# [Math] Poker Probabilities Driving Me Insane

• Bronze
Joined: 07.06.2010
In several books, I have seen a high pair v. low pair being a 4.5 to 1 and seeing that hitting a set it something like 8 in 1 to hit... Its driving me crazy to see where these figures have come form, and was wondering if someone knew where I could find where and how these odds are calculated, and if someone could help me understand where the professionals are getting these figures from.

Thanks. Chez.
• 4 replies
• Bronze
Joined: 03.08.2009
In several books, I have seen a high pair v. low pair being a 4.5 to 1 and seeing that hitting a set it something like 8 in 1 to hit... Its driving me crazy to see where these figures have come form, and was wondering if someone knew where I could find where and how these odds are calculated, and if someone could help me understand where the professionals are getting these figures from.

Thanks. Chez.
I'll give you a example of hitting a set off the flop and hopefully you will get the jist of it.

There are 2 possible cards you can hit for your set. And we "know" four of the cards so there are 48 cards left. 2 of these you can hit, and so the probability of you hitting your set on any one card dealt is 2/48 or 1/24.

However you have 3 "chances" to hit this since there are 3 cards dealt on the flop so you're probability is 1/24 * 3 = 3/24 = 1/8

Therefore for you to be getting breakeven odds you need to get 7:1 because for the 7/8 times you don't hit there is a 1/8 time where you hit.

The books will quote 8:1 because this is what you need for calling on the odds to be +cEV - since you get better odds than the expected odds of you making your hand.

I don't know what you mean by high pair vs low pair unless you mean the odds of low pair winning when all in preflop - but this is a little bit more complicated since you have to account for the times where the low pair will hit set but highpair redraws out.
• Bronze
Joined: 11.11.2009
U need pokerstrategy equilator
• Bronze
Joined: 07.06.2010
Originally posted by amplifyd
In several books, I have seen a high pair v. low pair being a 4.5 to 1 and seeing that hitting a set it something like 8 in 1 to hit... Its driving me crazy to see where these figures have come form, and was wondering if someone knew where I could find where and how these odds are calculated, and if someone could help me understand where the professionals are getting these figures from.

Thanks. Chez.
I'll give you a example of hitting a set off the flop and hopefully you will get the jist of it.

There are 2 possible cards you can hit for your set. And we "know" four of the cards so there are 48 cards left. 2 of these you can hit, and so the probability of you hitting your set on any one card dealt is 2/48 or 1/24.

However you have 3 "chances" to hit this since there are 3 cards dealt on the flop so you're probability is 1/24 * 3 = 3/24 = 1/8

Therefore for you to be getting breakeven odds you need to get 7:1 because for the 7/8 times you don't hit there is a 1/8 time where you hit.

The books will quote 8:1 because this is what you need for calling on the odds to be +cEV - since you get better odds than the expected odds of you making your hand.

I don't know what you mean by high pair vs low pair unless you mean the odds of low pair winning when all in preflop - but this is a little bit more complicated since you have to account for the times where the low pair will hit set but highpair redraws out.
I do, thank you =].

Carried on my research after posting this post, and many posts told me if it a case of having a computer doing extremely complex calculations here and there for many of the probabilties stated within books and websites.

Due to that, Im just going to take it all at face value, and accept I do not need to know the complete grassroot probabilites and calculations, and just work on my pot odds, outs and implied odds etc!

/Chez
• Black
Joined: 03.03.2008
lol extremely complex

hitting a set (or better) with pocket pair on the flop: 1-(48/50*47/49*46/48) = 11.76% or 1 : 7.5

as for lower pairs vs higher pairs, it's basically an all-in equity question, use Equilator or PokerStove to figure out the %s