It follows that the optimum strategy is ( 2, 2, 2 ) as it does not do worse than breaking even against any other strategy while beating one other strategy.
12.
Tic-tac-toe is a trivial example; two players who follow the easy-to-learn optimum strategy ( rather than making sub-par decisions of their own ) will always find their games end in a draw.
13.
In iterated prisoner's dilemma games, it is found that the preferred strategy is not to play a Nash strategy of the stage game, but to cooperate and play a socially optimum strategy.
14.
It may also give a better feel for the optimum strategy and the likely profits, but it does not give any feel for the cash flow, which was the main feature of the original matrix.
15.
The books that inspired Curtis grew out of a flowering of scientific gambling analysis that began with " The Optimum Strategy in Blackjack, " an article printed in the September 1956 issue of the Journal of the American Statistical Association.
16.
The subgame-perfect Nash equilibrium is normally deduced by " backward induction " from the various ultimate outcomes of the game, eliminating branches which would involve any player making a move that is Go has such an optimum strategy for all players.
17.
When the Nash equilibrium payoff is equal to the minmax payoff, then the player has no reason to stick to a socially optimum strategy and is free to play a selfish strategy throughout, since the punishment cannot affect him ( being equal to the minmax payoff ).
