getting into the math of poker

[TheWorm967]

I read a post the other day about the levels a poker player goes through, and it mentioned that you've reached a certain level when you start to get to the math of poker. I've also seen some of the better players do up seemingly complex equations when disussing a hand, like bayes therom which made me cry.

My question is how can i learn this math? Is it as difficult as it looks? what resources are there to help with this sort of thing? and lastly is it essential to becoming a great player?

[Ace10k]

The most essential pieces of math you should know for Poker are pod odds and outs. Pot odds basically symbolize what you need to call compared to what you can win ($600 call into a $1200 pot is 2:1 pot odds). In order to use outs properly, compare them to the pot odds in your call.

Example:

Hand: 5s-6s

Flop: Js-As-4h
Pot: $1500

Let's say your opponent bets $500, that means that your pot odds are 4:1. You basically know that you're currently beat but if you use pot odds and outs, you can decide whether it's worth the call to draw to a flush. You have 9 outs to draw to a flush (13 spades in a deck - 4 (2 in your hand, 2 on the board); to figure out what your % to get a flush is, multiply your outs by 4 (after the flop) or 2 (after the turn) depending on your situation. So alright, you have a 36% to make a flush and your pot odds are 4(80):1(20), to justify this call, you should have a 20% of making your draw, which you do.

Turn: 2h
$2500

Your opponent bets 1500, you now have a 18% to make your flush (9x2). This call is not justified by pot odds and outs because you would need at least 4:1 to make this call.

[tarheeljks]

you don't need to be a god of probability theory to succeed at poker, but if you don't understand fundamental probabilistic concepts your success will be bounded.

i suggest looking up the concepts of expectation and odds and counting principles for starters.

[mattak]

http://www.pokerstove.com/

use this to first figure out preflop equities. Then for a little more advanced stuff, put your opponent on a range of hands, make an educated guess as to what he calls or folds with and see what the best (most profitable) play is on any given flop. you can PM me if you need some help to start out.

[Rek]

"My question is how can i learn this math? Is it as difficult as it looks?"

School is a good place to learn.

Seriously, learn the fundamentals of probability. If you can fully grasp probability then pot odds, implied odds etc follow on easily.

I think to be truely successful at poker you need that understanding. That is not to say you need to be a math wizard and many people just have the ability to understand probability without studying. I think we all know players who you wonder how they know these things because otherwise they are generally dumb.

I think it is a character trait whether you will get it quickly or not. I know other very intelligent people that just can't get their head around the concept.

[pococurante]

Agreed with Rek. I had to take a bunch of lame required business classes to get my degree, but one of them turned out to be really interesting. If you can take a class on probability/decision analysis/whatevertheycallit, it will be about 50 times more interesting than you ever would have thought it could be.

I learned a lot of good stuff that can apply to poker in that class. There were also quite a few real-life examples of two choices that seem to be pretty equal, but if you do all the math it turns out one option is way better. Hard to explain without going into detail but it's one of the best classes I've ever had.

[Galwegian]

[ QUOTE ]
is it essential to becoming a great player?

[/ QUOTE ]



Roughly speaking, for a beginning/intermediate NLHE player there are three key skills required to play a hand of poker profitably (I'll ignore long term issues such as bankroll management/tilt avoidance). These skills are
1) Choosing your starting hands well, based on game conditions
2) The ability to read your opponents hand postflop
3) The ability to use your read to make the correct decision - this is where a lot of the mathematics comes in.

One problem (I think) that most beginning players have is that their reads often consist of fairly wide ranges and this makes the mathematics of 3) a little complicated. It is perhaps ironic that if you had superhuman hand reading skills, so that you could know your opponents cards perfectly, then the required mathematics would be very simple.

This also explins why it ispossible to be a great player without knowing a lot of mathematics. If you can make great reads, then you often only need very simple mathematics to make the correct decision. This particularly applies to live play, where the extra information available can allow some talented players to make very accurate reads of their opponents.

However, despite this, the more you understand the mathematics of 3), the better player you will be, especially for low level online play

[masman21]

I agree mathematics is essential, even more so in the beginning before you start getting too deep into the psychological aspects of the game. Knowing the correct math for pot, calling and implied odds not only help in making your decision to stay in a hand but it becomes very important in how YOU bet YOUR hand. I've seen many people complain about how their aces or kings got cracked only to find out they made it mathematically correct for people to call them down and out draw them. That said, I agree with Galwegian's #1 and 2 as being the foundation that the math and other parts of your game should be built upon.

[jstill]

bayes theorem/ counting combinations is far more important than people think or make of it esp beginners who fancy themselves "optimal players" who dont need to learn anything else or think math isnt that important. You cant use it though unless you can read hands.

truthfully though you gotta start off 1) learning basic probabilities and how to count outs in different situations and equity 2) when to push a pot equity edge with a drawing hand (or made hand on the turn or river) and most importantly when not to (this is a long subject based learned through specific examples and posting) 3) when to use fold equity to make a -EV raise from an equity standpoint +EV ie how much fold equity is the break even point 4) how to calculate the EV of bluffing in a pot with 0% equity ie the pot odds 5) peeling particularly in limit from an equity standpoint vs a preflop raisers range ( u have to be able to read hands ie know how to play poker or have some poker playing experience to apply much of this stuff) poker stove is most useful for this exact purpose in my opinion.

start by reading a book like SSHE for limit or NLTP or PNL for no limit then read mathematics of poker, which reads almost like the statistics/ econometrics book which rule my life at this point in grad school, and you'll be way way wayayayayayaya ahead of the game. Seriously from a game theory/ poker knowledge standpoint reading that book after getting a poker concept foundation will put you in the mensa club of poker ie top 2% thinking wise.

[Galwegian]

[ QUOTE ]
bayes theorem/ counting combinations is far more important than people think or make of it esp beginners who fancy themselves "optimal players" who dont need to learn anything else or think math isnt that important. You cant use it though unless you can read hands.

truthfully though you gotta start off 1) learning basic probabilities and how to count outs in different situations and equity 2) when to push a pot equity edge with a drawing hand (or made hand on the turn or river) and most importantly when not to (this is a long subject based learned through specific examples and posting) 3) when to use fold equity to make a -EV raise from an equity standpoint +EV ie how much fold equity is the break even point 4) how to calculate the EV of bluffing in a pot with 0% equity ie the pot odds 5) peeling particularly in limit from an equity standpoint vs a preflop raisers range ( u have to be able to read hands ie know how to play poker or have some poker playing experience to apply much of this stuff) poker stove is most useful for this exact purpose in my opinion.

start by reading a book like SSHE for limit or NLTP or PNL for no limit then read mathematics of poker, which reads almost like the statistics/ econometrics book which rule my life at this point in grad school, and you'll be way way wayayayayayaya ahead of the game. Seriously from a game theory/ poker knowledge standpoint reading that book after getting a poker concept foundation will put you in the mensa club of poker ie top 2% thinking wise.

[/ QUOTE ]

I agree with much of this post, but I'm not sure that "The Mathematics of Poker" is necessarily going to improve your winrate if you are a beginning/intermediate player. Don't get wrong - I do think that it is a good book.

As jstill pointed out there are various levels of mathematics involved in playing a single hand of poker. I would broadly identify 3 different levels - the divisions between them are not clear cut, there is certainly some overlap.

1) Simple probabalility estimates - eg. I have 9 outs to hit my flush, therefore I have about 1 in 3 chance of making it by the river.

2) Comparing the value of a various different lines of action. This means assigning a range to an opponent and a being able to calculate the expected value of a whole sequence of actions based on that range.

3) Understanding inexploitable play in the game theoretic sense. This involves solving a (usually) complicated optimisation problem using more advanced mathematical techniques, such as calculus and/or linear programming.

The Mathematics of Poker (MOP) is mostly (but not entirely) concerned with 3). Now certainly this is the most interesting aspect of poker from an intellectual point of view. However, if you are interested in poker purely as a money making exercise, then point 2) is the one that you must focus on. There are certain real life poker situations where 3) is relevant, eg short stack jam/fold situations, or STT bubble play. In general however, the way to make the most money in real games is to be able to exploit your opponents weaknesses. MOP does not spend a lot of time talking about exploitive play and for that reason, I would not necessarily recommend it, unless you are interested in poker from a intellectual viewpoint as well as a money making exercise.