math during a hand

Hello Mr. Obvious, long time reader first time poster. (Anyone that gets Bob and Tom will understand that one. Oh, and this is my second post but that's ok!)

I was wondering how much math people actually use while playing any given hand in NLHE. While reading the posts, and I have spent hours pouring over them, I see people analyzing hands using tons of math on things like implied odds, EV, FE, ROI, etc etc...

After playing for a year or so with play money, I have stepped up to real money and am taking the game very seriously. I devote as much time to reading these boards as I do to playing the game.

Currently I start out any hand by reading the overall table, then reading the people in the hand and my position. When a bet comes to me, and I feel I am an underdog (after the flop), I can pretty quickly figure out the pot odds vs. my outs minus any cards I think will help them. Those factors determine if I stay in the hand or not. Calling or raising then becomes more determined on my read than anything else.

Hind sight can tell me if I made the right choices or not, but in the middle of the hand, are there any other math factors anyone looks at?

This brings me to my next question. All the math in the world can be used on a hand when looking at HH and there is no pressure. Are there other odds that you know in certain situations just from memorization? For example, if I have two hearts in my hand and two hearts come up on the flop, I automatically know I have approximately a 35% chance of seeing another heart on the turn or the river. I don't do the math, I just know this. Are there any figures for any of the other numerous odds calculations that exist that people feel are important to just memorize?

Thanks so much to all of the people in this forum that lend their expertise to this forum. With your help, maybe I can convince my wife one of these days that this game is more than pure luck.

[quote="Percival"]Hello Mr. Obvious, long time reader first time poster. (Anyone that gets Bob and Tom will understand that one. Oh, and this is my second post but that's ok!) quote]

LMAO!!! Love it! WDVE??? Man, I miss that station!


There is a lot you can memorize. Some is useful, some is not. Also, playing on line, you can have a chart handy so you don't even have to memorize.

For me (primairly a Limit Hold'Em player). I don't find it too handy to memorize the percentage of hiting my draws by the river when I'm on the flop (i.e. Fush draw comes in 35% & gut shot comes in 16.4%) because people are almost never all-in on the flop in Limit and I will have to call bets on the turn as well. Also, If I'm going to memorize anything, I'm memorizing the required pot odds to call with a flush draw. Not just the win percentage, which I would then convert into win odds, and compair to pot odds. So, I have memorized the required pot odds in "bets" to call like below:

Outs Req' Pot Odds
(or size to call 1 bet)
4 10.8:1
5 8.4:1
6 6.9:1
7 5.8:1
8 4.9:1
9 4.3:1

So, if I have an opened straight draw, I know I need >4.9 small bets to call 1 small bet (and if I had to call two, it would be double 9.8). And I also use the same memorized numbers for the turn. I know I need 4.9 big bets to call 1 big bet on the turn (granted your odds are a little better on the turn since there are only 46 cards left instead of 47, so it would be 4.75 instead of 4.9. But I'm giving up less than 0.03bb of EV for the sake of simplicity... I can live with that. Plus this conservativeness helps make up for any mis-evaluations due to the ovelry large rake at the lower limits).

So, in my opinion this chart is worth memorizing for me because it has a lot of value. Memorizing the exact odds on the turn as well are of significant deminishing returns to me. And the exact odds of highing by the river when I'm on the flop is not as important as the odds in the chart above for me (for that I will just do the math).

There are a lot of other things you could evaluate and memorize, but beyond starting hand guidelines and drawing odds, there is a lot of deminishing return to trying to remember all of those numbers. You need to figure out what you find is the most efficient and helpful.

I personally have tried to do some evaluation of Cbetting and Free-Card-Raising opportunities and requirements and will probably try to remember some basic guidelines.

For example: When heads up with position. It is almost ALWAYS correct to Cbet. Even if only folds 20% of the time, you will profit over the long run. Becuase in a raised pot, you have 4:1 pot odds to bet and try to pick it up right there. And if you get it 20% of the time 1/5 = 1:4, you are break even. Sure you could get check/raised, but also you will usually have some outs to take the lead on the turn. And if you miss the turn, you will often get the opportunity to take a free card on the turn and hit the river. So these other drawing factors will usually make up for the times that you might get check/raised.

You can run through different evaluations and come up with lots of general rules to memorize and follow with various situations.

But like I said, three is a lot of deminision returns and it is up to you to determine what is most efficient for you.

But personally, I lean torwards wanting to memorize guidelines and general rules, especially if playing live, because I don't want people in a friendly game to realize I'm taking it too seriously and figuring out odds and math and crap in the middle of the hand. I think that takes some of the gamble out of them and causes them to play a little more seriously themselves.

^^ tl;dr

There is also the 2/4 rule. After you count the number of outs, multiply by 2 to get an approximate % to hit an out on the turn. If you think you get to see the river for free ("buying" the free card, your opponent sucks, etc) then multiply by 4.

So, AQs on K57 flop with the flush draw. You put your opponent on Kx, but not AK. So, you have 3 A which give you a higher pair, and 9 cards for a flush; 12 outs. The chance you hit the turn is approximately 12*2 = 24%, the chance of hitting on the turn/river is 12*4 = 48%.

Some people hate converting % to odds, which is a little more math.

There are many sorts of odds.

Ex. 'Situational odds':
Say, you've spotted a weakness but not sure ... well if you think that there's more than 50% chance that he'll fold to pot-sized bet then it's EV+ to bluff (in the long run, of course)

**********************

Or odds taking FE (folding equity) into consideration:
Say you called PFR with 78s and flopped nut straight draw.
Pot:9BB
Villain cbets 9BB ...
pot:18BB, you have, say 80BB behind, VILLAIN covers

What will happen if you shove (All in) right here on flop? You already know that for two more cards to come you'll make your str8 about 32% of the time (4 x 8 outs) or your odds are roughly about 1-to-2. If VILLAIN calls that'll be taking shot at 98BB pot with 80BB bet or about 1-to-1.2 , obviously not good. But what if VILLAIN will call 70% of the time and fold 30% (after all, hardly you will ever see situation that's 100% certain). Now there's some math to do:

1) 30%: you shove, he folds, you win = 18BB

2)70%: you shove, he calls:
- 32%(of 70%) you make str8 = 178BB
- 68%(of 70%) you lose = -80BB

Summary:
0.3*18BB + 0.7*0.32*178BB - 0.7*0.68*80BB = 7.19BB

So with 30% FE you are actually making EV+ play gaining on average 7BB+. The more likely he is to fold, the more you gain.

**********************

Or, you call PFR with 78s and flop comes: 5s 6s 8 ... Now you are free to shove even if you are 100% sure that he has AA and will call 100% of the time cause your open-ended-straight-flush-draw-one-pair combo hand (with 2 cards to come) is 65% mathematical favorite against his AA

Originally Posted by Percival

Thanks so much to all of the people in this forum that lend their expertise to this forum. With your help, maybe I can convince my wife one of these days that this game is more than pure luck.

I know exactly how you feel.

Can't think of anything else offhand that I use a lot besides normal pot odds and implied odds.

It's useful to know some odds for common all-in preflop matchups:
-Overcards v Underpair is about 1:1 (33 v J4)
-Overpair v Undercards is about 6:1 (AA v J4)
-Over/under v Middle cards is about 2:1 (A6 v K5)
-Over/under v Middle pair is about 2:5 (A6 v 77)
-Overpair v Underpair is about 9:2 (AA v 44)

Pretty good advice from everyone, and I sincerely thank you. I started with a $100 BR and so far in one weeks worth of play I am down about $11 playing mostly .05/.10 NLRs. With the bonus though at UB, I am up about $1 with another $88 of bonus left. The best part though is the amount of experience I have gained. I know a week is nothing, but every day I feel myself getting better and better. Patience and discipline are the hardest two things to learn. Notes to myself about my gameplay go something like this..."playing loose does not mean playing stupid!!! Even crappy players usually have at least middle pair!!!"; this after seeing people bluff and I try to catch them. Being a table cop has been my biggest weakness that I have pretty much overcome.

Originally Posted by Sheetah

Originally Posted by Percival

Thanks so much to all of the people in this forum that lend their expertise to this forum. With your help, maybe I can convince my wife one of these days that this game is more than pure luck.

I know exactly how you feel.

you all need to find new wives

welcome to ftr

Originally Posted by courtiebee

Originally Posted by Sheetah

Originally Posted by Percival

Thanks so much to all of the people in this forum that lend their expertise to this forum. With your help, maybe I can convince my wife one of these days that this game is more than pure luck.

I know exactly how you feel.

you all need to find new wives

welcome to ftr

I would but you won't hook up with me

Originally Posted by Percival

"playing loose does not mean playing stupid!!! Even crappy players usually have at least middle pair!!!"

Be careful with keeping that as a steadfast rule. Playing loose is a situational thing. Not every time will people be bluffing, but you can't say that every time someone is playing with their money that they have a hand.

You sound like you're coming along well though. Best of luck.

Originally Posted by spoonitnow

I would but you won't hook up with me

you're so smart

Originally Posted by courtiebee

Originally Posted by spoonitnow

I would but you won't hook up with me

you're so smart

You obv can't afford grade A meat like this

I don't know how much math people use during a session. It's pretty much predetermined form playing so many hands in the past.

Originally Posted by Sheetah

Or odds taking FE (folding equity) into consideration:
Say you called PFR with 78s and flopped nut straight draw.
Pot:9BB
Villain cbets 9BB ...
pot:18BB, you have, say 80BB behind, VILLAIN covers

What will happen if you shove (All in) right here on flop? You already know that for two more cards to come you'll make your str8 about 32% of the time (4 x 8 outs) or your odds are roughly about 1-to-2. If VILLAIN calls that'll be taking shot at 98BB pot with 80BB bet or about 1-to-1.2 , obviously not good. But what if VILLAIN will call 70% of the time and fold 30% (after all, hardly you will ever see situation that's 100% certain). Now there's some math to do:

1) 30%: you shove, he folds, you win = 18BB

2)70%: you shove, he calls:
- 32%(of 70%) you make str8 = 178BB
- 68%(of 70%) you lose = -80BB

Summary:
0.3*18BB + 0.7*0.32*178BB - 0.7*0.68*80BB = 7.19BB

So with 30% FE you are actually making EV+ play gaining on average 7BB+. The more likely he is to fold, the more you gain.

Just wondering. Are people able to calculate this whilst playing? Im sh*t at maths and have never been able to get my head around equations like this!!

Are these sums really that relevant whilst playing?

If so is there a way to learn these easily (for the mathematically challenegd) or does it just come from experience, as big spenda states?

cheers.

Originally Posted by Random_Hero

Just wondering. Are people able to calculate this whilst playing? Im sh*t at maths and have never been able to get my head around equations like this!!

Are these sums really that relevant whilst playing?

No one does this at the table. All you need to do is count your outs, and know how to calculate pot odds and implied odds. You either have to turn odds to a %, or the % to odds.

The thing to take from his post is the idea that a -eV situation can be turned into a +eV by raising. So, if the pot odds aren't there, but you think there is a decent chance he'll fold then raise. You can do these calcs off-line if you want specific numbers.

Originally Posted by Random_Hero

Originally Posted by Sheetah

Or odds taking FE (folding equity) into consideration:
Say you called PFR with 78s and flopped nut straight draw.
Pot:9BB
Villain cbets 9BB ...
pot:18BB, you have, say 80BB behind, VILLAIN covers

What will happen if you shove (All in) right here on flop? You already know that for two more cards to come you'll make your str8 about 32% of the time (4 x 8 outs) or your odds are roughly about 1-to-2. If VILLAIN calls that'll be taking shot at 98BB pot with 80BB bet or about 1-to-1.2 , obviously not good. But what if VILLAIN will call 70% of the time and fold 30% (after all, hardly you will ever see situation that's 100% certain). Now there's some math to do:

1) 30%: you shove, he folds, you win = 18BB

2)70%: you shove, he calls:
- 32%(of 70%) you make str8 = 178BB
- 68%(of 70%) you lose = -80BB

Summary:
0.3*18BB + 0.7*0.32*178BB - 0.7*0.68*80BB = 7.19BB

So with 30% FE you are actually making EV+ play gaining on average 7BB+. The more likely he is to fold, the more you gain.

Just wondering. Are people able to calculate this whilst playing? Im sh*t at maths and have never been able to get my head around equations like this!!

Are these sums really that relevant whilst playing?

If so is there a way to learn these easily (for the mathematically challenegd) or does it just come from experience, as big spenda states?

cheers.

what you'd try to do is work out your expectation if you're called. If it's "close" to what you'd get by folding (which is zero) and there's a chance they'll fold then stick it all in.

In any case, the example is flawed. You need heaps more fold equity with such a weak draw and a small pot. The mistake made is that winning does not win you 178BBs, it wins you 169BBs less what you put into the pot to win it. In other words, you get +89BBs.

So assuming 30% folds, your equity is still -12 BBs or so

Here's how I make my decision in the "heat of the moment"

1. What's my odds to win by showdown? About one third (8x4 = 32%). What's my odds to hit on the turn? About one sixth (8x2 = 16%) Do I have odds to call pot size (get 2:1 odds). No. I need 6:1 odds.

2. Is my draw to the nuts? If it is, can I get implied odds? How much implied odds to I need to call? I'd have to expect to win 54BBs by calling. So I'd have to swell the pot to about 110BBs. By then, villain would be pot committed. So, what must be the likelihood of him going all in when I hit my turn straight to make it profitable to call? If he goes all in against my straight and my straight holds I gain 89BBs. So, 54/89 = about 0.6

3. So can I call on implied odds? Only if I think he's at least 50-50 likely to get stacked if I call and hit my straight (I say 50-50 because you might win something the times he doesn't stack and you might be able to take the pot away from him)

3a. I can't really do 2 and 3 when playing. So I think, "how far away am I from getting direct odds (part 1) to call?" If I'm close (say I'm getting 3:1 for a half pot bet) then the implied odds are probably there. I also look at the size of the stacks in relation to the size of the bet and just give it my best judgment. As a rule, if the relevant stack size * likelihood of draw hitting is double the amount needed to call, then I can call.

4. Do I have odds to push, based on fold equity? No, been through that. If you don't have odds to call on implied odds, you usually don't have odds to push.

So, having gone through 1, 3a and 4 - which is possible because pot odds should be automatic to you and 3a and 4 is just "am I close to being offered the right direct odds" that's all the math done. The math indicates I should not call or go all in. Should I make a smaller raise? Well, to "math" that out is very difficult and you have to make lots of assumptions, so here you really have to use your gut. Math won't really help you there.

As for relevance... if you can't figure out your odds fast, look at the relevant stack sizes and evaluate what your implied odds if calling or pot equity if raising all in... (at least at a ball-park level), you really are in big trouble. The two most important sources of odds are flop odds if drawing one and two cards, and pre-flop all-in equity for your hand against common ranges (say TT+, AQ+ and 77+, AJ+ KQ+). That's all the essential math.

In the end, everything needs to be justified by math because the objective of poker is to make decision that maximize your expected utility based on a probability tree. But there are enough common generalized situations that you can rely on other people doing the math for you and you just remember it and apply it to those situations, that being a math retard is not fatal to your poker career

Originally Posted by salsa4ever

Originally Posted by Random_Hero

Originally Posted by Sheetah

Or odds taking FE (folding equity) into consideration:
Say you called PFR with 78s and flopped nut straight draw.
Pot:9BB
Villain cbets 9BB ...
pot:18BB, you have, say 80BB behind, VILLAIN covers

What will happen if you shove (All in) right here on flop? You already know that for two more cards to come you'll make your str8 about 32% of the time (4 x 8 outs) or your odds are roughly about 1-to-2. If VILLAIN calls that'll be taking shot at 98BB pot with 80BB bet or about 1-to-1.2 , obviously not good. But what if VILLAIN will call 70% of the time and fold 30% (after all, hardly you will ever see situation that's 100% certain). Now there's some math to do:

1) 30%: you shove, he folds, you win = 18BB

2)70%: you shove, he calls:
- 32%(of 70%) you make str8 = 178BB
- 68%(of 70%) you lose = -80BB

Summary:
0.3*18BB + 0.7*0.32*178BB - 0.7*0.68*80BB = 7.19BB

So with 30% FE you are actually making EV+ play gaining on average 7BB+. The more likely he is to fold, the more you gain.

Just wondering. Are people able to calculate this whilst playing? Im sh*t at maths and have never been able to get my head around equations like this!!

Are these sums really that relevant whilst playing?

If so is there a way to learn these easily (for the mathematically challenegd) or does it just come from experience, as big spenda states?

cheers.

what you'd try to do is work out your expectation if you're called. If it's "close" to what you'd get by folding (which is zero) and there's a chance they'll fold then stick it all in.

In any case, the example is flawed. You need heaps more fold equity with such a weak draw and a small pot. The mistake made is that winning does not win you 178BBs, it wins you 169BBs less what you put into the pot to win it. In other words, you get +89BBs.

So assuming 30% folds, your equity is still -12 BBs or so

Here's how I make my decision in the "heat of the moment"

1. What's my odds to win by showdown? About one third (8x4 = 32%). What's my odds to hit on the turn? About one sixth (8x2 = 16%) Do I have odds to call pot size (get 2:1 odds). No. I need 6:1 odds.

2. Is my draw to the nuts? If it is, can I get implied odds? How much implied odds to I need to call? I'd have to expect to win 54BBs by calling. So I'd have to swell the pot to about 110BBs. By then, villain would be pot committed. So, what must be the likelihood of him going all in when I hit my turn straight to make it profitable to call? If he goes all in against my straight and my straight holds I gain 89BBs. So, 54/89 = about 0.6

3. So can I call on implied odds? Only if I think he's at least 50-50 likely to get stacked if I call and hit my straight (I say 50-50 because you might win something the times he doesn't stack and you might be able to take the pot away from him)

3a. I can't really do 2 and 3 when playing. So I think, "how far away am I from getting direct odds (part 1) to call?" If I'm close (say I'm getting 3:1 for a half pot bet) then the implied odds are probably there. I also look at the size of the stacks in relation to the size of the bet and just give it my best judgment. As a rule, if the relevant stack size * likelihood of draw hitting is double the amount needed to call, then I can call.

4. Do I have odds to push, based on fold equity? No, been through that. If you don't have odds to call on implied odds, you usually don't have odds to push.

So, having gone through 1, 3a and 4 - which is possible because pot odds should be automatic to you and 3a and 4 is just "am I close to being offered the right direct odds" that's all the math done. The math indicates I should not call or go all in. Should I make a smaller raise? Well, to "math" that out is very difficult and you have to make lots of assumptions, so here you really have to use your gut. Math won't really help you there.

As for relevance... if you can't figure out your odds fast, look at the relevant stack sizes and evaluate what your implied odds if calling or pot equity if raising all in... (at least at a ball-park level), you really are in big trouble. The two most important sources of odds are flop odds if drawing one and two cards, and pre-flop all-in equity for your hand against common ranges (say TT+, AQ+ and 77+, AJ+ KQ+). That's all the essential math.

In the end, everything needs to be justified by math because the objective of poker is to make decision that maximize your expected utility based on a probability tree. But there are enough common generalized situations that you can rely on other people doing the math for you and you just remember it and apply it to those situations, that being a math retard is not fatal to your poker career

superb post... cheers.

I can work out pot odds, odds of hitting and can evaluate my implied odds good enough. It all comes with experience. the more you do it the easier it gets.

with regards to pre-flop all-in equity im sure I'll get better at that once I get myself SNGPT.

Was just worried my lack of "math skillz" would affect my game in the long run but I can work out odds easily enough.

Thank you very much Salsa for such a thorough post. This really helps me to understand the game better.

The first reply to my original post was from NWNewell, and he wrote, "...For example: When heads up with position. It is almost ALWAYS correct to Cbet. Even if only folds 20% of the time, you will profit over the long run. Becuase in a raised pot, you have 4:1 pot odds to bet and try to pick it up right there. And if you get it 20% of the time 1/5 = 1:4, you are break even."

I am a little lost with the 4:1 pot odds. Could someone break down exactly what that means and how that number was achieved?

Originally Posted by Percival

I am a little lost with the 4:1 pot odds. Could someone break down exactly what that means and how that number was achieved?

I'm pretty sure he is talking limit.

Pot starts at 1.5bb
you raise, pot is 3.5bb
BB calls, pot is 4.5bb

When you cbet, you are betting 1 to win 4.5, so if he folds 20% then you profit.

Originally Posted by swiggidy

Originally Posted by Percival

I am a little lost with the 4:1 pot odds. Could someone break down exactly what that means and how that number was achieved?

I'm pretty sure he is talking limit.

Pot starts at 1.5bb
you raise, pot is 3.5bb
BB calls, pot is 4.5bb

When you cbet, you are betting 1 to win 4.5, so if he folds 20% then you profit.

I now remember reading this before. My new question is (bear with me as I have so many lol), what would good odds be? 2:1, 3:1, 4:1???

Originally Posted by Percival

I now remember reading this before. My new question is (bear with me as I have so many lol), what would good odds be? 2:1, 3:1, 4:1???

It depends. Good odds are odds that will show a long term profit.

If your villain is a calling station and will never fold, betting as a bluff with 9:1 pot odds is terrible, because he won't fold the ~10% of the time you need to show a profit.

If your opponent is nitty-tight post flop and won't play unless he has TP or an overpair, then bluffing at a pot offering 2:1 odds will be profitable because he will fold >50% of the time.

So, if you have a 1:3 chance to win, the pot has to offer 3:1 for you to break even, 4:1 will show a profit, 2:1 will show a loss.

Originally Posted by salsa4ever

Originally Posted by Random_Hero

Originally Posted by Sheetah

Or odds taking FE (folding equity) into consideration:
Say you called PFR with 78s and flopped nut straight draw.
Pot:9BB
Villain cbets 9BB ...
pot:18BB, you have, say 80BB behind, VILLAIN covers

What will happen if you shove (All in) right here on flop? You already know that for two more cards to come you'll make your str8 about 32% of the time (4 x 8 outs) or your odds are roughly about 1-to-2. If VILLAIN calls that'll be taking shot at 98BB pot with 80BB bet or about 1-to-1.2 , obviously not good. But what if VILLAIN will call 70% of the time and fold 30% (after all, hardly you will ever see situation that's 100% certain). Now there's some math to do:

1) 30%: you shove, he folds, you win = 18BB

2)70%: you shove, he calls:
- 32%(of 70%) you make str8 = 178BB
- 68%(of 70%) you lose = -80BB

Summary:
0.3*18BB + 0.7*0.32*178BB - 0.7*0.68*80BB = 7.19BB

So with 30% FE you are actually making EV+ play gaining on average 7BB+. The more likely he is to fold, the more you gain.

Just wondering. Are people able to calculate this whilst playing? Im sh*t at maths and have never been able to get my head around equations like this!!

Are these sums really that relevant whilst playing?

If so is there a way to learn these easily (for the mathematically challenegd) or does it just come from experience, as big spenda states?

cheers.

what you'd try to do is work out your expectation if you're called. If it's "close" to what you'd get by folding (which is zero) and there's a chance they'll fold then stick it all in.

In any case, the example is flawed. You need heaps more fold equity with such a weak draw and a small pot. The mistake made is that winning does not win you 178BBs, it wins you 169BBs less what you put into the pot to win it. In other words, you get +89BBs.

So assuming 30% folds, your equity is still -12 BBs or so

Sorry. My bad.
salsa is right.
Actually there are two ways to do the math on this and I accidentally implemented way #2 logic into way #1 math. UGH!
Anyway, I just wanted to illustrate that there are many ways of thinking and many sorts of odds.

@ Random_Hero:
- Are people able to calculate this whilst playing?
No way. Not online in less than a minute. It's more like a homework: you do the math for some common scenarios, remember some referent values and when the hand comes - you already know solution so use this knowledge to get a little extra value.

-Are these sums really that relevant whilst playing?
Not really. It's exploiting thin edges. In the long run this is profitable but moves like this are heavy variance. It's more relevant in High stakes where good players might use this to get an edge on other good players.