Harrington p.135

[Marlow]

In his fantastic book, Dan Harrington dispences some great and (aside from the following) very clear practical advice for calculating and using odds to help with your hand analysis.

However, at the end of one example, he says the following:

[ QUOTE ]

Now, let's combine our estimate of the likelihood of each type of hand with the winning probabilities, and see what we get for an overall likelyhood of winning:

1. He holds a high pair: 50% times 92% = 46%

2. Hew holds trips: 40% times 10% = 4%

3. He's bluffing: 10% times 97% = 10%


[/ QUOTE ]

I've read this section several times and I have no idea why he's multiplying his hand estimates on the left with those percentages on the right. In other words, I understand that he thinks there's about a 40% chance that his opponent has a set. But why is he multiplying that number by 10%??

In fact, I don't even know where the numbers on the right come from! Can someone help me with this?

Thanks,
Marlow
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[TomCollins]

Those are the odds that he will win if his opponent has that hand?

[pzhon]

[ QUOTE ]
I understand that he thinks there's about a 40% chance that his opponent has a set. But why is he multiplying that number by 10%??

[/ QUOTE ]
The 10% is an estimate for the probability of winning against a set.

You can get this number in a variety of ways, such as from TwoDimes and using the program PokerStove.

The probability of winning is the sum over all cases of the probability of that situation times the probability of winning, given that situation. The case of a set contributes 0.40*0.10 = 0.04 to the probability of winning.

[Robertie]

Those are the probabilities of winning if the opponent has that particular hand. They're given at the top of page 132.

If you know the probability of having a hand, and the probability of winning if you have that hand, you multiply the two together to get the contribution to your winning chances from that subset of hands.