Verdict
Call
10 outs, flop, pot-size bet
- Chance to hit by the rivertwo cards to come38.39%
- Equity the call needs$100 into a pot of $30033.33%
- Margin over the priceyour chance minus the price+5.06 points
Reading the verdict
The odds you are given are better than the odds you need: 33.33% needed, 38.39% held, 5.06 points to spare.
A count of 10 outs is usually the sum of more than one draw. Out of 47 unseen cards, one card helps 21.28% of the time.
One hand, in dollars
- Pot before the bet$100
- Bet$100
- You call$100
- Pot after your call$300
- Net gain when you hit$200
- Loss on a miss$100
- How often you hit38.39%
- Average value of the call+$15.17
- Price of the call33.33%
- Your chance minus the price, unrounded+5.0570 points
- Outs that exactly reach the price8.53 outs
- Outs to spare, exactly+1.47 outs
Over many identical spots, with the whole pot won on every hit, the call lost on every miss and no extra betting, calling gains $15.17 on average. Hits bring in $76.78, misses cost $61.61, and the ratio is +0.152 per dollar called.
As odds, 1.6 : 1 against hitting meets pot odds of 2 : 1.
One easy error is to use 50.00%, the bet over the pot before your call, as the price. The right price is 33.33%, and the mistaken margin would be -11.6096 points.
How safe the call is
The fewest outs that still call a pot-size bet on the flop is 9. You hold 10, so you have 1 out to spare before the call flips to a fold.
If hitting means paying off a bigger hand later, the call survives a loss of $39.52. That is 0.40 times the $100 call.
| Given back later | Price with it | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 33.33% | +5.06 points | +$15.17 | Call |
| $10 | 34.48% | +3.91 points | +$11.33 | Call |
| $25 | 36.36% | +2.03 points | +$5.57 | Call |
| $50 | 40.00% | -1.61 points | -$4.02 | Fold |
| $100 | 50.00% | -11.61 points | -$23.22 | Fold |
One card or two
Here the cards to come matter. Two cards reach 38.39% and point to a call; one card reaches 21.28% and points to a fold. Which one applies depends on whether the turn brings another bet.
| Cards counted | Chance | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| By the river, two cards | 38.39% | +5.0570 points | +$15.17 | Call |
| Next card only | 21.28% | -12.0567 points | -$36.17 | Fold |
Draws around this one
How fast does the margin move? About 3.33 points per out on the flop. The rows below keep the pot-size bet fixed and change only the outs.
Bigger and smaller bets
Bet size sets the price, so the verdict changes as you scan the table. The pot-size bet of this page is marked in the first column.
10 outs stop paying at 1.65 times the pot ($165.34 on a $100 pot). The call holds up against 9 of the 12 bet sizes.
| 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 | 28.57% | +9.82 points | Call |
| three-quarter-pot | 30.00% | +8.39 points | Call |
| pot-size, this page | 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%.
Keep the assumptions in view: a full call ($100 into $300, or 33.33%), the whole pot on a hit, no more betting, and 47 unseen cards that are equally likely. The math does not know what the other player holds.
Computed from the closed form by the GeorgeLiPoker math library.
Updated
Questions
Does the math favor calling a pot-size bet with 10 outs on the flop?
Compare 38.39%, your chance to hit by the river, with 33.33%, the equity a pot-size bet needs. The gap is +5.06 points, so this is a call. In dollars on a $100 pot, the call averages +$15.17 when no more betting follows.
What is the fewest outs that can call a pot-size bet on the flop?
A call starts to work at 9 outs: 34.97% to hit versus 33.33% needed. One out fewer drops the chance to 31.45%. You hold 10, which is 1 more than the minimum.
Which hit chance fits a pot-size bet on the flop?
Match the number to the betting. All-in or checked down: 38.39%. Facing another bet on the turn: 21.28%. The price is 33.33%, so the verdicts are call and fold in that order.
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