Pot odds made simple: the equity you need to call any bet.
The total pot against what it costs to call, and the equity you need to call.
The initial size of the pot is everything in the middle before the bet you're facing: a pot-sized bet of 120 into 120 is an initial pot of 120 and a bet of 120. Callers are players who called the bet before you: 0 heads-up.
The most you can raise in pot-limit games like Pot-Limit Omaha (PLO).
The size of the pot is everything in the middle, including the bet you're facing. A pot-sized bet of 120 into 120 is a pot of 240 with 120 to call.
Pot odds compare the total size of the pot, the initial pot plus the bet you're facing, with the amount it costs you to call: pot odds = (total size of the pot) : (amount to call)
The equity you need to call is the amount to call divided by the size of the pot after you call:equity needed = (amount to call) / [(total size of the pot) + (amount to call)]If your equity is higher, calling wins money in the long run; if it is lower, calling loses it.
The key is calculating the pot correctly. The pot includes everything in the middle: money from earlier betting rounds, your opponent's bet, and any calls before yours. For the equity calculation, you include your own call:(total size of the pot) + (amount to call) = size of the pot after you callIf the pot is 100 and your opponent bets 50, the pot is now 150 and it costs you 50 to call: the pot odds are 150 : 50 = 3 : 1, and the final pot is 200. So you need 50 / 200 = 25.00% equity. If you leave out the bet, or your own call, you get 50 / 150 = 33.33% instead, and fold hands that are profitable calls.
With more players, add every call. If the pot is 100, one player bets 50 and another calls, the pot is now 200 and you call 50, pot odds of 4 : 1, so you need 50 / 250 = 20.00% equity.
The bigger the bet, the worse your pot odds and the more equity you need to call.
| Bet size | Pot odds | Equity needed | MDF |
|---|---|---|---|
| ¼ pot | 5.00 : 1 | 16.67% | 80.00% |
| ⅓ pot | 4.00 : 1 | 20.00% | 75.00% |
| ½ pot | 3.00 : 1 | 25.00% | 66.67% |
| ⅔ pot | 2.50 : 1 | 28.57% | 60.00% |
| ¾ pot | 2.33 : 1 | 30.00% | 57.14% |
| Pot | 2.00 : 1 | 33.33% | 50.00% |
| 1½ pot | 1.67 : 1 | 37.50% | 40.00% |
| 2× pot | 1.50 : 1 | 40.00% | 33.33% |
MDF is minimum defense frequency, a game-theory benchmark for how much of your range to continue with when heads-up, so that bluffs can't profit automatically. More on MDF below.
In pot-limit games like Pot-Limit Omaha, the biggest bet allowed is the size of the pot, and the biggest raise is the size of the pot after your call. The foolproof way to figure it: make the pot whole by calling the bet in front of you, then raise by the whole pot. With 120 in the pot and a bet of 120 to you, calling makes the pot 360, so you can raise 360 more, to 480.
Dealers use a shortcut: three times the last bet, plus the pot, where the pot is everything in the middle except that last bet. Some put it the other way around: the pot, counting the last bet, plus twice the last bet. Both give the same answer: 3 × 120 + 120 = 480, and 240 + 2 × 120 = 480: pot-sized raise = 3 × (last bet) + pot
The shortcuts only work when you have no chips in the pot yet this betting round. If you do, because you posted a blind or your own bet was raised, leave those chips out of the pot, or the shortcut comes out too high by exactly that much. At 1/2, if you are the big blind and a player raises to 7, the pot counting your blind is 3, so the shortcut gives 3 × 7 + 3 = 24, but the most you can raise to is 22: you call 5 more to make the pot 15, then raise 15 more, to 22. Making the pot whole always gets it right.
Counting the amount to call instead of the last bet makes the shortcut exact every time, as a count of the chips you put in: chips you put in = 3 × (amount to call) + pot where the pot is everything in the middle except the amount you have to call, your own chips included. For the big blind facing a raise to 7, that is 3 × 5 + 5 = 20 more chips, a raise to 22 with the 2 already in.
| Situation | Make the pot whole, then raise it | Raise to |
|---|---|---|
| 1/2 blinds, first in | call 2 → pot 5; raise 5 more | 7 |
| 1/2 blinds, one limper | call 2 → pot 7; raise 7 more | 9 |
| 1/2, big blind facing a raise to 7 | call 5 → pot 15; raise 15 more | 22 |
| Pot 120, pot-sized bet of 120 | call 120 → pot 360; raise 360 more | 480 |
| Pot 120, bet 60, one caller | call 60 → pot 300; raise 300 more | 360 |
| You bet 10 into 20, raised to 40 | call 30 → pot 100; raise 100 more | 140 |
Facing a pot-sized bet, your pot odds are always 2 : 1 and you need 33.33% equity. The bet equals the pot, so the total size of the pot is always twice the amount to call: bet 120 into 120 and the total is 240 with 120 to call, so you need 120 / (120 + 120 + 120) = 33.33%.
Pot odds tell you whether to call with the hand you hold. Minimum defense frequency (MDF) comes from game theory and answers a different question: how much of your whole range you need to continue with when heads-up, so that an opponent can't profit by bluffing with any two cards. A bluff of B into a pot of P, the pot before the bet, breaks even when you fold B / (P + B) of the time, so MDF = P / (P + B)That is 50.00% against a pot-sized bet and 66.67% against a half-pot bet.
MDF is a benchmark, not a rule for any single hand. It assumes heads-up play and an opponent who bluffs as often as game theory allows. Most players bluff less than that, and against them folding more often is right. Whether to call with a particular hand is still a question of pot odds and your equity.
Outs are the cards that improve your hand to the likely winner. The rule of 2 and 4 estimates your chance to hit: multiply your outs by 4 on the flop when you will see both the turn and the river, or by 2 with one card to come. It is close with a few outs and runs high with many.
Turn + River | |||
|---|---|---|---|
| Outs | Draw | Chance to hit | Rule of 4 |
| 4 | Gutshot | 16.47% | 16% |
| 8 | Open-ended straight draw | 31.45% | 32% |
| 9 | Flush draw | 34.97% | 36% |
| 12 | Flush draw + gutshot | 44.96% | 48% |
| 15 | Flush draw + open-ended | 54.12% | 60% |
River | |||
|---|---|---|---|
| Outs | Draw | Chance to hit | Rule of 2 |
| 4 | Gutshot | 8.70% | 8% |
| 8 | Open-ended straight draw | 17.39% | 16% |
| 9 | Flush draw | 19.57% | 18% |
| 12 | Flush draw + gutshot | 26.09% | 24% |
| 15 | Flush draw + open-ended | 32.61% | 30% |
To work it out exactly in Hold'Em, count the unseen cards: on the flop you have seen 5 cards, your 2 and the 3 on the board, so 47 are unseen; on the turn, 46. With one card to come, divide your outs by the unseen cards:chance to hit on the river = outs / 46With two cards to come, it is easier to work out the chance of missing twice and subtract it from 1:chance to hit by the river = 1 − [(47 − outs) / 47] × [(46 − outs) / 46]With 9 outs, that is 9 / 46 = 19.57% with one card to come and 1 − (38 / 47 × 37 / 46) = 34.97% from the flop. In Omaha you hold four cards, so 45 cards are unseen on the flop instead of 47, and each out is a little more likely: 9 outs hit 36.36% of the time from the flop to the river, against 34.97% in Hold'Em.
Pot odds count only the money already in the pot. Implied odds also count what you expect to win on later streets when you hit, which can make a call worth it even when the pot odds alone are not. Reverse implied odds are the opposite: what you can lose later when you hit your hand and are still beaten.
Reverse implied odds are what you lose on later streets when you make your hand and it is still beaten. Pot odds assume that when you hit, you win the pot. When hitting sometimes means paying off a better hand, part of your equity is worth less than it looks, and a call is worse than the pot odds alone say.
They come from hands that are often second best when they get there: a low flush draw when a higher flush is possible, a straight draw where the card that makes your straight also makes a higher one, or top pair with a weak kicker. In Omaha every player holds four cards and someone often has the nuts, so drawing to anything less is where reverse implied odds can cost the most.
When your reverse implied odds are high, you need more equity than the pot odds say to call.
Compare the total size of the pot, the initial pot plus the bet you're facing, with the amount it costs to call. Your opponent bets 50 into 100: the total size of the pot is 150 and it costs 50 to call, so the pot odds are 150 : 50, or 3 : 1.
pot odds = (total size of the pot) : (amount to call) Pot odds compare the total size of the pot, the initial pot plus the bet you're facing, with the amount to call. The equity you need is the amount to call divided by the size of the pot after you call: equity needed = (amount to call) / [(total size of the pot) + (amount to call)]
A pot-sized bet, or PSB, always gives you pot odds of 2 : 1. Once the bet is in, the total size of the pot is twice the amount to call. You need 33.33% equity to call.
You need 25.00% equity to call a half-pot bet. Facing 50 into 100, you call 50 into a final pot of 200, pot odds of 3 : 1.
Make the pot whole by calling the bet in front of you, then raise by the whole pot. With 120 in the pot and a bet of 120, calling makes the pot 360, so you can raise 360 more, to 480. A pot-sized raise by the first player to act in 1/2 is to 7. You call the blind bet, making the pot whole, then you raise the bet by 5, the size of the pot.
Three times the last bet, plus the pot: 3 × 120 + 120 = 480. It only works when you have no chips in the pot yet this betting round. If you posted a blind or your bet was raised, leave your own chips out: the big blind at 1/2 facing a raise to 7 can raise to 3 × 7 + 1 = 22, not 24. Counting the amount to call instead is always right: 3 × 5 + 5 = 20 more chips, a raise to 22.
Pot odds tell you the equity you need to call; equity is your share of the pot if the hand were played out many times. Continue when your equity is higher than the equity required by the pot odds.
Pot odds tell you whether a call is profitable with the hand you hold. Minimum defense frequency is the pot before the bet, divided by the pot plus the bet: MDF = (pot before the bet) / [(pot before the bet) + (size of the bet)] MDF is a game-theory benchmark for how much of your whole range to continue with when heads-up, so that bluffs can't profit automatically: 50.00% against a pot-sized bet. It isn't a rule for any single hand, and against players who rarely bluff, folding more often is right.
Multiply your outs by 4 on the flop to estimate your chance of hitting by the river, or by 2 with one card to come. With 9 outs, the rule of 4 gives 36%; the exact chance in Hold'Em is 34.97%.
Pot odds count only the money already in the pot. Implied odds also count what you expect to win on later streets when you hit; reverse implied odds count what you can lose when you hit and are still beaten.
Reverse implied odds are what you lose on later streets when you make your hand and it is still beaten, like a low flush that pays off a higher one. They make a call worse than the pot odds alone say, and they can cost the most in Omaha when you draw to anything less than the nuts.
The NextGenPoker Odds Calculator tells you the equity you have, against your opponent's range.