I'm trying to learn and understand some poker math. Please help me with this simple? problem:

LP steals, SB folds, I call in BB. Flop comes down. I check, he bets.

I'm getting 5.5:1, right? So, if effective stacks were this one bet, I'd need to win 15%, right? Here's the part I'm struggling with: But what if effective stacks were many bets, how often do I have to win then? The answer is always more than 15%? Is there any literature on this subject?

To call flop, turn, and river I'm getting 9.5:5(1.9:1), right? So, I'd need to win 34% if I know opponent would bet flop, turn, and river? Does the fact he won't always bet turn and river mean I need less than 34%? I have a feeling I'm missing something. I have a feeling it means I need more! The answer is always more than 34%?!

Is it fair to say to call flop I'd need between 15% and 34% chance of winning (usually showdown equity as I won't be able to bluff better than him out of position). That's the conclusion I would have come to however I think this is lower than what most good players suggest. So, I'm missing something? I'm missing reverse implied odds? I understand things get complicated when I put in a raise, etc - I'm just interested in calling math.

Thanks for any help!

I think your asking good questions and are close to the answers.

Generally, you need more than your immediate odds to call a c-bet on the flop, but less than your odds if you had to call 3 streets, so between 15-34% in your example.

This is because your flop equity assume you get to see the river, when in fact villain is betting the turn some % of the time and you may have to fold without seeing a river.

You can peel more widely with hands that when they improve, have a good chance of winning at showdown. For example, peeling gut-shots on the flop is common even though you only have 5.5:1 odds on an 11:1 shot. This is because you'll often win 6 small bets on the turn and river by C/R'ing the turn and value betting the river.

Conversely, you have to fold a few more hands that are marginal bluff catchers and don't win a lot when they improve. Say you have Q7 on A83ran flop vs a Btn Steal. Because you expect villain to bet the turn X% of the time and you won't win a lot when you do improve on the turn and river, you may want to fold on the flop even though your getting correctly immediate odds to peel.

Shorter version, peel more widely with hand that have good implied odds and fold a few more hands that have reversed implied odds (weaker bluff catchers).

You are correct that if that bet would put you all in, you would have to win >15% of the time at showdown to call profitably. It's not so cut and dry when considering the possabilities of future actions though. Alot depends on where your equity is coming from. If your hand has very little chance of improving, but has showdown value, then you will suffer from reverse implied odds. If your hand will never win at showdown unimproved, but has a sufficient chance of improving, then implied odds will be in your favor.

If you are planning to call all 3 streets, then you will need to win about 34% of the time vs your opponent's triple barrel range. You may actually need less than this since you can fold when the board gets ugly. Also, you may be able to win by bluffing on future streets.

You also need to consider that if you fold more than 18% of the time your opponent will profit immediatly by simply betting every time.

before OP starts peeling every flop though id like to add that ive never seen any reg who was not folding at least 25-30% to flop cbets

Thanks for the great responses!


My head is exploding! How is this possible? By regs I take it you mean decent to good players? My tracker says I fold to flop cbet 35%! and I come out a winner in the games I play. By folding we lose, but not as much as we would if we called (and necessarily made mistakes later in hand)?

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Is there anything I need to remember when applying this thinking to the slightly more complicated spot of peeling OOP in a 3bet pot? Now we're getting 8:1 (11%) on a flop call and 2.6:1 (27%) on a complete calldown. So I need between 11% and 27% equity to call the flop cbet? The pot is bigger but his range tighter so I'll be calling with far less hands on the flop. Also, people cbet turn far more often in 3bet pots? This would make folding even more attractive.

I think the assymetry of the ranges is the main reason. Even a BTN steal range is much stronger than a BB defend range. If it's significantly stronger, the BB can fold more frequently without being exploited. (he will lose less by folding a little too much than by paying off a stronger range) Also, against bad players there are several factors at play here. If they pay off too much, for example, we can afford to be a little more patient, knowing that we are both less likely to win without a showdown, and more likely to get paid off when we do take a hand to showdown.

I think this is a pretty solid op. You have the facts right, but you're having trouble seeing the correct conclusion because of the possibilities running through your head. Can't see the forest for the trees. Now that these guys have answered your questions you should be more able to come to correct conclusions on your own. Isn't 2+2 awesome?

Tbh I don't think it's much stronger, today btn steals are easily in the 55-60%ish range while people fold 35-40% of their BB vs a btn steal which means they are playing top 60-65%. Even top 55% vs top 65% is only about an 52-48 % favorite equity wise. What the main reason is, idk to be honest, but if I had to guess, it's the positional disadvantage which you can't really ovecome. Many flops are very hard to peel oop even if you have the best hand with your Ahi and Khi at the moment, and especially knowing you are gonna be facing lots of double and triple barrels.
So it's quite possible that even though you are being exploited by folding more than 18%, you could be exploited much harder if you were peeling too light and button can use his position to push you off your weak sd value on many cards later on after having invested more money, or he can decide to give up when you are obviously ahead and not folding, or draw free or whatever helps him more.
Or maybe the answer is something else, idk. Maybe if LHE was solved, bots could fold only 18% and not get exploited, who knows.

the reason why calculating an unexploitable fold vs flop cbet percent is extremely complicated is that we still have two streets more to come. But you are correct in that the right number will be somewhere in between the two cases where villain bets 0% and 100% turn and river.
Calculating unexploitable calling strategies is pretty easy on river but then becomes an order of magnitude more complicated for each street as we move backwards in the hand.

And then being OOP means we need to fold a fair bit more on flop compared to if we were IP, because it on avg is a pretty big disadvantage EV wise