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...

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...

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

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...

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...

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...

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...

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,...

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":...

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...

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 ,...

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

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...

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...

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

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...

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...

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

unilaterally change their strategy. Considering only situations where players play a single strategy without randomizing (a pure strategy) a game can have any...

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...

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...

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...

cannot end in a draw, then one of the two players must have a winning strategy (i.e. can force a win). An alternate statement is that for a game meeting...

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...

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...

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

played. These predictions are called "solutions", and describe which strategies will be adopted by players and, therefore, the result of the game. The...