What are some mathematical or scientific principles of poker?
May 5, 2016 7:40 AM   Subscribe

I'm trying to get a list of things (equations, theories, etc) we know about poker or gambling in general in terms of scientific or mathematic principles. It can't just be game theory. it's got to be specific aspects of it. And I mean ANY aspects of it. Hot hands. Beginner's luck. Inside straights.
posted by rileyray3000 to Sports, Hobbies, & Recreation (7 answers total) 6 users marked this as a favorite
It is mostly statistics.

Specifically, statistically speaking, poker players tend to care a lot about Expected Value especially in relation to the size of the pot and the likely behavior of the other players.

The thought of doing EV calculations on the fly and memorizing Odds charts (see the bottom of this page) are what stopped me from getting seriously into Hold 'em, during that era when all 20-somethings were getting seriously into Hold'em.
posted by sparklemotion at 8:04 AM on May 5, 2016 [1 favorite]

Hot hands and beginner's luck are myths, but also have a bit of a ring of truth because a lot of what "serious" poker players learn is based on having a rational opponent.

Beginning players (or players on some crazy streak) often make decisions that aren't "rational" just based on the cards and the odds, so they tend to act in ways that make "serious, but not truly skilled" players assume that they have different cards than they actually do. For example, a no-limit hold'em player going all-in on when they are holding pocket 7's might make players with other, better, hands fold earlier, leaving the pocket 7's to win even if the other hands had better odds.

That kind of behaviour is also how bluffing works, and can be used by good players too to throw folks off, which is why poker is not only about the numbers.
posted by sparklemotion at 8:14 AM on May 5, 2016

The Theory of Poker, by David Sklansky. It sets out to do a lot of what you are asking. Start there - there may be deeper dives around if you need that sort of thing, but Sklansky's tome on theory is the logical place to start.

Sklansky leans heavily on Bayes' Theorem.
posted by mosk at 8:53 AM on May 5, 2016 [1 favorite]

Steven Skiena is a computer science professor at Stony Brook who used numerical simulation to find exploitable inefficiencies in jai alai. His book Calculated Bets is a case study in making money by outsmarting other bettors. It is very specific about the strategies involved and why they work.
posted by drdanger at 9:12 AM on May 5, 2016

I was also going to suggest Sklansky. However, "Theory of Poker" is his densest, most difficult book. Depending on your experience level, you may prefer Small Stakes Hold 'Em, which he wrote with Ed Miller. Many of the same concepts are applied, but in a more practical and less theoretical way.
posted by Joey Buttafoucault at 10:00 AM on May 5, 2016 [1 favorite]

@Joey Buttafoucault: Not disagreeing at all that ToP is dense and SSHE is easier to follow, but the OP sounded like that he wanted full strength $MATH, rather than the diluted $math of SSHE.

All of Sklansky's books cover similar ground, IMO, but to me Theory of Poker is his most pure/academic/theoretical work. He restates its thesis throughout his other books, so it might be the sort of thing the OP is looking for.

OP, there are a ton of poker and gambling books out there that focus on tactics. Theory of Poker isn't one of those. Theory of Poker takes several steps back from the play of individual hands and looks at poker strategy from a broader, more theoretical perspective. It isn't the most fun poker book to read, but Sklansky does explain some very useful and hard-won truths. It isn't the only book on my poker shelf, and it isn't the best, but it does explain some not-necessarily-obvious concepts that have helped me win a lot of money over the years.
posted by mosk at 10:35 AM on May 5, 2016

If you really want to know about the underlying mathematics of poker, then Chen and Ankenman's Mathematics of Poker is the place to get it (and is more rigorous and theoretical than Sklansky). However, it's not clear to me if you want that, or a grab bag of fun poker facts that could be described as "scientific", or something in between. It would be helpful if you could give us some idea of what you're using this list for.
posted by dfan at 11:06 AM on May 5, 2016 [1 favorite]

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