Verdict
Call
10 outs, flop, two-thirds-pot bet
- Chance to hit by the rivertwo cards to come38.39%
- Equity the call needs$66.67 into a pot of $233.3328.57%
- Margin over the priceyour chance minus the price+9.82 points
What the numbers say
This is one of the easier spots. 10 outs on the flop reach 38.39% by the river, the two-thirds-pot bet asks for just 28.57%, and the 9.82-point margin favors the call.
Think of 10 outs as a running total of every card that improves you. 10 of the 47 unseen cards qualify, which is 21.28% on one card.
The $100 pot example
- The pot before betting$100
- Size of the bet$66.67
- You call$66.67
- Final pot if you call$233.33
- You can win on a hit$166.67
- You lose on a miss$66.67
- Your chance to hit38.39%
- Expected value of calling+$22.91
- Break-even equity28.57%
- Exact margin over the price+9.8190 points
- Fractional outs at the price7.20 outs
- Outs to spare, exactly+2.80 outs
Stay with simple rules: the whole pot on a hit, the call lost on a miss, no more money in. Under them calling gains $22.91 on average. The hit side averages $63.98, the miss side $41.07, and each dollar called returns +0.344.
Put as odds, the draw is 1.6 : 1 against, and the pot offers 2.5 : 1 for the call.
Watch the pot you divide by. Leaving your call out turns 28.57% into 40.00%, and the margin into -1.6096 points. Dividing by the starting pot gives 66.67% and a margin of -28.2763 points, further from the truth.
Your cushion over the price
With 10 outs you sit 2 outs above the minimum of 8 that a two-thirds-pot bet requires on the flop.
Later betting can cut into the call. You may surrender $59.68, or 0.90 times your call, after a hit and still break even.
| Given back later | Price with it | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 28.57% | +9.82 points | +$22.91 | Call |
| $10 | 29.85% | +8.54 points | +$19.07 | Call |
| $25 | 32.00% | +6.39 points | +$13.31 | Call |
| $50 | 36.36% | +2.03 points | +$3.72 | Call |
| $100 | 50.00% | -11.61 points | -$15.48 | Fold |
The next card against the whole runout
Do not mix up the two chances. 38.39% is for seeing both cards and supports a call; 21.28% is for one card and supports a fold. A second bet makes the one-card view the right one.
| Cards counted | Chance | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| By the river, two cards | 38.39% | +9.8190 points | +$22.91 | Call |
| Next card only | 21.28% | -7.2948 points | -$17.02 | Fold |
The call as outs change
Same bet, same street, different draws. The row for 10 outs is marked, and every out is worth about 3.33 points.
How bet size moves the answer
One draw, 12 bets. Each row gives the equity the call needs, the margin over it, and the verdict for 10 outs on the flop.
The largest bet this draw can call on the flop is 1.65 times the pot ($165.34 on a $100 pot). 10 outs call 9 of the 12 bet sizes listed.
| Bet size | Equity needed | Margin | Verdict |
|---|---|---|---|
| quarter-pot | 16.67% | +21.72 points | Call |
| third-pot | 20.00% | +18.39 points | Call |
| two-fifths-pot | 22.22% | +16.17 points | Call |
| half-pot | 25.00% | +13.39 points | Call |
| two-thirds-pot, this page | 28.57% | +9.82 points | Call |
| three-quarter-pot | 30.00% | +8.39 points | Call |
| pot-size | 33.33% | +5.06 points | Call |
| 1.25x-pot | 35.71% | +2.68 points | Call |
| 1.5x-pot | 37.50% | +0.89 points | Call |
| 2x-pot | 40.00% | -1.61 points | Fold |
| 3x-pot | 42.86% | -4.47 points | Fold |
| 4x-pot | 44.44% | -6.05 points | Fold |
How this is computed
The chance rests on counting, not on a rule of thumb. Blank pairs: 666 out of 1,081; hit chance: 38.39%.
Four assumptions sit behind the verdict: you call the full bet, a hit wins the entire pot, no money goes in after the call, and every one of the 47 unseen cards is equally likely. The price is $66.67 / $233.33 = 28.57%. No card is taken out for what an opponent might hold.
Computed from the closed form by the GeorgeLiPoker math library.
Updated
Questions
Is a call correct with 10 outs against a two-thirds-pot bet on the flop?
Your chance, 38.39%, set against the 28.57% price gives +9.82 points and a call. With a $100 pot, a $66.67 call and no more betting, the average value of the call is +$22.91.
At what count of outs does a two-thirds-pot bet on the flop become a call?
To call a two-thirds-pot bet on the flop you want 8 outs or more. 8 reach 31.45% and 7 reach 27.84%, with 28.57% as the bar. Your 10 outs are 2 over.
When is the next-card chance the better comparison?
It depends on what follows. If the hand ends here, count both cards: 38.39%. If another bet is coming on the turn, count one card: 21.28%. Compared with 28.57%, that is a call in the first case and a fold in the second.
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