Verdict
Call
10 outs, flop, half-pot bet
- Chance to hit by the rivertwo cards to come38.39%
- Equity the call needs$50 into a pot of $20025.00%
- Margin over the priceyour chance minus the price+13.39 points
What the numbers say
The price is 25.00% and your chance is 38.39%. You sit 13.39 points above the line, which is a wide gap, so you call.
Few single draws land on exactly 10 outs, so add up each way to improve and check the total. One card hits 21.28% of the time here.
The same spot in dollars
- Pot before the bet$100
- Your opponent bets$50
- Your call$50
- Final pot if you call$200
- What a hit wins$150
- Loss on a miss$50
- Probability of a hit38.39%
- Expected value of calling+$26.78
- Equity the call needs25.00%
- Unrounded margin+13.3904 points
- Outs that exactly reach the price6.23 outs
- Outs above the price+3.77 outs
With no more betting, the whole pot won on a hit and the call lost on a miss, the call gains $26.78 on average. The hit side averages $57.59, the miss side $30.80, and each dollar called returns +0.536.
As odds, 1.6 : 1 against hitting meets pot odds of 3 : 1.
Watch the pot you divide by. Leaving your call out turns 25.00% into 33.33%, and the margin into +5.0570 points. Dividing by the starting pot gives 50.00% and a margin of -11.6096 points, further from the truth.
How much room the call has
The fewest outs that still call a half-pot bet on the flop is 7. You hold 10, so you have 3 outs to spare before the call flips to a fold.
If hitting means paying off a bigger hand later, the call survives a loss of $69.76. That is 1.40 times the $50 call.
| Given back later | Price with it | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 25.00% | +13.39 points | +$26.78 | Call |
| $10 | 26.32% | +12.07 points | +$22.94 | Call |
| $25 | 28.57% | +9.82 points | +$17.18 | Call |
| $50 | 33.33% | +5.06 points | +$7.59 | Call |
| $100 | 50.00% | -11.61 points | -$11.61 | Fold |
Two views of the same draw
Same draw, two answers. Count both cards and the chance is 38.39%, a call; count just the next card and it is 21.28%, a fold. The price in both cases is 25.00%.
| Cards counted | Chance | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| By the river, two cards | 38.39% | +13.3904 points | +$26.78 | Call |
| Next card only | 21.28% | -3.7234 points | -$7.45 | Fold |
Counts close to yours
How fast does the margin move? About 3.33 points per out on the flop. The rows below keep the half-pot bet fixed and change only the outs.
Changing the bet, keeping the draw
Look down the margin column to see where the draw stops paying. Every row uses 10 outs on the flop and a bet of a different size.
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, this page | 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 | 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
Everything is computed from the closed form. Pairs without an out: 666 of 1,081. The rest, 38.39%, hold at least one out.
Read the verdict with its limits in mind. The call is the full bet, so the break-even equity is $50 / $200 = 25.00%. 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
How should you respond to a half-pot bet on the flop when you hold 10 outs?
By the numbers it is a call. 10 outs on the flop hit 38.39% by the river, a half-pot bet needs 25.00%, and the margin is +13.39 points. That assumes you call the full $50 and no more betting follows, and it values the call at +$26.78 per $100 pot.
What count of outs clears the price of a half-pot bet on the flop?
The threshold is 7 outs. It gives 27.84%, clearing 25.00%, whereas 6 gives only 24.14%. Holding 10 puts you 3 above it, with a chance of 38.39%.
One card or two: which number belongs next to the 25.00% price?
Pick the number that matches the street plan: 38.39% for seeing both cards for one bet, 21.28% for paying card by card. Both face 25.00%, and they lead to call and fold in that order.
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