How reliable is poker math

F

FreshmanJoe

Guest
Joined
Jul 9, 2021
Total posts
44
The question is simple, and might have been asked before. How reliable is poker math?

Let's say I'm on a nut flush draw, on the flop, in a 9 handed no limit Hold'em game. I would like to think that I have 9 outs and I need atleast 4:1 to make a call. However I have no way of knowing how many of my nine outs have already been dealt to and folded by some of the other 8 players (not to forget the burn card).

So how reliable is this math really? And what can we do?
 
flail1

flail1

Legend
Joined
May 6, 2021
Total posts
1,059
Awards
3
I use the rough math as a guide only. I seem to hit less often than the calculations say, and part of it is the unknown dealt cards for sure. So I usually don't chase much unless pot odds are really high. And I always try to avoid getting railed chasing a hand.
 
P

ph_il

...
Joined
Feb 5, 2005
Total posts
9,845
Awards
1
The question is simple, and might have been asked before. How reliable is poker math?
,
Let's say I'm on a nut flush draw, on the flop, in a 9 handed no limit Hold'em game. I would like to think that I have 9 outs and I need atleast 4:1 to make a call. However I have no way of knowing how many of my nine outs have already been dealt to and folded by some of the other 8 players (not to forget the burn card).

So how reliable is this math really? And what can we do?
you only use the cards you know of. if you know 2 in your hand, 3 on the flop and you have a flush draw, then you have 9 outs to hit the flush. whether you play the flush draw or not depends on the pot odds compared to the odds of hitting, depending on which method you use. for ratios, you want pot odds > hand odds. for percentages, you want hand odds > pot odds.

your hand vs pot odds will also depend on if you're calling to see a turn, and have to face another bet on the turn. or if you're calling to see the turn and river. the best way to look at is is: will there be any more action in the hand.

1. if your opponent can bet on the turn if you miss your draw, then you need to calculate the odds of hitting for each street individually or about 18% chance for. so you want the pot odds to be < 18% to be profitable to call on the flop-to-turn. and again for the turn-to-river, assuming you didn't hit. implied odds do exist, but i'm just looking at the basics of hand vs pot odds.

2. if your opponent cant bet on the turn and you're guaranteed to see the river card, you calculate the odds of hitting for both streets or a 36% chance. again, as long as pot odds are < 36% its a profitable call.

the math is 100% reliable given the limited information you have. since its impossible to calculate for folded cards, you simply don't.

to add, this doesn't mean you need to chase just because you are getting the proper odds. it depends on the situation. for example, if you have an 8 high flush draw on a flop showing 3 of the same suit and there are 5 players in the hand, it's unlikely you'll have the best draw. if you're on the final table bubble and one player only has 2 big blinds. you have a decent stack and you're on a flush draw vs the big stack, it's ok to fold your draw even if you're getting the best odds to call.

getting right odds to call doesn't mean you need to, it just means it's a profitable one in the long run.
 
Last edited:
cardplayer52

cardplayer52

Cardschat Elite
Joined
Mar 28, 2009
Total posts
1,232
The math is reliable. You need to keep in mind that if you need 4:1 odds to call, that means you will call and lose 4x more often than you will win. Its a tough concept to grasp. You often need to call off your stack knowing your likely behind most of the time.
 
1

1nsomn1a

Visionary
Joined
May 24, 2020
Total posts
767
I think in cases with a flash draw, the potential chances are more important, that is, whether you can earn enough with your flash to cover the costs. You can also sometimes raise the check in a semi-bluff, which will give you the opportunity to win the pot earlier.
 
vinnie

vinnie

Legend
Joined
Apr 12, 2013
Total posts
1,197
The question is simple, and might have been asked before. How reliable is poker math?

Let's say I'm on a nut flush draw, on the flop, in a 9 handed no limit Hold'em game. I would like to think that I have 9 outs and I need atleast 4:1 to make a call. However I have no way of knowing how many of my nine outs have already been dealt to and folded by some of the other 8 players (not to forget the burn card).

So how reliable is this math really? And what can we do?

It is complicated, but we can prove that the unknown cards other players folded do not change the long-term odds of our draws. You need to combine the odds that they folded our outs, and how that affects our chances, with the odds that they folded cards that we didn't need, and how that affects our chances. When you properly weight and combine these odds, the end result is exactly the same as ignoring their unknown cards entirely.
 
daddybrooks

daddybrooks

Rock Star
Joined
Jul 8, 2021
Total posts
303
Awards
9
The math always works, it's just math, can't mess it up in itself.

You can go crazy if you start trying to factor in the unknown's like who you think "may" have folded "x" number of your outs. Can't do that as it's not a real number, just something you're imagining in that situation.

The thing to remember about the math, is it's only a guide. It's also just an indication of your chances, not a guarantee by any means or any way you look at it!

I've called/pushed etc enough times with a shitload of outs with a good hand that could get better. I'll admit, at times I've even thought in my mind "how the hell did not ONE of my 19 outs hit with 2 to go?!?" It's only a fleeting thought because I do my best to keep the "it's just a chance, not guaranteed" in my mind at all times. If you feel "cheated" in that situation, it's time to take a break because you're forgetting it's all probabilities.
 
vinnie

vinnie

Legend
Joined
Apr 12, 2013
Total posts
1,197
As a follow up for the "it's complicated" comment, I'll attempt to do the math for a simple example to show you why.

You're over at a friend's house and playing 4-handed hold'em. You're on the turn with a spade flush draw and your opponent is holding 2 red aces. The other two players folded before the flop. Example:

:ks4::js4: VS :ah4::ad4:

The board is :3s4::7s4::qh4::2d4:

Now, you can see 8 cards. So there are 44 unknown cards. 9 of those unknown cards give you a winning hand. Your 'naive' odds are 9/44 or about 20.45%.

You don't know what your opponents folded, but you can figure out the probabilities that they folded outs of yours.

Odds they folded 0 spades: 52,360/135,751 ~= 38.57%
Odds they folded 1 spades: 58,905/135,751 ~= 43.39%
Odds they folded 2 spades: 21,420/135,751 ~= 15.78%
Odds they folded 3 spades: 2,940/135,751 ~= 2.17%
Odds they folded 4 spades: 126/135,751 ~= 0.09%

Since we 'know' the 4 folded cards now, there are only 40 unknown cards left.

Your adjusted odds for them folding 0 spades: 9/40 = 22.5%
Your adjusted odds for them folding 1 spades: 8/40 = 20.0%
Your adjusted odds for them folding 2 spades: 7/40 ~= 17.5%
Your adjusted odds for them folding 3 spades: 6/40 ~= 15.0%
Your adjusted odds for them folding 4 spades: 5/40 ~= 12.5%


But, we need to adjust these odds with the probability that we're facing them.

Weighted total odds 0 spades folded: 52,360/135,751 * 9/40 = 471,240/5,430,040 ~= 8.68%
Weighted total odds 1 spades folded: 58,905/135,751 * 8/40 = 471,240/5,430,040 ~= 8.68%
Weighted total odds 2 spades folded: 21,420/135,751 * 7/40 = 149,940/5,430,040 ~= 2.76%
Weighted total odds 3 spades folded: 2,940/135,751 * 6/40 = 17,640/5,430,040 ~= 0.32%
Weighted total odds 4 spades folded: 126/135,751 * 5/40 = 630/5,430,040 ~= 0.00%

The total weighted odds are 1,110,690/5,430,040 ~= 20.45%

You will note that 1,110,690/5,430,040 is equivalent to 9/44. (Multiply the top and bottom by 123,410 to get the larger fraction.)

So... ALL that work to try and account for the fact that some of our outs might have been folded, and the end result is the exact same value we got by ignoring those cards to begin with. And those calculations are not easy to get. I didn't show all my work for how to get the number of different ways they could hold your out.

And this was a SIMPLE example with only 2 people who folded. Imagine trying to do all this math for a 9 handed table where 7 people folded. Fortunately, for everyone, we don't need to because it will work out the same in the end. Burn cards work the same way. In the end, cards we don't know the value of do not change our odds in any way.
 
Phoenix Wright

Phoenix Wright

Legend
Loyaler
Joined
Feb 18, 2020
Total posts
2,592
Awards
4
The question is simple, and might have been asked before. How reliable is poker math?

Let's say I'm on a nut flush draw, on the flop, in a 9 handed no limit Hold'em game. I would like to think that I have 9 outs and I need atleast 4:1 to make a call. However I have no way of knowing how many of my nine outs have already been dealt to and folded by some of the other 8 players (not to forget the burn card).

So how reliable is this math really? And what can we do?

Poker math is correct, but it is only as good as our accuracy in the range of hands we put them on. Also note that GTO is an attempt to play as close to mathematically optimal as possible given the spot based on probabilistic decisions. This math-approach isn't recommended (or best!) is certain situations though. The GTO approach is best when your opponent plays close to optimally themselves (for example: a pro at your table you know little about), but in most poker games (especially micro stakes), everyone will make plenty of exploitable mistakes which allow exploitative strategy to profit even more than the balanced GTO play-style.

The math is "correct" but only to as good as your human ability to put your opponent on a range or how they are likely to play/adapt in future hands.
 
henriquemaduro

henriquemaduro

Visionary
Joined
Dec 14, 2013
Total posts
884
The question is simple, and might have been asked before. How reliable is poker math?

Let's say I'm on a nut flush draw, on the flop, in a 9 handed no limit Hold'em game. I would like to think that I have 9 outs and I need atleast 4:1 to make a call. However I have no way of knowing how many of my nine outs have already been dealt to and folded by some of the other 8 players (not to forget the burn card).

So how reliable is this math really? And what can we do?

U don't know the cards that people fold and the burned cards, so, u have all the 9 outs to do the math.
 
Top