Art and Science Article vs. HoH

[d1sterbd]

The analysis done in this article is slightly different than the analysis done in Harrington on Holdem Vol 1.

The math in this article estimates whether you are ahead or behind but doesn't seem to factor in the times you will lose when you are ahead in the decision process. However, it does mention that you will sometimes still lose when you are currently ahead.

The analysis in HOH (the problem when hero had AA and villian had a set of 9s) takes the fact that you will sometimes still lose when you are ahead, but the fact that there are more ways to make up certain hands than others is not part of the math.

I think that Harrington's method allows you to take into account the fact that there are more ways to make up certain hands than others in the weights assigned to each possible hand.

Can someone discuss what they think is the best way to do this? Does anyone have a different method that they use because it is quicker?

[2ndGoat]

Hi d1sterbd,

The "ways" to make each hand are those weights for each hand- actually the number of permutations (or was it combinations? it comes out the same) by which each hand could occur. Note that QQ can only happen one way, the other two queens, and JJ can happen three ways- JsJh, JsJd, and JhJd. Thus JJ is three times more likely than QQ.

I also did take into account possibilities of catching up:

<<but he wins about 29.4 percent of the time when you're ahead, and you win about 12.2 percent of the time when you're behind (percentages obtained by manipulating results from a Monte Carlo simulator). >>

This is included in all the math below it, though I had to resort to some arm-waving to keep the essay from becoming completely bogged down in the numbers (and obliterating length restrictions). The reader is, of course, encouraged to perform the analysis himself or herself.

So basically, Harrington and I did the same thing. He happened to write an extremely valuable 240 or so pages to sandwich it, and is making a not-insignificant amount of money as a result. I wrote only an essay, and thus I am not getting rich. The point of the article, in my eyes, is not so much to show how to do the analysis as to prove that you can keep diving further and further into the math of it all and just about never be "done." It gets 10x worse when there's money left to bet. At some point you have to leave the numbers behind and switch over to estimations based on experience. Thus the relationship between the "art" and "science" of hand reading.

Thanks for posting. I'm glad at least one person read it the whole way through!

2nd

[Mathieu]

Hi 2ndgoat,

I liked your essay. I found that it was interesting how the probability that our opponent would play given holdings in a certain way, could turn a fold into a call.

I usually make those assessments by "feel", but often overlook them when doing a mathematical analysis afterwards (tend to figure out a range of hands, and only use card distribution, like in method #1). So it was instructive to see how the estimation of an opponent's tendencies could be included into a formal (but not too scary!) procedure to analyse the hand.

I will definitely recommend this essay to all my poker buddies.

Cheers,
Mathieu

[DonkeyChip]

Please excuse the stupid question but there's something I don't understand about the following:
[ QUOTE ]

his probability of playing that hand the way he has (which comes from assigning a numeric best guess from the analysis above).

AA: 6 * .40 = 2.4

KK: 6 * .50 = 3.0

QQ: 1 * .50 = 0.50

JJ: 3 * .10 = 0.3

TT: 3 * .10 = 0.3

AK: 16 * .50 = 8

[/ QUOTE ]

Are you assigning 40% to "his probability of playing AA the way he has" and 50% to "his probability of playing KK or QQ the way he has" etc.? In the text, it appeared that AK was considered separately from KK/QQ. Or put another way, it looks like there's 150% total (i.e. 40% for AA + 50% for KK/QQ + 10% for JJ/TT + another 50% for AK). I'm probably missing something very obvious but I'm not sure what it is.

[2ndGoat]

Hi Donkeychip,

You are correct, the percentage do not add up to 100%; they are not peices of a pie. What I am quanitifying is the idea that an opponent will not do the same thing all the time- sometimes he will check a flopped boat, sometimes he will lead out with it.

So these numbers represent how likely our opponent is to make the 2x pot-size all-in bet. If he was a simple player and DID do the same thing every time, all the probabilities would be 100% or 0%. But I figure he will make that all-in bet 40% of the time he has aces, 50% of the time he has AK, and 10% of the time he has JJ.
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Explanation over. More confusion ahead.
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Going off on a bit of a tangent- it may seem strange to figure anyone to bet into a preflop reraiser for twice the pot all-in 50% of the time with ANY hand. I would tend to agree. But once I've seen it happen, I *have* to figure it's in his bag of tricks- that he'll pull it out with some frequency. That is, of course, unless I've played with him forever and never seen it before. In that case I'd probably give more credence to him anti-slowplaying a set and less to the other chances.

2nd

[DonkeyChip]

Thanks for response 2nd. I think I see what your saying. But it seems that if he will only push with AA 40% of the time that he has AA, then when you add up the probabilities of him actually pushing here you get way less than 100% (i.e. he will only have AA 6 out of 34 times and he will only push 40% of the time he does have them + the same for all the other hands in the range). But our original assumption was that IF he pushed, he must have one of the hands in the range (i.e. TT-AA and AK). Otherwise, what is he pushing with if it's not AA-TT or AK? Using the given probabilities, he only pushes about 43% of the time he DOES hold one of those hands. I realize that there could be a 'bluff' factor or 'fudge' factor but...well I still don't get it.

Bear with me 2nd, I don't want to just gloss over this and think; "Yea, I get it". I want to make sure I really do get it.

[2ndGoat]

It does not add up to 100% because he would not push all of the time [img]/images/graemlins/wink.gif[/img] Just because he pushed this time does not mean it's a certainty he'll do it every time in this situation- in fact that's what the percentages capture. It's like a coin coming up heads- even after it has happened, there's no way to reason that it was 100% probable to happen.. still 50%.

2nd