Matches in DBpedia 2016-04 for { ?s ?p "In combinatorial game theory, the strategy-stealing argument is a general argument that shows, for many two-player games, that the second player cannot have a guaranteed winning strategy. The strategy-stealing argument applies to any symmetric game (one in which either player has the same set of available moves with the same results, so that the first player can \"use\" the second player's strategy) in which an extra move can never be a disadvantage.The argument works by obtaining a contradiction. A winning strategy is assumed to exist for the second player, who is using it. But then, roughly speaking, after making their first move - which by the conditions above is not a disadvantage - the first player may then also play according to this winning strategy. The result is that both players are guaranteed to win - which is absurd, thus contradicting the assumption that such a strategy exists.Examples of games to which the argument applies are hex and the m,n,k-games such as gomoku. In hex ties are not possible, so the argument shows that it is a first-player win."@en }
Showing triples 1 to 1 of
1
with 100 triples per page.
- Strategy-stealing_argument abstract "In combinatorial game theory, the strategy-stealing argument is a general argument that shows, for many two-player games, that the second player cannot have a guaranteed winning strategy. The strategy-stealing argument applies to any symmetric game (one in which either player has the same set of available moves with the same results, so that the first player can \"use\" the second player's strategy) in which an extra move can never be a disadvantage.The argument works by obtaining a contradiction. A winning strategy is assumed to exist for the second player, who is using it. But then, roughly speaking, after making their first move - which by the conditions above is not a disadvantage - the first player may then also play according to this winning strategy. The result is that both players are guaranteed to win - which is absurd, thus contradicting the assumption that such a strategy exists.Examples of games to which the argument applies are hex and the m,n,k-games such as gomoku. In hex ties are not possible, so the argument shows that it is a first-player win.".