Trying to understand Pot odds and how to calculate them
So far my understanding of Pot odds and the formula to find them is like this:
What you do is calculate the final potsize. Then you take the size of the bet to call and divide that up by the final potsize. For example a final pot is 500 and the price to call is 100. You then divide 100/500 which is 0.20. Then multiple 0.2 * 100 which equals 20%. So we need to win more than 20% of the time to be profitable right?
I hope i explained that well enough, i have a question for you guys though. Is there a way to do the math in your head easier when you divide the final potsize with the calling bet? I am kind of hung up on this. Also when i calculate the pot odds in my holdem manager it doesnt line up with holdem managers's pot odds? This is throwing me off a bit too.
3 Replies
Pot odds are your call amount divided by everything in the middle which includes the bet and your call. In your example it is a little confusing to me because you say "final pot is 500"... so if there was 300 in the middle and your opponent bet 100, then that would be correct—100/(300+100+100).
Yes, to have a profitable call with no other implied odds, then your equity needs to be greater than your pot odds. It is already quite simple math, so I'm not sure I can offer an easier alternative other than memorization or just having a diagram of pot odds as a function of bet size that you can look at near you.
It seems pot odds has two definitions. My take has been that it is a reward to risk ratio, win to lose, as the odds term is usually used. The reward is amount in the pot before you have to make a call and the call amount is the risk.
So, for OP’s example, if villain bet 100 into a 300 pot, the reward is 400. Then the pot odds by the above definition is 400/100 = 4 to 1.
It can be shown that the break-even equity needed is 1/(1+Pot Odds) ) = 1/(1+4) =20%, as gotten by the other pot odds definition.
I like to think the above method is best described as follows. After villain bet to make the pot 400, if hero calls he invested 100 to make the total pot 500. The winner will then win the 500. Since hero contributed 100 of the 500 or 20% (earlier bets don’t count) that is frequency he should win to break even.
This is an example of the fact that for many probability/stat problems there are several ways to obtain an answer.
It seems pot odds has two definitions. My take has been that it is a reward to risk ratio, win to lose, as the odds term is usually used. The reward is amount in the pot before you have to make a call and the call amount is the risk.
So, for OP’s example, if villain bet 100 into a 300 pot, the reward is 400. Then the pot odds by the above definition is 400/100 = 4 to 1.
4 to 1 and 1/5 are equivalent.
1/5 means "Out of 5 total chances, you will win one."
4:1 means "You will lose 4 times and win 1 time (i.e. thre are 5 total chances)."
They're different representations of the same thing.
@OP - I think it's simpler if you remove the long conversions to/from percent, and just learn a simple process and some basic percentages.
For example:
If your opponent bets 1/3 pot, you need to win 1/5 of the time.
You get there by adding the numerator (the "1" of "1/3") to the denominator (the "3" of "1/3") for each bettor (a "bettor" is the initial bettor and any callers, including yourself).
So heads up - if your opponent bets (fraction of the pot):
- 1/2, you need to win at least 1/4 times.
- 1/4, you need to win at least 1/6 times.
- 2/5, you need to win at least 2/9 times (because we add the numerator "2" to the denominator "5" for each bettor, which is 2: you and the initial bettor).
- 3/2 (150% overbet), you need to win at least 3/8 times (I'll explain how to convert this to percentage easily below.)
If there's a caller between you and the initial bettor you add the numerator 3 times because there are 3 bettors:
- 1/2 bet means you need to win at least 1/5 times.
- 1/4 bet means you need to win at least 1/7 times.
- 2/5 bet means you need to win at least 2/11 times.
Etc.
You can also do the reverse. If you know you'll hit your draw 1/5 times, you can subtract the numerator ("1") from the denominator ("5") for the number of bettors. So if you're heads up, your maximum bet size would be 1/3.
If you expect a third caller, you can increase the bet size to 1/2.
If you need to convert between percentages (e.g., when using the 2/4 rule), then just learn that
1/2 = 50%
1/3 = 33%
1/4 = 25%
1/5 = 20%
1/6 = 17%
1/7 = ~14%
1/8 = ~13%
1/9 = ~11%
1/10 = ~10%
And so on. Most, if not all, of those are probably already intuitive. And weird fractions (like 2/9) are just the percent of 1/9 times the numerator, so
1/9 = 11%
2/9 = 22% (11% times the numerator; or 11% x 2)
3/9 = 33% (11% x 3)
...
3/8 = 39% (13% x 3)
etc.
This also works if there is only one bettor (because you're bluffing, and don't expect your opponent to call)—same logic.
If you think your opponent will fold 1/5 of the time, your maximum bet size is 1/4 (subtract the numerator from the denominator one time, because you're hoping there's only one bettor.) And so on.
If you're planning to bet 1/2 pot as a bluff, you need your opponent to fold 1/3 of the time (i.e., add the numerator to the denominator) (33% fold equity).
With an hour of practice, this will be super natural and intuitive at the table.
