Verdict
Call
10 outs, flop, three-quarter-pot bet
- Chance to hit by the rivertwo cards to come38.39%
- Equity the call needs$75 into a pot of $25030.00%
- Margin over the priceyour chance minus the price+8.39 points
Reading the verdict
A three-quarter-pot bet needs 30.00% equity from the call, and 10 outs on the flop supply 38.39%. Clearing the price by 8.39 points is far from a close decision.
10 out of 47 unseen cards is a combined count rather than one named draw, and one card hits 21.28% of the time.
The same spot in dollars
- The pot before betting$100
- Size of the bet$75
- Cost to call$75
- Total pot after calling$250
- Net gain when you hit$175
- What a miss costs$75
- Your chance to hit38.39%
- Average value of the call+$20.98
- Break-even equity30.00%
- Margin, to four decimals+8.3904 points
- Break-even count of outs7.59 outs
- Outs above the price+2.41 outs
If you win the whole pot on a hit and lose your call otherwise, with no more betting, calling gains $20.98 on average. Hits add $67.18 on average and misses cost $46.21 on average, or +0.280 per dollar called.
Odds say the same thing. Hitting is 1.6 : 1 against, and the pot lays 2.33 : 1.
One easy error is to use 42.86%, the bet over the pot before your call, as the price. The right price is 30.00%, and the mistaken margin would be -4.4668 points. The bet over the starting pot, 75.00%, would claim -36.6096 points.
What could go wrong before the call flips
The call survives losing up to 2 outs. At 8 outs the chance is 31.45%, just enough for 30.00%.
Your margin is worth $54.64 in later losses. Past that, 0.73 times your call, folding would have been better.
| Given back later | Price with it | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 30.00% | +8.39 points | +$20.98 | Call |
| $10 | 31.25% | +7.14 points | +$17.14 | Call |
| $25 | 33.33% | +5.06 points | +$11.38 | Call |
| $50 | 37.50% | +0.89 points | +$1.78 | Call |
| $100 | 50.00% | -11.61 points | -$17.41 | Fold |
Pricing one card at a time
38.39% for two cards says call, while 21.28% for one card says fold, both against 30.00%. If you will have to pay again on the turn, trust the one-card number.
| Cards counted | Chance | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| By the river, two cards | 38.39% | +8.3904 points | +$20.98 | Call |
| Next card only | 21.28% | -8.7234 points | -$21.81 | Fold |
One out more or less
Move up or down a few outs and watch the verdict. Every extra out is worth about 3.33 points on the flop, and the price stays at 30.00%.
Where the bet size flips the call
Your 38.39% chance is fixed, so the only thing that moves is the price. The 12 rows below price the call at every bet size on the flop.
Your draw can face a bet of up to 1.65 times the pot ($165.34 on a $100 pot) and still break even. 9 of the 12 sizes fall at or under that line.
| 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, this page | 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 hit chance comes straight from combinations. Out of 1,081 pairs of unseen cards, 666 miss every out, so you hit 38.39% of the time.
Read the verdict with its limits in mind. The call is the full bet, so the break-even equity is $75 / $250 = 30.00%. A hit takes the whole pot, no later betting happens, and the 47 unseen cards are all equally likely, with none removed for an opponent's cards.
Computed from the closed form by the GeorgeLiPoker math library.
Updated
Questions
What is the right play with 10 outs when a three-quarter-pot bet comes on the flop?
Compare 38.39%, your chance to hit by the river, with 30.00%, the equity a three-quarter-pot bet needs. The gap is +8.39 points, so this is a call. In dollars on a $100 pot, the call averages +$20.98 when no more betting follows.
At what count of outs does a three-quarter-pot bet on the flop become a call?
8 outs is the line. At 8 the chance is 31.45%, enough for 30.00%; one fewer gives 27.84%, which is not. Your 10 outs sit 2 above it on the flop, at 38.39%.
Is the by-the-river chance the right one to use on the flop?
Both figures are right for their own situation. 38.39% fits a hand with no more betting, 21.28% fits one where the turn brings a bet, and 30.00% is the price for each, giving a call and a fold.
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