Verdict
Fold
7 outs, turn, two-thirds-pot bet
- Chance to hit by the riverone card to come15.22%
- Equity the call needs$66.67 into a pot of $233.3328.57%
- Margin over the priceyour chance minus the price-13.35 points
Comparing the draw with the bet
15.22% against 28.57%: the draw trails the price by 13.35 points. On this turn against a two-thirds-pot bet, that is an easy fold.
Think of 7 outs as a running total of every card that improves you. 7 of the 46 unseen cards qualify, which is 15.22% on one card.
Counting the chips on a $100 pot
- The pot before betting$100
- Bet$66.67
- You call$66.67
- Total pot after calling$233.33
- Net gain when you hit$166.67
- Net loss when you miss$66.67
- How often you hit15.22%
- Average value of the call-$31.16
- Price of the call28.57%
- Your chance minus the price, unrounded-13.3540 points
- Break-even count of outs13.14 outs
- Outs above the price-6.14 outs
If you win the whole pot on a hit and lose your call otherwise, with no more betting, calling loses $31.16 on average. Hits add $25.36 on average and misses cost $56.52 on average, or -0.467 per dollar called.
As odds, 5.57 : 1 against hitting meets pot odds of 2.5 : 1.
A common slip is to divide the bet by the pot after the bet but before your call. That gives 40.00% instead of 28.57% and would put your margin at -24.7826 points. Using the bet over the starting pot, 66.67%, is further off and would put it at -51.4493 points.
Implied odds that would change the answer
Think of it as a missing $204.76. When the draw hits you must collect that much beyond the pot for the $66.67 call to pay for itself, 3.07 times your call.
Outs are the other lever. At 14 outs you reach 30.43% by the river, enough for a two-thirds-pot bet, and you are 7 outs away.
| Future winnings | Price with them | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 28.57% | -13.35 points | -$31.16 | Fold |
| $50 | 23.53% | -8.31 points | -$23.55 | Fold |
| $100 | 20.00% | -4.78 points | -$15.94 | Fold |
| $250 | 13.79% | +1.42 points | +$6.88 | Call |
| $500 | 9.09% | +6.13 points | +$44.93 | Call |
The same draw on the flop
Compare the streets. With two cards left, 7 outs hit 27.84% (a fold); with one card left they hit 15.22% (a fold). The difference is 12.63 points.
| Street | Chance by the river | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| Flop, two cards to come | 27.84% | -0.7268 points | -$1.70 | Fold |
| Turn, one card to come | 15.22% | -13.3540 points | -$31.16 | Fold |
How the answer moves with outs
A few outs either way, against a two-thirds-pot bet that needs 28.57%. The chance climbs about 2.17 points with each extra out.
Bigger and smaller bets
Bigger bets ask for more equity while your chance stays at 15.22%. Here is every bet size against the same draw, with the row for this page marked.
Your draw can face a bet of up to 0.22 times the pot ($21.88 on a $100 pot) and still break even. That is under the quarter-pot bet, so none of the 12 sizes is a call.
| Bet size | Equity needed | Margin | Verdict |
|---|---|---|---|
| quarter-pot | 16.67% | -1.45 points | Fold |
| third-pot | 20.00% | -4.78 points | Fold |
| two-fifths-pot | 22.22% | -7.00 points | Fold |
| half-pot | 25.00% | -9.78 points | Fold |
| two-thirds-pot, this page | 28.57% | -13.35 points | Fold |
| three-quarter-pot | 30.00% | -14.78 points | Fold |
| pot-size | 33.33% | -18.12 points | Fold |
| 1.25x-pot | 35.71% | -20.50 points | Fold |
| 1.5x-pot | 37.50% | -22.28 points | Fold |
| 2x-pot | 40.00% | -24.78 points | Fold |
| 3x-pot | 42.86% | -27.64 points | Fold |
| 4x-pot | 44.44% | -29.23 points | Fold |
How this is computed
The number is exact rather than estimated. 7 of the 46 cards that could come are outs, which is 15.22%.
The numbers are a baseline rather than a prediction for one hand. The price is 28.57%, from $66.67 into $233.33, and the chance assumes a whole pot won on a hit, no more betting, 46 equally likely unseen cards, and no cards removed for the other player.
Computed from the closed form by the GeorgeLiPoker math library.
Updated
Questions
Should you call a two-thirds-pot bet with 7 outs on the turn?
By the numbers it is a fold. 7 outs on the turn hit 15.22% by the river, a two-thirds-pot bet needs 28.57%, and the margin is -13.35 points. That assumes you call the full $66.67 and no more betting follows, and it values the call at -$31.16 per $100 pot.
What is the fewest outs that can call a two-thirds-pot bet on the turn?
14 outs is the line. At 14 the chance is 30.43%, enough for 28.57%; one fewer gives 28.26%, which is not. Your 7 outs sit 7 below it on the turn, at 15.22%.
Should you use the chance on the next card or by the river?
The question belongs to the flop. On the turn, 7 outs among 46 cards give 15.22% either way, and against 28.57% that is a fold by 13.35 points.
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