Poker winners seem to come from all walks of life. If success in poker is largely based on successfully calculating and playing the odds, why don’t mathematicians and other math maven types dominate the game?

They *are *overrepresented. The number of people with quantitative reasoning backgrounds among the poker elite is relatively large, I believe.

No one says Poker is all probability. It is probability and ability to read your opponents and pick up on subtle social factors. Perhaps the sorts of skills that are rarer among our math nerd brethren?
Because you only need to have a sense of the odds. In other words, if you know the odds “good enough” and have the ability to read people, then you can dominate. You don’t need to calculate the odds to the nth digit.
Stolen joke:
Q: What’s the difference between an introverted mathematician and an extroverted mathematician?
A: An introverted mathematician looks at his shoes when he talks to you. An extroverted mathematician looks at your shoes when he talks to you.
This is one reason why one only sees Texas Hold’em tourneys on TV draw poker is a mathematically run snoozefest. But Texas Hold’em is a game of math 1st, then bluffing and the bluffing is critical not to mention showy.
First, many of the best poker players have a strong math background, whether formal or informal, but it isn’t wholly necessary. The biggest challenge is not the calculation of odds, although that takes practice, it is assigning hand ranges to your opponent.
So let’s imagine a hand where mid position open raises and you call on the button with AJ. You get a flop of J92 and your opponent leads into you with a large bet. You can’t figure the odds that your AJ is good without making an accurate estimate of the types of hands your opponent would make that size bet with. Once you can assign a range of hands you can calculate the odds your hand is good now, or will be good by the river. Most mediocre players fail in understanding their opponents betting tendencies and hand ranges, not on calculating the odds per se.
There are lots of mathematicians in poker.
Paul Magriel (the “Quack, Quack” guy) was a math professor and has published a couple of mathematically based poker theories.
Many more have educations in other branches of mathematics, statistics and game theory.
There is also the luck factor. There is so much emphasis placed on calculating the odds that good old fashioned luck is overlooked. Don’t forget…Doyle Brunson won the WSOP twice with a 10  2! One good lucky hand can knock a mathematician out of the game.
(I think this is technically called a bad beat. )
It’s a hard fact in many multiperson games of incomplete information that there cannot exist a fixed winning strategy. If you were supposed to always play X in situation Y, then the opponents would have an improved idea as to what you know and modify their strategies to defeat you.
Walter Penney invented a game called “Penney Ante” that clearly shows this effect. PDF
Betting in Final Jeopardy is another example.
As mentioned, the more Math you know, the better you can do, but psychology plays an important role.
If poker is ultimately a game of calculating odds why aren’t mathematicians dominant?
I would contend that poker is not ultimately a game of calculating odds. As Daniel Craig’s James Bond said (more or less) in the recent Casino Royale, he put a little work into learning how to play the cards, and a lot of work into learning how to play the people.
I think all of the preceding grossly over estimate the “numbering” required in poker. The mathematical component is really arithmetic rather than mathematics and you don’t need a Nobel prize to work out your odds when drawing.
It is totally different factors that make the difference between winners and losers.
That’s a particulary poor example. His poker playing in the movie was terrible, he just got amazing cards. In the first part of the movie, he wins by having a pair of aces when the bad guy has a pair of kings. In the climactic hand, he wins by drawing a straight flush, beating out two separate full houses and a three of a kind. Bond would raise a $50,000 pot by $50,000 as if this would scare off anyone. He never bluffed anyone out with bad cards, or appeared to try. He never seemed to have any sense of position play. The villian, supposedly the best player in the world, has a frighteningly obvious tell.
(I blogged this in a bit more detail here. A great movie ruined by idiotic poker.)
Risking a hijack, it was important they make the movie easy to understand for everyone, not just poker players. It was quite obvious from the first couple of hands some incredibly bad beat was going to ensue. The point was for regular people to think, “Wow!!! Bond is really good! He got a STRAIGHT FLUSH!” Not for poker players to think, “Jesus Christ Bond is a lucky MOFO, TWO OUTS!” (Or however many it was).
Having bond win with a 9high straight over a flopped set isn’t nearly as good cinema.
Well that would also require some ridiculous luck, assuming he didn’t also flop his straight.
What is your evidence that poker success is largely based on successfully calculating and playing the odds?
It’s true that it helps you rate your hand if you have some knowledge of odds. But in Texas Hold’em for example, there are many other factors.
What position are you in?
How big is your stack compared to the other players and the blinds?
Can you ‘read’ the other players?
What is your current table image?
How many players are left?
Take a pair of 9’s, for example. A pleasant starting hand.
If you are on the button; one player has limped in and the rest folded, then you would probably raise.
If you are on the button; two players have limped in, 1 has raised and the rest folded, then you would might call (or raise, depending on your current style).
If you are on the button; there has been a raise and two reraises, then you would consider folding.
The poker game in the movie is not a good example (but some interesting insight on that here), but that’s not what I was referring to. My point was in the comment I paraphrased, which points out that there’s more involved in dealing with the other players than in dealing with the cards. It’s part of a refutation of the OP’s false premise.
Three raises in front of you, two players left to act behind you and you have a pair of nines, and you’re only considering folding?
You have much more experience than me, so I’m glad that you say folding is correct.
My point was that the value of a hand changes for many reasons, including first round actions.
A player rigidly using calculating odds would not realise how bad his hand had become.
To answer the OP directly, pure odds don’t play into it because no poker game is long enough for the actual cards to catch up with probability.
In other words, even if hand X may win 58% of the time, in a small sample such as a single ring game it will probably win a lot more or a lot less, since that hand will only appear a dozen times at most.
If you were to play in a game that spanned an entire month, though, the actual fall of the cards over time would match the odds much more closely.
What does that mean? Basically, if my hand is favored by, say, 5% over yours, our chances of winning this particular hand are all but equal.
I didn’t mean to criticize the main point. It’s a good quote, it’s unfortunate that the character didn’t live by it. Thanks for the link also.