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.
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.
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.