# What mathematics should I learn to get better at Poker?

I have learnt about pot odds, but that's about it right now. I mean to get "The Mathematics of Poker" at some point but in the mean time I'm trying to figure things out myself. What other mathematics should I learn?

I think that learning about weighted probabilities is very useful to improving your game, especially when reviewing hands and developing an intuition for your true chances of creating a profitable outcome.

Simple probability is saying that you have x% chance of winning a hand. But things aren't usually that simple. With weighted probabilities, you can do something like the following (a real generic example):

You are facing an all-in bet on the turn. There is x% chance your opponent is on a draw in which case your expected outcome is \$X...additionally, there is a y% chance they have a certain range of hands that already beats you in which case your expected outcome would be \$Y...and there's a z% chance they have a worse hand or bluff and your expected outcome is \$Z. Then x+y+z = 100% because it's all your opponents possible holdings, and your overall expected outcome is (xX)+(yY)+(z*Z). Any of X,Y, or Z could be negative, but if the overall total is positive, you can expect to make a profitable call.

The benefit to this is that you can adjust the weights (x,y,z) based on your opponent and the prior streets of the hand. In some cases, their bluffing range might be very small and in other cases they could be a lot more likely to have bluffing hands.

The Mathematics of Poker very much focuses on statistical mathematics, which is useful for both theorising strategies as well as post hand analysis and review.
Common themes included standard deviation and distributions.

When it comes to directly calculating equity, you should look into combinatorics, as this is the easiest way to accurately calculate probabilities.

• I've just started reading the Mathematics of Poker, but its tricky stuff Aug 30 '17 at 13:55
• Pot odds
• Implied odds
• EV - Expected Value
used for making advanced decisions using probability
• Combinations
this is used for probability with multiple cards to come
• Game theory pretty advanced but useful for certain spots
• Binomial Distribution
used for odds with multiple players

You don't need mathematics to play poker. All you need is basic arithmetic. For more complex calculations, like icm calculations computers are used.

What you should know:

• Pot odds.
• Win percentages of pre-flop hands (for example AKo vs 78o) where you are at most 3 or 4% off.
• Odds of hitting a certain amount of outs.
• Optional: How much equity certain backdoor draws add.
• What about fold equity and the like? Pretty sure there are other well known techniques in books but I can't afford to buy a lot of books at the moment Aug 27 '17 at 16:03
• @charlie I am not too sure. Can you give me an example? I dont think it should be in this list, but I could be wrong. Aug 27 '17 at 16:06
• That's really why I'm asking. Ice heard of other mathematical principles but I can't recall them and thus can't research and learn them, but they do exist. Aug 27 '17 at 16:14
• @Charlie well perhaps there are some principles, but I don't think they are too relevant for most player, for most games. Aug 27 '17 at 16:24
• @Charlie go to two plus two and buy some books. The mathematics that can be used in poker is a huge field. Whatever you learn about it helps your game. The books are twenty bucks and less for the most part, and almost instantly pay for themselves.
– Jon
Aug 28 '17 at 0:06

It all depends on how deeply you want to investigate the game. If you wish to understand odds and strategies at the deepest level, you'll be looking at game theory. If you do want to go that deeply you'll first have to learn about Linear algebra, single/multi variable calculus, methods of proof in mathematics, possibly some real analysis and definitely differential equations.

You'll then progress to game theory where you'll learn about imperfect information games which is a field of current research as well, so from there you'll go as deeply in to the theory of poker as is currently known.

If you don't want to go too deeply, some simple arithmetic and some probability theory is enough to set you up very well.

• Do you have any links for reading? Aug 27 '17 at 21:32
• I don't really have any online sources. For standard poker maths, Pokerstar's academy is pretty good. If you want to investigate game theory, I recommend the following books: Start with Velleman's How to Prove It, and continue to Hoffman & Kunze's Linear Algebra, Apostol's Calculus (I & II) after which you're ready for Rudin's real analysis (optional) and for game theory you'll be looking at a plethora of books depending on your desires (Combinatorial game theory, discrete game theory are important in poker.) John William's The Compleat Strategyst is a dated but decent introduction to basics. Aug 27 '17 at 21:44
• @Paparazzi Calculus is of extreme importance in moving from few to many hands. It is what drives forth the law of large numbers and without it probability theory doesn't exist. As a mathematician, I can tell you that 95% of people underestimate the importance and use of calculus. Though you won't be doing calculus at the table, it will be absolutely vital if you plan on developing your own mathematically sound strategies and even more so if you're searching for game theory perfect plays. In fact, at that point you'll need real analysis, which essentially builds calculus from counting numbers. Aug 27 '17 at 21:48
• I have references for game theory used in poker. Calculus and real analysis are used in game theory. Aug 28 '17 at 5:55