Poker Mathematics

Pokerroomace . Start posting questions about poker here

http://www.flopturnriver.com/phpBB2/...d4be43f7819cff


Post your questions about SNG's and HH's here in this forum. If you look at the majority of the posts in this forum they have to do with a way someone played a certain hand (line) . We will all evaluate your play in a hand and offer advice. Alot of the questions you are asking can be easily found the in the link I posted above.

Good Luck -

The only actual "maths" you use in poker is basic probability.

The reason most people struggle with it is that it's often difficult to work it out quickly, especially without a calculator.

But, a lot of people learn the rough probabilities of things.

eg probability of a flush draw on the flop completing by the river is slightly better than 1 in 3 so that's the kind of pot odds to look for if you have a flush draw.

Most of the numbers can be worked out without any difficult maths, it just takes a little while. Normally pen, paper and a calculator are useful too.

Just a little tip I use for calculating % to hit my hand... the 4/2 rule.

Lets say you have 78 and the flop is 5 6 J . Now, count your outs. You have four 4s and four 9s for your straight. That is a total of 8 outs to hit your hand. Now, multiple 8 by 4 to get 32%. You have appx 32% to improve your hand by the river. Now lets say the turn is a meisly 2. You still have 8 outs to hit your hand, but only 1 card to come, so multiple your 8 outs by only 2 this time (hence 4/2 rule) to get 16% to hit your straight with 1 card to come. If the turn card had been a 2 instead, you would have picked up 9 more outs for the flush, for a total of 17. Multiple 17 by 2 to get a 34% chance to hit your hand by the river.

This is a pretty close estimate that you will hit your hand and is very easy to calculate at the table. The actual % that you will outdraw a hand like AJ on this flop would be 36.9%, and if the turn was 2 if would be 34.1%.

What you can take from this is if you estimate about a 35% chance to hit your hand, you should be getting about 3:1 (it's actually like 2.86:1) on your money for the call. If the pot was 200, and your opponent bets 50 into you, you would have to call 50 to win 250 if you hit your hand, giving you 5:1 odds. But, if villian bets 200 into a 200 pot, you would have to call 200 to win 400, 2:1 on your money. Your odds are now incorrect to hit your hand. (Of course there is so much more to think about in poker than just drawing odds and some reasons you can justify calling without odds - which is why poker is so great!)

Note that this doesn't mean you have 32% to win the hand, only to improve your hand. If someone has a higher flush draw, or higher straight draw, your outs might not be totally clean. This is just a really rough way to estimate odds and justify a call.

Now after saying all that ramble, odds really aren't what make poker go round. It is nice to know the math and all, but I would work on fundamentals before you start working on implieds odds/chasing draws. Not saying you already don't have these down, but it is just something that I did. Don't turn into a calling station!

I'm open to any criticism/discussion.

Also since you're looking for direction to learn more, not sure if you came across this article on FTR: http://www.flopturnriver.com/start_pot_odds.html - Explained better than my jumbled post.

Originally Posted by givememyleg

Just a little tip I use for calculating % to hit my hand... the 4/2 rule.

Lets say you have 78 and the flop is 5 6 J . Now, count your outs. You have four 4s and four 9s for your straight. That is a total of 8 outs to hit your hand. Now, multiple 8 by 4 to get 32%. You have appx 32% to improve your hand by the river. Now lets say the turn is a meisly 2. You still have 8 outs to hit your hand, but only 1 card to come, so multiple your 8 outs by only 2 this time (hence 4/2 rule) to get 16% to hit your straight with 1 card to come. If the turn card had been a 2 instead, you would have picked up 9 more outs for the flush, for a total of 17. Multiple 17 by 2 to get a 34% chance to hit your hand by the river.

This is a pretty close estimate that you will hit your hand and is very easy to calculate at the table. The actual % that you will outdraw a hand like AJ on this flop would be 36.9%, and if the turn was 2 if would be 34.1%.

What you can take from this is if you estimate about a 35% chance to hit your hand, you should be getting about 3:1 (it's actually like 2.86:1) on your money for the call. If the pot was 200, and your opponent bets 50 into you, you would have to call 50 to win 250 if you hit your hand, giving you 5:1 odds. But, if villian bets 200 into a 200 pot, you would have to call 200 to win 400, 2:1 on your money. Your odds are now incorrect to hit your hand. (Of course there is so much more to think about in poker than just drawing odds and some reasons you can justify calling without odds - which is why poker is so great!)

Note that this doesn't mean you have 32% to win the hand, only to improve your hand. If someone has a higher flush draw, or higher straight draw, your outs might not be totally clean. This is just a really rough way to estimate odds and justify a call.

Now after saying all that ramble, odds really aren't what make poker go round. It is nice to know the math and all, but I would work on fundamentals before you start working on implieds odds/chasing draws. Not saying you already don't have these down, but it is just something that I did. Don't turn into a calling station!

I'm open to any criticism/discussion.

Also since you're looking for direction to learn more, not sure if you came across this article on FTR: http://www.flopturnriver.com/start_pot_odds.html - Explained better than my jumbled post.

OK. I've read through the pot odds and basic probabilities around the net already.
You got some things wrong in the number of outs there are for a open straight/flush. You only have 15 outs and not 17, because to of the cards that will give you a flush are already included in the straight draw (the 4 of clubs and the 9 of clubs). I know most of the probabilites off by heart and those that I don't know I can estimate close to.
Odds for percentage after the flop is: 4 x no. of outs.
That only works up to 8 outs though. For 9 its 35% and for a number like 12/13/15. Just multiply by 4 and subtract a few. eg. 15 x 4=60. subtract a few and you get close to the actual percent. I think I remember this one to be 54%.

But all of that stuff is very basic and I could work out those probabilities by myself at the age of 15/16. I remember working out 35% for a flush draw.

I'm sure there's a much higher level of maths involved in Poker. I think EV might be it. Going to research it now.

This site shows alot of the math that goes into calculating odds in poker http://www.tightpoker.com/

Originally Posted by pokerroomace

You got some things wrong in the number of outs there are for a open straight/flush. You only have 15 outs and not 17, because to of the cards that will give you a flush are already included in the straight draw (the 4 of clubs and the 9 of clubs).

Right on, totally slipped my mind.

Originally Posted by nickthefool

The only actual "maths" you use in poker is basic probability.

The reason most people struggle with it is that it's often difficult to work it out quickly, especially without a calculator.

But, a lot of people learn the rough probabilities of things.

eg probability of a flush draw on the flop completing by the river is slightly better than 1 in 3 so that's the kind of pot odds to look for if you have a flush draw.

Most of the numbers can be worked out without any difficult maths, it just takes a little while. Normally pen, paper and a calculator are useful too.

So, how does the math around expected value work if everything is JUST about probabilities?

EV = (probability of A happening)*(amount won/lost if A happens) + (probability of B happening)*(amont won/lost if B happens) + ...

No?

Which I call probability.

Originally Posted by nickthefool

EV = (probability of A happening)*(amount won/lost if A happens) + (probability of B happening)*(amont won/lost if B happens) + ...

No?

Which I call probability.

LOL, just for shits and giggles.

EV = (probability of A happening)*(amount won/tournament equity gained) + (1-(probability of A happening))*(amont lost/tournament equity lost)

It appears that even in your example, the math you need to know is beyond just probabilities.

I don't want to beat the horse here. You are mostly correct.

And I'd recommend the Theory of Poker by Sklansky as a good basic read on the subject.

Well, if event B = event A not happening, that is the same i think. I know how to work out EV (i think) but am not very good at putting it into a general form. My main point really is that the actual maths behind poker is not that complicated (though rather long sometimes). In my opinion much more difficult (and important) is putting your opponent on an accurate hand range (ie working out the probabilities of each separate event). Without being able to put opp on a range, a lot of the maths in poker become useless.

To expand on my post, EV calculations or ICM calculations are not too difficult, although they can take some thinking about but if you have a decent grasp of probability i would assume it's not too difficult.

Wicked. So EV will really help my game? I'm ordering HOH1 and 2 today and I'll be reading them next week. hopefully my game will improve and my maths too.

One of the best things about poker math is that it's easy..

You dont need to know the answer to 6 significant figures... because any decision that is so close that the math is hard to do, is so close that each option is only slightly right/wrong anyway...

After a while you will not even be thinking about the math... you will just know what is the mathematically correct decision...