Verdict
Call
11 outs, flop, half-pot bet
- Chance to hit by the rivertwo cards to come41.72%
- Equity the call needs$50 into a pot of $20025.00%
- Margin over the priceyour chance minus the price+16.72 points
The price of the call
With 11 outs on the flop you hit 41.72% of the time by the river, and a half-pot bet only asks for 25.00%. That 16.72-point cushion makes this a clear call.
Few single draws land on exactly 11 outs, so add up each way to improve and check the total. One card hits 23.40% of the time here.
The arithmetic of this call
- Pot before the bet$100
- Size of the bet$50
- Cost to call$50
- Pot after your call$200
- What a hit wins$150
- What a miss costs$50
- Chance to hit by the river41.72%
- Expected value of calling+$33.44
- Equity the call needs25.00%
- Margin, to four decimals+16.7206 points
- Fractional outs at the price6.23 outs
- Margin measured in outs+4.77 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 $33.44 on average. The hit side averages $62.58, the miss side $29.14, and each dollar called returns +0.669.
Written as odds, the pot lays 3 : 1 while the draw is 1.4 : 1 against.
One easy error is to use 33.33%, the bet over the pot before your call, as the price. The right price is 25.00%, and the mistaken margin would be +8.3873 points. The bet over the starting pot, 50.00%, would claim -8.2794 points.
What could go wrong before the call flips
Count how many outs the call needs: 7 reach the 25.00% price, and you have 11. That leaves 4 outs of slack.
If hitting means paying off a bigger hand later, the call survives a loss of $80.16. That is 1.60 times the $50 call.
| Given back later | Price with it | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 25.00% | +16.72 points | +$33.44 | Call |
| $10 | 26.32% | +15.40 points | +$29.27 | Call |
| $25 | 28.57% | +13.15 points | +$23.01 | Call |
| $50 | 33.33% | +8.39 points | +$12.58 | Call |
| $100 | 50.00% | -8.28 points | -$8.28 | Fold |
Two views of the same draw
The two figures land on opposite sides, or on the line. 41.72% gives a call and 23.40% gives a fold against 25.00%, so check whether more betting is likely before you rely on the river number.
| Cards counted | Chance | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| By the river, two cards | 41.72% | +16.7206 points | +$33.44 | Call |
| Next card only | 23.40% | -1.5957 points | -$3.19 | Fold |
Nearby draws
One out can change the answer, so the table lists the counts on either side of 11. Each out adds roughly 3.24 points against the 25.00% price.
Changing the bet, keeping the draw
The same 11 outs on the flop meet a different price at each bet size. The table runs from the smallest bet to the largest, and the row for this page is marked.
With 41.72% to hit, you can call a bet up to 2.52 times the pot ($251.96 on a $100 pot) and no more. That covers 10 of the 12 sizes in the table.
| Bet size | Equity needed | Margin | Verdict |
|---|---|---|---|
| quarter-pot | 16.67% | +25.05 points | Call |
| third-pot | 20.00% | +21.72 points | Call |
| two-fifths-pot | 22.22% | +19.50 points | Call |
| half-pot, this page | 25.00% | +16.72 points | Call |
| two-thirds-pot | 28.57% | +13.15 points | Call |
| three-quarter-pot | 30.00% | +11.72 points | Call |
| pot-size | 33.33% | +8.39 points | Call |
| 1.25x-pot | 35.71% | +6.01 points | Call |
| 1.5x-pot | 37.50% | +4.22 points | Call |
| 2x-pot | 40.00% | +1.72 points | Call |
| 3x-pot | 42.86% | -1.14 points | Fold |
| 4x-pot | 44.44% | -2.72 points | Fold |
How this is computed
Counting is exact: the pairs of unseen cards with no out number 630 out of 1,081, so hitting by the river has chance 41.72%.
These figures describe a clean spot. You pay the whole bet, which costs $50 of a $200 pot (25.00%), collect the whole pot on a hit, meet no more bets, and draw from 47 equally likely cards, with no adjustment for an opponent's hand.
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 11 outs?
By the numbers it is a call. 11 outs on the flop hit 41.72% by the river, a half-pot bet needs 25.00%, and the margin is +16.72 points. That assumes you call the full $50 and no more betting follows, and it values the call at +$33.44 per $100 pot.
What is the minimum number of outs for 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 11 puts you 4 above it, with a chance of 41.72%.
Does it matter whether you count one card or two against a half-pot bet?
Both figures are right for their own situation. 41.72% fits a hand with no more betting, 23.40% fits one where the turn brings a bet, and 25.00% is the price for each, giving a call and a fold.
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