Equity a call needs
33.33%
against a pot-size bet
- Pot oddsfor every 1 you call2 : 1
- Bet on a $100 potthe full pot$100
- Pot after your callyou put in $100$300
The price of a pot-size bet
A price of 33.33% sits in the middle of the range, so draws are a close call and the exact count of outs decides.
e = f / (1 + 2f)f = 1e = 1 / (1 + 2 x 1) = 33.33%Pot odds = (1 + 1) / 1 = 2 : 1
Turn the percent into odds and you get 2 : 1. The bigger the first number, the cheaper the call.
A $100 pot facing a pot-size bet
The pot is $100 and your opponent puts in $100. You are now asked to match $100 to see the next card.
- Pot before the bet$100
- Opponent bets$100
- You call$100
- Pot after your call$300
- You risk$100
- You can win$200
- Equity needed33.33%
Add your $100 and the pot reaches $300. The price of 33.33% is simply your call as a share of that total.
Which draws can call a pot-size bet
Every row shows how a draw stacks up against a pot-size bet. Take the chance to hit, subtract 33.33%, and the sign tells you the call.
You can continue from the flop with 3 of the 8 draws, and a flush draw is the first on the list that qualifies.
Not one draw beats 33.33% on the turn. A flush draw with an open-ended straight draw, the best of the eight with 15 outs, hits 32.61%.
| Draw | Outs | Flop: hit by the river | Flop margin | Flop verdict | Turn: hit on the river | Turn margin | Turn verdict |
|---|---|---|---|---|---|---|---|
| A pocket pair that wants a set | 2 | 8.42% | -24.92 points | Fold | 4.35% | -28.99 points | Fold |
| One overcard to top pair | 3 | 12.49% | -20.84 points | Fold | 6.52% | -26.81 points | Fold |
| A gutshot straight draw | 4 | 16.47% | -16.87 points | Fold | 8.70% | -24.64 points | Fold |
| Two overcards | 6 | 24.14% | -9.19 points | Fold | 13.04% | -20.29 points | Fold |
| An open-ended straight draw | 8 | 31.45% | -1.88 points | Fold | 17.39% | -15.94 points | Fold |
| A flush draw | 9 | 34.97% | +1.63 points | Call | 19.57% | -13.77 points | Fold |
| A flush draw with a gutshot | 12 | 44.96% | +11.63 points | Call | 26.09% | -7.25 points | Fold |
| A flush draw with an open-ended straight draw | 15 | 54.12% | +20.78 points | Call | 32.61% | -0.72 points | Fold |
Implied odds against a pot-size bet
Future bets can lower the price. The rule is C / (T + W), where C is your call of $100, T is $300, and W is what you expect to win later.
At $500 of future winnings the price falls from 33.33% to 12.50%, a drop of 20.83 points.
Nine outs on the turn mean 19.57%, below 33.33%. Closing the gap takes $211.11 of winnings still to come.
Implied odds change the answer when your hand is close to 33.33% and your opponent is likely to pay you off. A draw far below 33.33% gains little from them.
Reverse implied odds are why some draws that look like calls at 33.33% should be folded: the cards that complete them do not always win.
| Future winnings W | Pot after call plus W | Equity needed | Change from the plain price | Flush draw margin from the flop |
|---|---|---|---|---|
| $0 | $300 | 33.33% | 0.00 points | +1.63 points |
| $50 | $350 | 28.57% | -4.76 points | +6.40 points |
| $100 | $400 | 25.00% | -8.33 points | +9.97 points |
| $250 | $550 | 18.18% | -15.15 points | +16.79 points |
| $500 | $800 | 12.50% | -20.83 points | +22.47 points |
Pot-size next to the other sizes
Step down to a three-quarter-pot bet and the price falls to 30.00%, which is 3.33 points lower than 33.33%.
Compared with 1.25x-pot, this bet is 2.38 points cheaper to call: 33.33% against 35.71%.
- Pot odds facing a three-quarter-pot bet: Needs 30.00%, 3.33 points less.
- Pot odds facing a 1.25x-pot bet: Needs 35.71%, 2.38 points more.
The outs that justify a call
To call a pot-size bet on the flop, hold 9 outs or more. The chance to hit by the river is 34.97% at that count.
Once the turn card is out, you need 16 outs to call. That is 34.78%, compared with 32.61% one out lower.
- 9 outs on the flop: 34.97% by the river against 33.33%.
- 16 outs on the turn: 34.78% on the river against 33.33%.
To check a particular hand, open a call-or-fold page for this bet size; the draw and the price are already set.
- Flush draw on the flop against a pot-size bet: 9 outs, 34.97% to hit, against 33.33%.
How this is computed
This page works out the equity a call needs when a $100 pot faces a bet of the full pot, and it compares that price with the chance to hit common draws on the flop and on the turn.
The price comes from a single line of algebra, e = f / (1 + 2f). With f = 1 it returns 33.33%, and flipping it into odds gives 2 : 1.
Nothing is added for future bets, and a hit is taken to win the entire pot. The deck is counted as 47 unseen cards on the flop and 46 on the turn, each equally likely to come.
Method: the closed form f / (1 + 2f) computed by the GeorgeLiPoker math library, with draw chances counted from the unseen cards.
Updated
Questions
What equity do you need to call a pot-size bet?
Against a bet of the full pot you need 33.33%. The math is f / (1 + 2f) with f = 1, and it matches the dollar check: $100 over $300. Anything above 33.33% equity makes the call profitable.
How many outs do you need against a pot-size bet?
The line is 9 outs on the flop, where you hit 34.97% by the river. On the turn you need 16 outs. Fewer outs than that fall below 33.33%, so the call needs help from implied odds.
How much do implied odds help against a pot-size bet?
They can swing a close call. Going from 33.33% with no future winnings to 12.50% with $500 is a change of 20.83 points, so a draw that is just short may become a call when stacks are deep.
Can you call a pot-size bet with a flush draw?
Nine outs is the usual count for a flush draw. On the flop its chance to hit by the river is 34.97%, which is above 33.33%, so it is a call. On the turn the chance is 19.57%, which is below 33.33%, so it is a fold. The decision can move with implied odds, so look at the stacks.
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