Theory of Poker Game theory and bluffing section

[tdiddy]

I was studying the game theory and bluffing section of Sklansky's Theory of Poker today and I completely understand the lowball example there. In the lowball example you have about a 43% chance of improving your hand to beat your opponent. And Sklansky shows that their is an optimal bluffing strategy that actually has positive expectation. (We are assuming (it seems to me) that after the draw you may only fold or bet and your opponent may only call or fold)

Okay now in the summary section he gives another example where you are drawing to a four flush (in regular draw poker) and your opponent draws three cards (which I take to mean that we assume he has a pair). Each of you has anted $10 before draw. Now same rules of betting after the draw as stated. Sklansky applies same method to come up with optimal bluffing strategy. But in this case you will still have negative expectation even using the bluffing frequency that he suggests. There are 42 cards remaining. 9 cards make you a winner and you will bet. You will bluff 3 times and fold 30 times. If you do this and he either always calls or always folds, then you lose $180. So, it seems that in this case, optimal bluffing strategy is used to minimize your losses. But no matter what your strategy, it is a losing scenario. I think this should have been pointed out in the text so as not to mislead anyone. Even though I suppose it would be naive to believe that one could acheive positive expectation in this scenario with such a small pot.

According to my calculations, in order to acheive positive expectation in this situation, you must have more than a 37.5% chance of outdrawing your opponent. Otherwise, the optimal bluffing strategy is only going help you to lose less money. By the way, if we make the bet after the draw much larger than the ante, we can acheive positive expectation if chances of outdrawing are greater than 25%.

Am I interpreting all of this correctly? I just want to test to see if my thinking is correct.

[tdiddy]

Also, I don't understand why he views half of the anted money as being his. Isn't the usual stance that anted money is no longer yours?

[Phat Mack]

I think it might be a mistake to assume that you can achieve a positve expectation through game theory bluffing alone. The examples in TOP are meant to illustrate optimal bluffing frequencies in different situations. But optimal bluffing frequencies beget optimal calling frequencies (DS discusses what happens when the opponent calls all of the time, and when the opponent calls none of the time, but doesn't discuss in these examples what happens when he calls some of the time), so two equally game-theory-savy opponents would always push over the long haul.