the standard assumptions, the switching strategy has a ⁠2/3⁠ probability of winning the car, while the strategy of keeping the initial choice has only...

This strategy can also be seen successfully used in a viral video, in which a contestant of Golden Balls (in a game also known as split or steal) persisted...

In game theory, grim trigger (also called the grim strategy or just grim) is a trigger strategy for a repeated game. Initially, a player using grim trigger...

game complexity and the existence of optimal strategies through methods like the strategy-stealing argument. Combinatorial game theory arose in relation...

have one value per argument, and many reaction correspondences will be undefined, i.e., a vertical line, for some opponent strategy choice. One constructs...

game Misère Partisan game Solved game Sprague–Grundy theorem Strategy-stealing argument Zugzwang Games Chess Chomp Clobber Cram Domineering Hackenbush...

strategy profile s' such that ui (s') ≥ ui (s) for every player i and uj (s') > uj (s) for some player j. In this equation s represents the strategy profile...

that exceed (v < α or v > β) the α and β bounds set by its function call arguments. In comparison, fail-hard alpha–beta limits its function return value...

game Misère Partisan game Solved game Sprague–Grundy theorem Strategy-stealing argument Zugzwang Games Chess Chomp Clobber Cram Domineering Hackenbush...

pure strategy Nash equilibria, one where both players go to the prize fight, and another where both go to the ballet. There is also a mixed strategy Nash...

point-loss independent of the opponent's strategy. This leads to a linear programming problem with the optimal strategies for each player. This minimax method...

animals, and computers. Modern game theory began with the idea of mixed-strategy equilibria in two-person zero-sum games and its proof by John von Neumann...