Verdict
Call
14 outs, flop, half-pot bet
- Chance to hit by the rivertwo cards to come51.16%
- Equity the call needs$50 into a pot of $20025.00%
- Margin over the priceyour chance minus the price+26.16 points
Chance against price
Pay the half-pot bet and you get a better deal than the draw needs. You need 25.00%, you have 51.16%, and the 26.16-point difference is large.
A count of 14 outs is usually the sum of more than one draw. Out of 47 unseen cards, one card helps 29.79% of the time.
The $100 pot example
- Starting pot$100
- Bet$50
- Cost to call$50
- Pot with your call in$200
- What a hit wins$150
- What a miss costs$50
- Your chance to hit51.16%
- Average value of the call+$52.31
- Break-even equity25.00%
- Exact margin over the price+26.1563 points
- Break-even count of outs6.23 outs
- Your outs minus break-even outs+7.77 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 $52.31 on average. The hit side averages $76.73, the miss side $24.42, and each dollar called returns +1.046.
Written as odds, the pot lays 3 : 1 while the draw is 0.95 : 1 against.
Skipping your own call in the pot gives a price of 33.33% where 25.00% is correct, and a margin of +17.8230 points instead of +26.16 points. The starting pot gives 50.00% and a margin of +1.1563 points, which is wrong by even more.
How safe the call is
With 14 outs you sit 7 outs above the minimum of 7 that a half-pot bet requires on the flop.
The call keeps its edge until you lose $102.26 on later streets after hitting. That is 2.05 times the $50 you pay now.
| Given back later | Price with it | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 25.00% | +26.16 points | +$52.31 | Call |
| $10 | 26.32% | +24.84 points | +$47.20 | Call |
| $25 | 28.57% | +22.58 points | +$39.52 | Call |
| $50 | 33.33% | +17.82 points | +$26.73 | Call |
| $100 | 50.00% | +1.16 points | +$1.16 | Call |
One card or two
Use either number and the verdict is a call. The next card is 29.79%, the full runout is 51.16%, and the price is 25.00%.
| Cards counted | Chance | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| By the river, two cards | 51.16% | +26.1563 points | +$52.31 | Call |
| Next card only | 29.79% | +4.7872 points | +$9.57 | Call |
How the answer moves with outs
One out can change the answer, so the table lists the counts on either side of 14. Each out adds roughly 2.96 points against the 25.00% price.
Where the bet size flips the call
How much does bet size matter? The price climbs from 16.67% to 44.44% across the list, while 14 outs stay at 51.16%.
Your 51.16% chance tops every price in the table, so every bet size is a call: the largest price, 44.44%, is still below it.
| Bet size | Equity needed | Margin | Verdict |
|---|---|---|---|
| quarter-pot | 16.67% | +34.49 points | Call |
| third-pot | 20.00% | +31.16 points | Call |
| two-fifths-pot | 22.22% | +28.93 points | Call |
| half-pot, this page | 25.00% | +26.16 points | Call |
| two-thirds-pot | 28.57% | +22.58 points | Call |
| three-quarter-pot | 30.00% | +21.16 points | Call |
| pot-size | 33.33% | +17.82 points | Call |
| 1.25x-pot | 35.71% | +15.44 points | Call |
| 1.5x-pot | 37.50% | +13.66 points | Call |
| 2x-pot | 40.00% | +11.16 points | Call |
| 3x-pot | 42.86% | +8.30 points | Call |
| 4x-pot | 44.44% | +6.71 points | Call |
How this is computed
No sampling is involved. On the flop there are 1,081 pairs of unseen cards, and 528 of them contain no out, which leaves 51.16% for at least one out.
The price is call / (pot + bet + call), here $50 / $200 = 25.00%, and the margin is your chance minus it. The page assumes you call the whole bet, win the whole pot whenever you hit, and see no more betting. All 47 unseen cards are equally likely and none is removed for an opponent's hand, so this is the chance to hit your outs, not your equity against one hand.
Computed from the closed form by the GeorgeLiPoker math library.
Updated
Questions
Should you call a half-pot bet with 14 outs on the flop?
Math says call. The half-pot bet of $50 needs 25.00% equity, 14 outs on the flop give 51.16%, and the margin is +26.16 points. Assuming a whole pot won on a hit and no further bets, the call is worth +$52.31 on average.
How many outs do you need to call a half-pot bet on the flop?
Look for 7 outs. That is the smallest count whose chance, 27.84%, reaches the 25.00% price; 6 manages 24.14%. You have 14, so you are 7 ahead of the minimum.
Is the by-the-river chance the right one to use on the flop?
Pick the number that matches the street plan: 51.16% for seeing both cards for one bet, 29.79% for paying card by card. Both face 25.00%, and the verdict is call either way.
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