Chance to hit on the river
30.43%
14 outs, one card to come
- Odds against2.29 : 1
- Rule of 2 estimate-2.43 points from the exact chance28%
- Unseen cards46
The count behind 14 outs on the turn
One hit in about 3.3 tries is what 30.43% means. It is neither a favorite nor a long shot, so the bet you face decides the answer.
- Unseen cards46
- Your outs14
- Cards that miss32
- Chance on the river30.43%
- Chance on the next card (the river)30.43%
- Odds against hitting2.29 : 1
- Estimate from the rule of 228%
- Error of the rule of 2-2.43 points
Chance on the river = k / u, with u = 46 unseen cardsFor 14 outs: 14 / 46 = 30.43%
32 of the 46 unseen cards miss. A single deal picks one of 46 equally likely cards, which lands on an out 14 times in 46, or 30.43%.
The true chance is 30.43%, which beats the 28% that the rule of 2 reports by 2.43 points.
Here the shortcut is simply 2 per out: 28% in total, with no adjustment at this count.
Which holding has 14 outs?
This count has no one textbook draw behind it. It is the total you get after adding up several draws and checking for overlap.
Count carefully: a card that gives you the draw and gives an opponent a better hand should come off the list. One shared out takes the chance down by 2.17 points, to 28.26%.
| Shared outs | Effective outs | Chance on the river | Chance given up |
|---|---|---|---|
| 0 | 14 | 30.43% | 0.00 points |
| 1 | 13 | 28.26% | 2.17 points |
| 2 | 12 | 26.09% | 4.35 points |
| 3 | 11 | 23.91% | 6.52 points |
The bets 14 outs can call on the turn
Each row compares your 30.43% chance with the equity a call needs. You can call 6 of the 12 bet sizes with 14 outs on the turn.
The biggest bet you can call is 77.78% of the pot, which is $77.78 on a $100 pot.
| Bet size | Equity a call needs | Margin over it | Verdict |
|---|---|---|---|
| 1/4 pot | 16.67% | +13.77 points | Call |
| 1/3 pot | 20.00% | +10.43 points | Call |
| 2/5 pot | 22.22% | +8.21 points | Call |
| 1/2 pot | 25.00% | +5.43 points | Call |
| 2/3 pot | 28.57% | +1.86 points | Call |
| 3/4 pot | 30.00% | +0.43 points | Call |
| full pot | 33.33% | -2.90 points | Fold |
| 1.25x pot | 35.71% | -5.28 points | Fold |
| 1.5x pot | 37.50% | -7.07 points | Fold |
| 2x pot | 40.00% | -9.57 points | Fold |
| 3x pot | 42.86% | -12.42 points | Fold |
| 4x pot | 44.44% | -14.01 points | Fold |
Nearby counts on both streets
Neighboring counts help you judge a close draw. One out more or less shifts the chance by roughly 2.17 points on this street.
- 14 outs on the flop: 51.16% by the river.
- 13 outs on the turn: 28.26% on the river.
- 15 outs on the turn: 32.61% on the river.
The river is the last card
With 14 outs and one card to come, a single number answers both questions: 30.43%. Against the 25.00% that a half-pot call needs, the margin is +5.43 points.
How this is computed
The chance to hit on the river from the turn is k / 46, where 46 is the number of unseen cards and k is your effective outs. For 14 outs that is 14 / 46 = 30.43%. The next card is the river, so both chances are the same.
The rule of 2 figure is 2 x k, here 28%, and its error is that figure minus the exact chance in percentage points, here -2.43 points.
Model notes: every unseen card among the 46 has the same chance of coming, no rival hand is removed, and each bet is matched by one call on a $100 pot, which is the whole amount a hit wins.
Computed from the closed form by the GeorgeLiPoker math library.
Updated
Questions
How should I read the hit chance for 14 outs on the turn?
With 14 outs on the turn you hit on the river 30.43% of the time, about 30 of every 100 hands, because 14 of the 46 unseen cards are outs. The odds against are 2.29 : 1.
How accurate is the rule of 2 for 14 outs?
The rule of 2 gives 28% for 14 outs against an exact 30.43%, an error of -2.43 points. The shortcut sits below the true chance, so the exact figure is better for you.
Do 14 outs on the turn justify a call, and against which bets?
At 30.43% on the river, you can call 6 of the 12 bet sizes. A half-pot bet needs 25.00%, a margin of +5.43 points, so against half the pot the verdict is Call. The largest bet you can call is 77.78% of the pot, or $77.78 on a $100 pot.
How do I adjust a count of 14 for outs that help an opponent?
Take them off the count first. With one shared out the chance on the river falls from 30.43% to 28.26%, and with 3 shared it falls to 23.91%, a loss of 6.52 points. The effective count is then 11 outs.
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