Math and Poker

[pzhon]

I don't know of a solid, comprehensive book on NL.

Some books present speculation and recommendations out of context, e.g., recommending that in some situation you should move in without mentioning the size of the stacks. That is a horrible omission. It is very different to make a pot-sized push versus one that is 10 times the size of the pot or more. The authors know better, but the books are bad or incomplete.

Harrington and Robertie are both backgammon players. Robertie won the backgammon world championship twice. Some ideas are very natural to backgammon players but apparently they are unnatural to poker players, such as equity and quantifying mistakes. I hope their book injects these ideas into the poker literature, including equity from implied odds, reverse implied odds, and bluffing.

[uuDevil]

[ QUOTE ]
I don't know of a solid, comprehensive book on NL.

Some books present speculation and recommendations out of context, e.g., recommending that in some situation you should move in without mentioning the size of the stacks. That is a horrible omission. It is very different to make a pot-sized push versus one that is 10 times the size of the pot or more. The authors know better, but the books are bad or incomplete.


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I agree with this assessment and I don't play NL seriously because I haven't been able to understand the game very well from the books I've read. I wouldn't be surprised if we soon see a flood of new NL books that are similarly poor, so I hope you're right about the Harrington/Robertie book.

I've also seen mention of Jerrod Ankemann possibly writing a book, but have seen no details.

[srblan]

Some "great players" have the math skills as well as the people skills to put their opponents on a range of hands, and based on the size of the pot and the average probability of their hand beating each of the possible holdings, how much they can be expected to win with a call.

[provee]

To be a good poker player you do not have to be a great mathematician. However, the skills and thought patterns used are similar, so being a decent mathematician may give you an edge at the poker table.

[pzhon]

[ QUOTE ]
To be a good poker player you do not have to be a great mathematician. However, the skills and thought patterns used are similar, so being a decent mathematician may give you an edge at the poker table.

[/ QUOTE ]
As a mathematician and a poker player, I don't think the thought processes are at all similar. In mathematics, I investigate Platonic (ideal) phenomena, trying to find patterns. Then I try to establish these by building certainty upon certainty. I can take a minute or a year to solve a problem. I try to find deep connections between different problems. I don't see anything more than superficially similar with playing poker, where it is very rare to have any certainty and the observed phenomena change from game to game.

Poker is more similar to table-tennis. I try to make the percentage plays. I may find myself attacking (being aggressive) or defending, and these do not correspond to whether I am better than my opponent. My opponents often surprise me, and I try to surprise them. I don't have time to optimize at the table, but must come up with something good. I can plan a couple of steps ahead, but the situation can change dramatically and make my plans worthless. I try to identify and exploit opponents' weaknesses. Further, the game itself can change, with the increase in popularity of Hold'em versus draw poker and the increase in the size of the regulation ball and banning of some paddle surfaces.

Perhaps I am different from other mathematicians. However, here is one factoid: Mathematicians very rarely listen to music while creating mathematics. There was a theory that the same part of the brain may be used for both activities, but I think that theory was discredited. Nevertheless, many poker players listen to music while playing, and this is very much unlike mathematics.

[Boopotts]

I said nothing about logic.

[Boopotts]

Maybe we mean different things when we say 'a great mathemetician'. Personally, I've never had to do a calculation related to poker that couldn't be handled by an AP 9th grader, since all the 'odds of making your draw' stuff has been published. When you get into logical analysis, we're talking about a different beast alltogether.

Also, all the pros I see on TV do in fact make what I think are monstrous analytical errors all the time in the big tourneys. Yet, I'm under the impression that most of them are probably long term winners. As you know, you don't have to be a wizard to beat the game; you just have to know more than the idiot next to you.

[ACW]

[ QUOTE ]
I don't know of a solid, comprehensive book on NL.

[/ QUOTE ]

As a bridge player who's turned poker player, this has struck me too. I've bought about 10 poker books, and they've definitely helped me significantly, but they all leave me with one clear impression - the poker literature is still very immature. The depth and analysis present in quite ordinary bridge books is completely lacking from the best poker books I've read. I realise there is a problem that the best action in poker is often player dependent, but surely that should open opportunities for writers not close then because they're too difficult.

Just one example - probabilities. Sklansky's theory of poker is the best I've read on this, but it's not a patch on Michael Glauerts book on bridge probabilities.

I have found one glowing exception to the general lack of depth, in Jon Vorhaus's Killer Poker and Killer Poker Online, both of which give good coverage of the self-awareness and preparedness side of the game.

Some of Mason's poker essays also start to dig a little deeper into the game, but are unfortunately too short to take the reader very far.

Maybe I feel this way because I haven't yet read HEFAP or Super System, but my experience so far suggests they may not live up to my high expectations.

[luckycharms]

[ QUOTE ]
I was watching the World Series of Poker or something, and I heard a couple people say that to be a great poker player, you have to be a "great mathematician". I don't understand. In terms of the extent of math in poker, doesn't it stop when trying to find the pot odds, and the probability of making a hand (# of outs/number of cards). Is there more math in poker than this?

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I personally think mathematics is EXTREMELY important to poker. I think that if I could sit down for 10 mins. with a pencil, paper, and calculator, I could make MUCH better decisions. It would allow me to perfectly gage the size of my bets in accordance to the table texture and game theory. Every decision is mathematically based in poker, making it an entirely mathematical game. Even psychology can be translated to math. If your opponent is on tilt, he can be predicted to play a larger percentage of hands, adding to your EV if you can identify it.

Additionally, I'd be able to make the best calling decisions with perfect math. For example, say my opponent only 3-bets with QQ, KK, AA, and AK. I 2 bet him with TJs, and he 3-bets. AK is slightly less likely than QQ, KK, or AA combined. However, when they have that overpair, they're a huge favorite. With AK, they're only a slight (about 60-40) favorite. Mathematics will be able to tell you how much money in the pot there must be to call that bet knowing they've got one of those ranges of hands. It is a very in-depth analysis, but IS mathematical. Some people call this analysis "feel," but in reality, it's mathmatical analysis, whether conscious (or correct) or not.

[Lawrence Ng]

I think you bring up a very good point to the nature of the game and that is apart from the mathematics, there are a wide array of skills that need be honed, sharpened and gradually mastered to be truly successful at the game.

When I first started playing the game, I did what most most amateurs did and focussed heavily on the technical aspects (learning to properly read boards, learning to properly count outs, odds, pot sizes) This took a while for to do because I was use to having more time calculating problems and now if I took more than 5 seconds to calculate a pot, I would get yelled it.

But eventually if a good player plays this game long enough, the technical aspects of the game become secondary. It becomes a natural part of the flow and they know whether or not they have right odds, and how much is in the pot or whether or not they believe they should raise or draw cheaply.

With this burden out the way the player can focus on the more intricate and delicate parts of the game which happens to also the least understood aspect of the game - pyschology. For example, why is my opponent betting/raising or calling. What could he have? Etc etc.

Eventually even this becomes someone of a secondary skill and the progression moves on towards more advance techniques and skill development in other areas such as feel and intuition which is a combination of every other skill that is developed and applied to making a decision that ultimately gives you that greater edge and can be built on ultimately increasing that edge.


I do believe that a good player who is open and objective enough to learn can be successful enough to eventually master the game through experience which is greatest teacher of all in this game.