[AtticusFinch]

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Aside: A good 2+2-er that I have talked with before has a theory that when someone's hand range is small for a given situation... the chance that they are bluffing goes way up. It relates to Bayes' Theorem and I don't feel like explaining it right now. And sure enough, it applies here.


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Good point, and I think you are right. What is Bayes' theorem? I hear it mentioned all the time, but I haven't studied it in.... 8 years.

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This is a fantastic point, and deserves further discussion. Bayes' Theorem, stated as simply as I can, says that when there is a limited set of possible explanations for an event (call them E1, E2, . . . En), then the probability of any one (Ei) of them being true is:

Ei/(E1 + E2 . . . + En)

It's best understood by example. Sklansky's discussion from TOP is a good one. Say you have a horse race with 10 horses, only 3 of which were mares (Let's say horses 1, 2, and 3). Let's say you know that a mare won, but not which. We know horse 2 is a mare. What is the chance horse 2 won?

Normally the answer is 1/10, but we have more information, now: we know a mare won. There are 3 possible explanations for a mare winning: Horse 1 won, horse 2 won, or horse 3. So the probability that horse 2 won is:

.1/(.1 + .1 + .1) = 1/3

This idea may seem obvious from this example, but its application is not always intuitive. Let's look at the case before us.

Say your initial range for opponent inclues 50 hands. You eventually narrow the range down to 5 hands. Let's further accept as true Harrington's postulate that any opponent bluffs at least 10% of the time. For the tight opponent in this problem, we'll say it's exactly 10%.

So now you have 6 possible explanations. Your 5-hand range, and a bluff. From your initial range of 50 hands, the 5 hands each has a probability of .02. The odds of a total bluff now are: .1/((.02 * 5) + .1) = 50%!

This is assuming your range is perfect, and it might be better to analyze this just one street at a time, as opposed to between PF and the final river decision. But the point is, this is a very powerful idea that merits further investigation.

Hope this helps.

Edit: I'm not sure if it's appropriate to use Harrington's 10% estimate in this manner, and I'm going on 3 hours of sleep. Don't worry so much about the above figure for now, it's the concept that's important. I'll firm up the math when I'm more coherent.



-AF