Verdict
Call
14 outs, flop, pot-size bet
- Chance to hit by the rivertwo cards to come51.16%
- Equity the call needs$100 into a pot of $30033.33%
- Margin over the priceyour chance minus the price+17.82 points
What the numbers say
A pot-size bet needs 33.33% equity from the call, and 14 outs on the flop supply 51.16%. Clearing the price by 17.82 points is far from a close decision.
You will reach 14 outs by adding up separate draws. With 47 cards unseen, the next card helps 29.79% of the time.
A $100 pot, step by step
- Starting pot$100
- The bet$100
- Your call$100
- Pot after your call$300
- You can win on a hit$200
- You lose on a miss$100
- Chance to hit by the river51.16%
- Average value of the call+$53.47
- Equity the call needs33.33%
- Unrounded margin+17.8230 points
- Outs at break-even8.53 outs
- Margin measured in outs+5.47 outs
Assume the whole pot goes to you when you hit, the call is lost when you miss, and nothing more is bet. Calling then gains $53.47 on average: $102.31 from hits, minus $48.84 from misses, +0.535 per dollar called.
As odds, 0.95 : 1 against hitting meets pot odds of 2 : 1.
Skipping your own call in the pot gives a price of 50.00% where 33.33% is correct, and a margin of +1.1563 points instead of +17.82 points.
How safe the call is
With 14 outs you sit 5 outs above the minimum of 9 that a pot-size bet requires on the flop.
After a hit you could give back up to $104.52 on later streets, 1.05 times your call, before the call stops paying.
| Given back later | Price with it | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 33.33% | +17.82 points | +$53.47 | Call |
| $10 | 34.48% | +16.67 points | +$48.35 | Call |
| $25 | 36.36% | +14.79 points | +$40.68 | Call |
| $50 | 40.00% | +11.16 points | +$27.89 | Call |
| $100 | 50.00% | +1.16 points | +$2.31 | Call |
Next card or river
The two figures land on opposite sides, or on the line. 51.16% gives a call and 29.79% gives a fold against 33.33%, 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 | 51.16% | +17.8230 points | +$53.47 | Call |
| Next card only | 29.79% | -3.5461 points | -$10.64 | Fold |
Draws around this one
Same bet, same street, different draws. The row for 14 outs is marked, and every out is worth about 2.96 points.
Other bet sizes for this draw
Keep 14 outs and change only the bet. The price rises from the smallest size to the largest, and the pot-size row is marked as this page.
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 | 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, this page | 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 model is deliberately simple: call everything, win everything on a hit, face no more bets, deal from 47 equally likely unseen cards, and ignore an opponent's holding. With the price at $100 / $300 = 33.33%, later streets and shared outs are what change the real answer.
Computed from the closed form by the GeorgeLiPoker math library.
Updated
Questions
Does the math favor calling a pot-size bet with 14 outs on the flop?
The verdict is call. Your chance is 51.16% and the price is 33.33%, which leaves +17.82 points. On a $100 pot with a $100 bet, calling is worth +$53.47 on average if the whole pot is won on a hit and nothing more is bet.
How many outs do you need to call a pot-size bet on the flop?
The threshold is 9 outs. It gives 34.97%, clearing 33.33%, whereas 8 gives only 31.45%. Holding 14 puts you 5 above it, with a chance of 51.16%.
When is the next-card chance the better comparison?
Both figures are right for their own situation. 51.16% fits a hand with no more betting, 29.79% fits one where the turn brings a bet, and 33.33% is the price for each, giving a call and a fold.
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