Harrington on Hold em page 125 (Hand Analysis)

[_AFK]

On page 125 there is an example where he estimates the probability of winning with a pair of aces.

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9h 5c 2s

It is a no limit game and the opponent makes a large bet.

He makes a reasonable assumption that the guy has either trips, a high pair (TT-KK), or is bluffing with two high cards.

He attaches probabilities to these conditions.

y(trips) ~ 40% because there are fewer of of them (ignoring 222)
y(high pair) ~ 50% because there are more of them
y(bluff) ~ 10% by harringtons law of bluffing.

He then estimates the probability that he will win with each condition.

P(trips) ~ 10%
P(high pair) ~ 92%
P(bluff) ~ 97%

The overall hand probability is the summation of yP = (.4)(.1) + (.5)(.92) + (.1)(.97) ~ 60% chance of winning.

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Here is the question:

Whe I redo this calculation and include the low trips (222) and all the 2-pair combos that beat my Aces, the overall hand probability drops from around 60% to around 49%.

How does Harrington justify ignoring the two-pair and the low end trips in his calculation?

Are there some rules of thumb about this?

Where can I find similar worked out hand probability estimates. (not for outs but for made hands).

[edthayer]

I haven't read Harrington's book, but I assume the reason he doesn't account for 2-pairs is because a 2-pair on this board is virtually impossible against a reasonable player (I'm assuming one of the conditions of this situation is that you raised preflop). Most fish don't even play 92.

[the alex]

The way that people play Harrington, I'm a little surprised that he includes 55 with as much scrutiny as 99. The 2 pair thought would be just ridiculous and unlucky.

[Ozzzz]

[ QUOTE ]
The way that people play Harrington, I'm a little surprised that he includes 55 with as much scrutiny as 99. The 2 pair thought would be just ridiculous and unlucky.

[/ QUOTE ]

First of all why should it matter how people play Harrington? The book is intended for other people who by default will not be recognized like Harrington would be.

Second, it surprises me that he includes a set of 5s but not a set of 2s. It's true that calling the raise with 55 is a little better than calling with 22 - but not by much. In both cases, you're pretty much hoping your opponent has 2 big cards. Either holding is unlikely - 99 is probably more likely than 55 and 22 combined, but it's far from impossible.

This makes the analysis imperfect in my opinion.

A corollary to Harrington's law of bluffing should be Ozzzz's law of stupidity - Never COMPLETELY rule out any possible holding for an opponent, no matter how moronic it makes your opponent look like.

Of course, for the sake of simplicity it doesn't hurt the calculations much to not include 22 and 2 pair in the calculations. It usually won't change things by more than 1 or 2 percent and the time involved in adding them to your calculations probably isn't worth it.

[lighterjobs]

sounds like the hand was over analyzed.

[pzhon]

[ QUOTE ]
sounds like the hand was over analyzed.

[/ QUOTE ]
This situation is extremely important in NL when the stacks are deeper than about 50 BB. I haven't read this book yet, but I hope this situation is analyzed thoroughly.

[dabluebery]

Didn't Harrington also go on to describe that even if his Equity in the hand was around 35% (guessing), it would still be a justified call, because of the pot odds?

I Like "Ozzz's Rule of Stupidity"

But I think Harrington's analysis of this hand is excellent. Even if you throw in 2-pair combos, and the low set, it's a call.

I'm trying to make analysis like this a part of how I play hands more and more.

Rob

[_AFK]

I think I figured it out.

It is assumed that the opponent is a decent poker player. This means that the possible cards in his hand does not include every single unknown card, it only includes what a decent poker player would have seen past the flop.

This means that the probability of him having the necessary low cards for 2-pair is close to 0. By this assumption he would have probably also folded a pocket pair of 2's.

And I agree with some of the other posters - he would have probably also folded the pocket pair of 5's.

[the alex]

This is pretty much what I'm saying. Many players that would make the call with 55 would do so with 22. i haven't read Harrington's book yet and listening to him give examples of hands would seem a little weird to me as the range of hands that he'll put a player on are different from the reader just from him so well known and how he's "expected" to play, I would think.