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This is optimum bluffing strategy — it makes no difference how your opponent plays. We can say, then, that if you come up with a bluffing strategy that makes your opponent do equally badly no matter how he plays, then you have an optimum strategy. And this optimum strategy is to bluff in such a way that the odds against your bluffing are identical to the odds your opponent is getting from the pot.

 

In the situation we have been discussing, I had 18 good cards, and when I bet my $100, creating a $300 pot, my opponent was getting 3-to-1 odds from the pot. Therefore, my optimum strategy was to bluff with six additional cards, making the odds against my bluffing 3-to-1, identical to the pot odds my opponent was getting. Let’s say the pot was $500 instead of $200 before I bet. Once again I had 18 winning cards, and my opponent could only beat a bluff.

 

The bet is $100, and so my opponent would be getting $600-to-$ 100 pot odds when he called. Now my optimum strategy would be to bluff with 3 cards. With 18 good cards and 3 bluffing cards, the odds against my bluffing would be 6-to-1, identical to the pot odds my opponent would be getting to call my bet. If the pot were $ 100 and I bet $ 100, I’d have to bluff with 9 cards when I had 18 good cards, making the odds against my bluffing identical to the 2-to-l odds my opponent would be getting from the pot.