http://www.math.wisc.edu/~swanson/instructional/game_theory.pdf

 In this paper, the author discusses the optimal bluffing strategies for players in a simplified version of poker.  We say that player A bluffs if he bets in a hand where he is certain to have the worst hand, i.e the only way he can win the hand is by forcing the other player to fold the better hand.  It is noted that David Sklansky, the author of “The Theory of Poker”, claims that the optimal bluffing frequency is such that “the chances against your bluffing are identical to the pot odds your opponent is getting.”  The paper gives the example of when Player A bets $20 into a $100 pot, and the odds against him bluffing are 6:1.  If Player B always calls this $20 bet, his expectation is 1/7*(120)+6/7*(-20)=0.  If Player B always folds in this situation, then he neither gains nor loses anything, and so his expectation is also 0.  Thus based on these expected value calculations, it is impossible for Player B to determine whether he should call or fold and therefore this strategy is an equilibrium.

 Although the optimal strategy is an equilibrium, as the paper points out, it is not necessarily the best play.  In the example in the paper, the optimal strategy has an EV of 0 regardless of how the oponnent plays  However, if we know more about our opponents’ tendencies, and what they believe our tendencies to be, we can use this knowledge to our advantage to give ourselves a positive expectation.  Thus we can conclude that these “optimal strategies” should only be used against superior opponents or opponents who have an edge on our play.  For example, if I were to play Rock-Paper-Scissors champion, the optimal strategy would be for me to randomly pick each choice with probability 1/3 to neutralize the champion’s edge.  These examples seem to demonstrate a weakness in game theory.  

 Though game theory allows us to study simplified versions of games, it seems that most games, such as poker, are too complex to be fully understood using game theory.  If player A is capable of understanding his opponents tendencies, what his opponent believes A’s tendencies to be and so on, clearly it is not the best strategy for A to use the neutral EV “optimal strategy” given by game theory.