The Mathematics of Poker

[Shandrax]

I would like to suggest a follow-up to Mathematics of Poker.

It could be called like "Practical Application" and it should contain sample hands that are analysed in the same fashion as the Stud 8/b hand in the early chapters. The examples should cover a variety of different poker forms - basically HORSE - and it should also cover different types of limits and cash/tournament structues.

[cowhead]

Is there a posted errata besides this thread? I searched but didnt' find anything

[Sharikov]

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Is there a posted errata besides this thread? I searched but didnt' find anything

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http://www.conjelco.com/mathofpoker/...ker-errata.pdf

[Gelford]

Grunch


That is some annoying small typesetting you've got there, if the book was in a bigger format it be a straight 10

[Patrick Sileo]

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[ QUOTE ]
Is there a posted errata besides this thread? I searched but didnt' find anything

[/ QUOTE ]
http://www.conjelco.com/mathofpoker/...ker-errata.pdf

[/ QUOTE ]

The posted correction to page 48 fixes the text, but not the equations. It should go on to say that the last two of the three expressions for <B,call> should be divided by (0.2 + x), with appropriate consequent adjustments to the following table and graph.

[mosquito]

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You're right. It's gone now. I bet it's out of stock. I'd keep checking back there tho. I'm sure it will be back in stock soon.

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Back in stock. Just ordered today. [img]/images/graemlins/cool.gif[/img]

[burningyen]

Question re bluff-raising in the toy game on page 204: in what sense does bluff-raising with the top of your check-behind region "dominate" bluff-raising with the bottom of that region?

[Jerrod Ankenman]

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Question re bluff-raising in the toy game on page 204: in what sense does bluff-raising with the top of your check-behind region "dominate" bluff-raising with the bottom of that region?

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In the situation described, the opponent has already bet, and we're trying to decide what to do with our hands that are too weak to raise for value or call. Some of them will be folded; others will be bluff-raises.

Most of the time, it won't matter which hands we bluff-raise with (as long is it is the proper frequency); our opponent won't call with any hands that can't beat a bluff-raise anyway, so whatever. In fact, choosing any subset of hands (such that you raise-bluff with the proper frequency) from the folding region to bluff-raise is a co-optimal strategy. The opponent can't exploit it -- try it and see!

However, suppose you're playing against someone silly, who will bluff with his worst hands and then call your bluff-raise. Then it's better for you to bluff when the very strongest hands of your (fold+bluffraise) region, since you get some extra value from the silly guy. You don't lose anything against reasonable players by doing this - they only call with hands that can beat you anyway.

So raise-bluffing with the best of the hands you would fold dominates other strategies because it performs better against silly strategies and the same against reasonable ones.

This is different than the case where the guy checks to you. Now you should bluff your worst hands in your "check behind" region, because they have less value from checking than the others. But if we're selecting bluffs from a region which would otherwise be folded, we select the strongest hands to bluff.

jerrod

[Troll_Inc]

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Is this the appropriate place for extensive content discussion? So far, I like it and expect it to spawn some lively discussion.

I did pick up one error on page 48. The unconditional probabilities p(A_has_the_nuts) and p(A_has_a_bluff) in the equation for <B,call> should be replaced by probabilities conditional on the event "A_bets".

p(A_has_the_nuts|A_bets) = 0.2/(0.2+x)

p(A_has_a_bluff|A_bets) = x/(0.2+x)

Notice that these will sum to 1. This change leaves the critical value x*=0.04 unaffected, but game value will now be seen to be a non-linear function of x. The primary conclusions don't depend on linearity and are unaffected.

A similar error occurs on page 56 in the expression for <A,call>.


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I'm trying to use this formula to solve a problem on river bluffing, and I don't get your comment on non-linearity.

It seems that if you convert to a formula where 0.2 is really 1-x. (In the book example, x=80% as a given value of bluffing, so 1-x = 0.2.)

So if you plug 1-x into everywhere you have 0.20 doesn't the denominator sum to 1 (as you state), and therefore revert to the original formula (which doesn't have a fraction)? And further, then isn't it linear?

Or are you saying that the solution is non-linear if player A doesn't bet 100% of the time? Presumably this would be done with the expectation of sometimes being able to check-raise?

[HelixTrix]

Quote:

"What do the authors think of he Sklansky-Chubukov Rankings in NLHTAP as compared to their own push/fold tables in the jam or fold game?

Sklansky-Chubukov's raising standards are a lot tighter than those advocated in the table on page 135 of MoP, but the MoP strategy is in jam-fold-only scenarios.

What's the value of the Sklansky-Chubukov numbers in late, huge blinds (efective stacks say 6-12 Big Blinds) Tournament play. It seems MoP advocates pushing a lot more often than S-C. I know that the S-C charts are based on an oppt. 'knowing' our holecards and still playing an unexploitable game, but does the pushing strategy in MoP not lead to oppts calling with a very wide range after we pushed into them a few times consecutively, decreasing our fold equity to a point that a heads-up ecounter becomes a coinflip+? Goldmund"


Yeah, this has been bothering me too. I use the S-C numbers constantly towards the end of sit n gos, but when I glance at these 'jam or fold' tables they scare me. At the moment I am struggling to think of these as more than a mathematical curiosity, although I have yet to get round to sitting down and trying to see how jam-or-fold, S-C numbers and ICM calculations can be brought together into a coherent strategy. I do think there is a danger that people will start using these unnecessarily in blind v blind and headsup situations thinking that 'optimal' means best, particularly given the authors' claim that these tables justify the price of the book alone.

Previous posters have mentioned the ambiguous use of the word 'optimal'. Speaking as someone with no background in any of the specialist disciplines that use the term, it seems to me that what could have been stressed a lot more, is that when the authors talk about a strategy being 'optimal', what they mean is that it is part of a 'co-optimal pair', i.e. if you are playing against a 'nemesis' opponent who would otherwise instantly switch to counter everything you do. While this approach is extremely helpful in other pre- and post-flop situations as a default option when you feel you might be outclassed or just generally can't think of a way to exploit anything,I'm not convinced these numbers are anywhere near the 'best' strategy in actual low-M situations that will come up. No opponent is likely to call my jam with 87o with an M of 7 (4.7 BB), as apparently he should as part of a co-optimal strategy pair, so why on earth would I jam with T5o(!) with an M of 6 (4.1 BB), reasoning 'it's optimal so it must be better than folding'? Actually my point about the opponent is a bit spurious since if he is generally calling tighter then I could theoretically be pushing even looser. More important is Sklansky's idea of passing up on a slightly good bet today if you're likely to be able to make a better one tomorrow. And yes, I know there isn't much time to wait for a hand with a short stack, but it must be reasonable to fold T5o since you are a favourite to be dealt at least one card higher than a ten on the next hand. My point about the opponent not using the optimal strategy certainly does apply to calling though. Now clearly you shouldn't call with 87o if he isn't going to push with T5o. I also don't like the author's recommendation to begin 'jam-or-fold' at an M of 7, or as high as 9 (I'm switching from their use of BBs as a unit). Or rather, I agree all-in is generally the only option at this point, but again, that doesn't mean 'it must be best to blindly start following the tables'.

As a final point, many opponents play extrememly exploitably, by continuing to allow you to limp in in the small blind, getting 3 to 1 headsup on the button, which you should do with any hand, and also never limp themselves with a good hand so you can then jam with any 2. Anyway, I'd love to hear others' opinions on this; I was surprised reading through this thread not to have seen more mention of the scale of difference between the MOP numbers and the S-C ones. The rest of the book I think is fantastic btw.