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Old 09-01-2005, 01:16 PM
WhiteWolf WhiteWolf is offline
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Join Date: Mar 2005
Posts: 87
Default Re: Technical question on bluffing in limit Hold\'em

It is actually lots more complicated than that. To bluff at the optimal frequency from a game-theory perspective, you need to look at it from your opponent's point of view. If he is facing a 1 BB bet from you, and the total pot is now 9BB, he has to think that you are bluffing 10% of the time here (and beating him the other 90%) to make him indifferent between calling or folding. This means that the probablity (from his point of view) that you actually had a made hand before you bet comes into play - this is the important point. Some examples which will hopefully make this clearer:

Say there was a 20% change you had a made hand, 80% that you don't. You need to bet 22.2% percent of the time to make his call EV neutral (20% with the made hand, 2.2% bluffing). Thus, you need to bluff 2.2/80 = 2.75% of the time when you miss.

Now assume that you actually have a 50% chance of having a made hand. You need to bet 55.5% of the time here (50% with a made hand + 5.5% on a bluff), meaning you bluff 5.5/50 = 11% of the time you do not have a made hand.

Finally, say there is an 80% chance you have a made hand. Now you bet 88.8% (80% made hand + 8.8% bluffing), and the times you bluff when you miss is 8.8 / 20 = 44%.

As you see, the probablity that you have a made hand (from your opponent's point of view) has a big influence on how often you should bluff when you don't.
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