Equity a call needs
20.00%
against a third-pot bet
- Pot oddsfor every 1 you call4 : 1
- Bet on a $100 pota third of the pot$33.33
- Pot after your callyou put in $33.33$166.67
The price of a third-pot bet
This is a light price. You get 4 : 1 from the pot, so a bet of a third of the pot costs a draw little to see through.
e = f / (1 + 2f)f = 0.3333 (rounded)e = 0.3333 / (1 + 2 x 0.3333) = 20.00%Pot odds = (1 + 0.3333) / 0.3333 = 4 : 1
Put 4 : 1 next to 20.00% and you have one price in two forms; the call is right when your equity beats it.
A $100 pot facing a third-pot bet
With $100 in the middle, a bet of $33.33 makes the pot $133.33. Calling costs $33.33.
- Pot before the bet$100
- Opponent bets$33.33
- You call$33.33
- Pot after your call$166.67
- You risk$33.33
- You can win$133.33
- Equity needed20.00%
You put in $33.33 and the pot grows to $166.67. Below 20.00% equity the call loses money over time, and above it the call gains.
Which draws can call a third-pot bet
Against a bet of a third of the pot, the line is 20.00%. These rows show who is above it from the flop and who is above it on the turn.
Counting rows rather than outs, 5 of the 8 draws beat 20.00% on the flop, and two overcards is the weakest of them.
Turn count: 2 of 8. A flush draw with a gutshot is the first draw to clear 20.00% on the turn, with 12 outs.
| 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% | -11.58 points | Fold | 4.35% | -15.65 points | Fold |
| One overcard to top pair | 3 | 12.49% | -7.51 points | Fold | 6.52% | -13.48 points | Fold |
| A gutshot straight draw | 4 | 16.47% | -3.53 points | Fold | 8.70% | -11.30 points | Fold |
| Two overcards | 6 | 24.14% | +4.14 points | Call | 13.04% | -6.96 points | Fold |
| An open-ended straight draw | 8 | 31.45% | +11.45 points | Call | 17.39% | -2.61 points | Fold |
| A flush draw | 9 | 34.97% | +14.97 points | Call | 19.57% | -0.43 points | Fold |
| A flush draw with a gutshot | 12 | 44.96% | +24.96 points | Call | 26.09% | +6.09 points | Call |
| A flush draw with an open-ended straight draw | 15 | 54.12% | +34.12 points | Call | 32.61% | +12.61 points | Call |
Implied odds against a third-pot bet
Implied odds count the money you expect to win after you hit. Call it W, and the equity you need becomes C / (T + W), with C = $33.33 and T = $166.67 here.
The last row shows the largest effect: 5.00% instead of 20.00%, so $500 of future winnings takes 15.00 points off the bar.
Using 9 outs on the turn, you hold 19.57%. Break-even asks for $3.70 of future winnings against this third-pot bet.
Be careful with obvious draws. If the board shows the flush and your opponent can fold, the extra money you hoped to win may never come.
Some outs are poisoned: they make your hand, and also make a better one for your opponent. Count those cards at less than full value against a third-pot bet.
| Future winnings W | Pot after call plus W | Equity needed | Change from the plain price | Flush draw margin from the flop |
|---|---|---|---|---|
| $0 | $166.67 | 20.00% | 0.00 points | +14.97 points |
| $50 | $216.67 | 15.38% | -4.62 points | +19.58 points |
| $100 | $266.67 | 12.50% | -7.50 points | +22.47 points |
| $250 | $416.67 | 8.00% | -12.00 points | +26.97 points |
| $500 | $666.67 | 5.00% | -15.00 points | +29.97 points |
Third-pot next to the other sizes
At the next size below, quarter-pot, the equity needed is 16.67%. The gap to 20.00% is 3.33 points.
Step up to a two-fifths-pot bet and the price climbs to 22.22%, which is 2.22 points higher than 20.00%.
- Pot odds facing a quarter-pot bet: Needs 16.67%, 3.33 points less.
- Pot odds facing a two-fifths-pot bet: Needs 22.22%, 2.22 points more.
The outs that justify a call
The line on the flop is 5 outs. At that count you hit 20.35%, above 20.00%.
Once the turn card is out, you need 10 outs to call. That is 21.74%, compared with 19.57% one out lower.
- 5 outs on the flop: 20.35% by the river against 20.00%.
- 10 outs on the turn: 21.74% on the river against 20.00%.
Here are call-or-fold pages for typical draws against a third-pot bet, built on the cut-off counts.
- Flush draw on the flop against a third-pot bet: 9 outs, 34.97% to hit, against 20.00%.
- 5 outs on the flop against a third-pot bet: The cut-off count, 20.35% to hit.
How this is computed
For a $100 pot and a third-pot bet, the page computes your call, the pot after it, the equity you need and the pot odds ratio. Draw chances come from counting unseen cards.
Because the bet and the call are the same amount, the algebra is short: e = B / (P + B + B) = f / (1 + 2f). The value for f = 0.3333 is 20.00%, and the odds are 4 : 1.
The figures assume you call the full bet, no more betting follows, you win the whole pot when you hit, and every unseen card is equally likely. The flop leaves 47 unseen cards and the turn leaves 46.
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 third-pot bet?
You need 20.00% equity. A third-pot bet of $33.33 into $100 means you pay $33.33 to win a pot that ends at $166.67, and $33.33 divided by $166.67 is 20.00%. If your hand wins more often than that, calling pays over time.
How many outs do you need against a third-pot bet?
Two cards to come mean 5 outs are enough: 20.35% beats 20.00%. On the turn you need 10 outs. Keep the count honest, since shared outs shrink your real chance.
How much do implied odds help against a third-pot bet?
Implied odds can help a lot. With $500 of expected future winnings, the equity you need falls from 20.00% to 5.00%. Use a number you can defend, because the extra money only arrives when your opponent pays you off after you hit.
Can you call a third-pot bet with a flush draw?
Check both streets. On the flop its chance to hit by the river is 34.97%, which is above 20.00%, so it is a call. On the turn the chance is 19.57%, which is below 20.00%, so it is a fold. Neither figure includes future winnings, which can tip a close spot.
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