Calculating pot odds and how often your opponent needs to fold to your bluff
After all of that more advanced discussion, let’s backtrack and make sure you have some of the basics down. Pot odds and figuring out how often you need to get a fold are not as complex of expectation calculations, but they are still important to be able to do, and quickly.
Calculating how often you need a river call to be good for it to be better than folding:
Your pot odds are the amount you have to call, divided by the size of the pot if you call. For example, if your opponent bets t100 into a pot of t200, the bet to call is t100, and the pot size if you call is t400. So, your pot odds are 100/400, or 25%. Another way of saying this is that you're getting 3-1, which represents the 300 already in the pot against the 100 you have to call. Over time, if you win the t300 that was out there 1/4 of the time, and lose an extra $100 3/4 of the time, you will break even. (.25)(+300) + (.75)(-100) = .75 - .75 = 0EV.
Potsized bets are laying you 2-1, or 33% pot odds. A bet of t200 into t200 means that when you call, there will be t600 in the pot, and 200/600 simplifies to 1/3 or 33%.
If your opponent bets a quarter of the pot, like t50 into t200, the pot will be t300 if you call, and 50/300 simplifies to 1/6, or 17%.
Here’s an easy trick: Most of the time in game, you do not really have to do any math - just estimate based on the probabilities you already know - potsized bets are 33%, half pot bets are 25%, and quarter pot bets are 17%. Just pick where it seems to be in between, and you won't have to bring up a calculator when you are trying to figure out how often you need to be good.
As an aside, do not get confused when you are facing a raise, and not just a bet. If you bet t100 into a pot of t200, and your opponent raises to t300, you just have to look two places: Down, at how much you have to call (t200 more), and then add that number to what's displayed as the pot size (It will say 600, which makes it 800 if you decide to call). 200/800 is 25%. The general formula remains the same: How much you have to call, divided by the total pot if you call.
Quick Check Problems:
1. Your opponent bets t275 into a pot of t450 on the river. What percent of the time do you need to have the best hand for calling to have a better expectation than folding?
2. On the river, you block bet t150 into a pot of t400, and your opponent jams for t650 more (800 total). How often do you need to be good for calling to have better expectation than folding?
3. You are facing a bet of t366 into a pot of t427. Without using a calculator, estimate how often you need to be good for calling to have better expectation.
Calculating how often your opponent needs to fold for a river bluff to be +EV:
If you assume you have zero equity when you are called, and have no chance at winning the pot if you do not bet, this one is pretty simple to calculate. Just take your bet size, and divide it by how much will be in the middle once you make your bluff. For example, if the pot is t300, and you want to bet t200, you need a fold 200/500 of the time, or 40%. A potsized bluff needs to work 50% of the time, and a half pot bluff needs to work 33% of the time – those are good landmarks to use so that you do not have to do much math in-game.
If you are considering a bluff raise, the equation is the same - how much money you are putting into the pot instead of folding, divided by that quantity plus whatever was in the pot that you are trying to steal. So if the pot on the river was t300, your opponent bets t150, and you want to try a raise to t450, you need a fold 450/(450 + 450) of the time, or 50%. You are risking t450 to get that t450 out there – it needs to work half the time.
What complicates this calculation is that in many situations, your expectation from checking and deciding not to bluff, is not zero, as we assume here. Sometimes you decide not to bluff with queen high and end up having the best hand against a missed draw. When this is true, you need a higher percentage of folds for bluffing to be better than giving up.
Quick Check Problems:
4. On the river, you know you have no showdown value. The pot is t320. How often does a t180 bluff need to work for it to have better expectation than checking behind?
5. Your opponent blockbets t100 into a t500 pot. You have t900 behind. How often does a jam have to work to be better than folding if you have no showdown value?
6. In this article, I say that your opponent having missed draws in his range means that you need to get a bigger percentage of folds when you have marginal showdown value in order for a bluff to be good. However, when your opponent has a missed draw, bluffing and checking behind have exactly the same result - you win - so it doesn't matter what you do against those hands. So why does it matter if our opponent has them in his range when we're deciding whether to bluff? Isn't this a contradiction?
Answers to Quick Check Problems:
1. 27.5%
2. 32.5%
3. Anywhere above 25% and below 33% seems reasonable to me, bonus points if you said 30%!
4. 180/500 = 36% of the time.
5. 900/1500 = 60% of the time.
6. If all our opponent is folding is hands we beat, it's clearly better just to give up. So it matters, don't be silly (or some variation of the argument that if we still win sometimes by checking, we need to do better than a 0EV bluff).
