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Old 01-07-2005, 04:45 PM
Ed Miller Ed Miller is offline
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Join Date: Sep 2002
Location: Writing \"Small Stakes Hold \'Em\"
Posts: 4,548
Default Re: Ed Miller\'s Response to Briar Probability Error???

You aren't wrong on either count. Most of this confusion is due to a little sloppiness on my part.

On your first point, that I include better one pair hands in one place but not another... you should understand that I am making a lot of approximations in this calculation. I'm making one huge approximation regarding the range of hands your opponent will have (the 27/7 approximation, and then again with the 1/1 approximation).

In other words, I know my opponent's range of hands so inexactly that it does me no good to calculate the rest of the parameters exactly. There are two main things I want people to glean from this calculation:

1. This is the general mathematical approach you should use to get the answer. You can make approximations if you like, or you can try to be as exact as possible. Just remember the process and that the accuracy of your results will vary depending on the assumptions you make.

2. Calling that turn raise becomes correct at a surprisingly low bluffing percentage. While I didn't try to crunch exact numbers, I don't have to to prove this point. If you change a few of the assumptions, my 5% bluffing rate might drop to 3% or rise to 8%. But it isn't going to rise to 30% unless you make some very strange assumptions. And that's really the point of my article. Don't say, "He can't be bluffing" when you really mean, "Over 90% of the time he won't be bluffing."

So in other words, the article is merely designed to spark your interest, not prove a result beyond a shadow of a doubt. You taking the math and running with it is great. Just make sure you understand the large role your approximations and assumptions play in getting results...

On your second point, that it isn't right to call a river bet if you know 100% you are behind... well, obviously you are right. That was sloppiness of wording on my part... something I should have caught. What I intended to say was, "Calling down automatically is better than folding to the turn raise." It's better to call and then call again on the river (throwing away a bet with zero chance to win) than it is to fold to the turn raise. That's because your chance to draw out against two pair on the river card is worth more than the bet you sacrifice on the river.

But it may be better still GIVEN SOME STRANGE ASSUMPTIONS (like 0% bluffing frequency) to call on the turn and fold on the river.

However, IN PRACTICE, that is rarely correct. Usually against typical opponents you should call and call again.

I hope that clears up your confusion.
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