NSchandler
04-27-2005, 02:27 AM
I am a relative newcomer to poker, and just read through TOP. It's quite an amazing book, and while it is clearly an invaluable resource to those who want to improve their game, I feel that the section on game theory and bluffing requires a slight adjustment.
Specifically, it seems that the section on "optimum bluffing strategy" could have you bluffing slightly less than is optimal. Let me give an example.
Sklansky recommends bluffing with such a frequency that the odds you are bluffing are equivalent to the pot odds. That is, if there is a $100 pot, for example, and bets are $20, your opponent is getting 6:1 odds to call your bet. Therefore, you should present your opponent with 6:1 odds that you are bluffing, making him indifferent to calling or folding (the sign of an optimal mixed strategy).
Now, suppose you are playing Hold 'Em, and after the turn, you will have 1 of 2 hands. 7 out of 8 times, you will have a hand with 18 outs. The other 1 out of 8 times, you will have a cinch hand. Again assume that the pot is $100 and bets are $20. How often should you be bluffing with your hand that gives you 18 outs? It would seem that you should bluff with 3 additional cards, presenting your opponent with 18:3 or 6:1 odds that you are bluffing. The problem, however, is that you aren't truly bluffing 1 out of 7 times as you should be. You are bluffing less often. That is, 1 out of 8 times, you have a lock on the hand - you cannot bluff.
Think about your opponent now. He's thinking, "There's a 1/8 chance that I was drawing dead. If this is the case, he can't be bluffing. There is also a 7/8 chance that he had 18 outs. If this is the case, there's a 1/7 chance that he's bluffing. Putting these together, there's only a 1/8 chance that he's bluffing. Therefore, I'm not getting proper odds to call. I will fold."
Notice what happened. While you are indeed bluffing 1 out of 7 times with your 18-out hand as suggested, you are only bluffing 1 out of every 8 total hands because you're unable to bluff with your cinch hand.
So how often should you bluff with your 18-out hand? In this case, you should choose about 3.512 cards to bluff with (yes, again, I know you can't bluff with 3.512 cards - as a decent approximation, you could choose 3 cards to bluff with and 1 additional card that you will bluff with if you flip a coin and it lands heads-up).
If you bluff with 3.512 cards, now your opponent is being given about 6:1 odds. 1/8 times you again have the cinch hand and are never bluffing. The other 7/8 times, you are bluffing 3.512/21.512 = 16.33% of the time. Putting this together, you will be bluffing a total of 14.29% (16.33% * 87.5%) of the time, which is 1 out of every 7 times, giving your opponent 6:1 odds to call your bet.
If you do the math, you should find that bluffing with 3.512 cards here is superior to bluffing with only 3 (assuming your opponent can't tell whether you have the cinch hand or the 18-out hand).
Sklansky is not wrong - his solution is obviously the theoretically correct solution. However, since you can't bluff with cinch hands (or can't bluff often enough with near-cinch hands), you need to "transfer" bluffs you would like to make with these hands to your non-cinch hands in order to give your opponent the proper odds.
I don't want to be so presumptuous to think that I can find a serious flaw in a book as amazing as TOP. I have probably either overlooked something or Sklansky felt that discussing such a complicated scenario would not be worth it. But if I did make a mistake, I want to be corrected so I can re-align my thinking. And if not, I think this is a very interesting topic, as it opens up all sorts of issues (but that's for another post).
njs
Specifically, it seems that the section on "optimum bluffing strategy" could have you bluffing slightly less than is optimal. Let me give an example.
Sklansky recommends bluffing with such a frequency that the odds you are bluffing are equivalent to the pot odds. That is, if there is a $100 pot, for example, and bets are $20, your opponent is getting 6:1 odds to call your bet. Therefore, you should present your opponent with 6:1 odds that you are bluffing, making him indifferent to calling or folding (the sign of an optimal mixed strategy).
Now, suppose you are playing Hold 'Em, and after the turn, you will have 1 of 2 hands. 7 out of 8 times, you will have a hand with 18 outs. The other 1 out of 8 times, you will have a cinch hand. Again assume that the pot is $100 and bets are $20. How often should you be bluffing with your hand that gives you 18 outs? It would seem that you should bluff with 3 additional cards, presenting your opponent with 18:3 or 6:1 odds that you are bluffing. The problem, however, is that you aren't truly bluffing 1 out of 7 times as you should be. You are bluffing less often. That is, 1 out of 8 times, you have a lock on the hand - you cannot bluff.
Think about your opponent now. He's thinking, "There's a 1/8 chance that I was drawing dead. If this is the case, he can't be bluffing. There is also a 7/8 chance that he had 18 outs. If this is the case, there's a 1/7 chance that he's bluffing. Putting these together, there's only a 1/8 chance that he's bluffing. Therefore, I'm not getting proper odds to call. I will fold."
Notice what happened. While you are indeed bluffing 1 out of 7 times with your 18-out hand as suggested, you are only bluffing 1 out of every 8 total hands because you're unable to bluff with your cinch hand.
So how often should you bluff with your 18-out hand? In this case, you should choose about 3.512 cards to bluff with (yes, again, I know you can't bluff with 3.512 cards - as a decent approximation, you could choose 3 cards to bluff with and 1 additional card that you will bluff with if you flip a coin and it lands heads-up).
If you bluff with 3.512 cards, now your opponent is being given about 6:1 odds. 1/8 times you again have the cinch hand and are never bluffing. The other 7/8 times, you are bluffing 3.512/21.512 = 16.33% of the time. Putting this together, you will be bluffing a total of 14.29% (16.33% * 87.5%) of the time, which is 1 out of every 7 times, giving your opponent 6:1 odds to call your bet.
If you do the math, you should find that bluffing with 3.512 cards here is superior to bluffing with only 3 (assuming your opponent can't tell whether you have the cinch hand or the 18-out hand).
Sklansky is not wrong - his solution is obviously the theoretically correct solution. However, since you can't bluff with cinch hands (or can't bluff often enough with near-cinch hands), you need to "transfer" bluffs you would like to make with these hands to your non-cinch hands in order to give your opponent the proper odds.
I don't want to be so presumptuous to think that I can find a serious flaw in a book as amazing as TOP. I have probably either overlooked something or Sklansky felt that discussing such a complicated scenario would not be worth it. But if I did make a mistake, I want to be corrected so I can re-align my thinking. And if not, I think this is a very interesting topic, as it opens up all sorts of issues (but that's for another post).
njs