Chance to hit by the river
51.16%
14 outs, two cards to come
- Chance on the next card29.79%
- Odds against by the river0.95 : 1
- Rule of 4 estimate+4.84 points from the exact chance56%
The count behind 14 outs on the flop
Counts this high behave differently. At 51.16%, the equity a call needs is below your chance for most bet sizes, and sometimes for all of them.
- Unseen cards47
- Your outs14
- Cards that miss33
- Pairs of cards with no out528
- Pairs with at least one out553
- Chance by the river51.16%
- Chance on the next card29.79%
- Odds against hitting0.95 : 1
- Estimate from the rule of 456%
- Error of the rule of 4+4.84 points
- Adjusted rule 4k - (k - 8)50%
- Error of the adjusted rule-1.16 points
Chance by the river = 1 - C(u - k, 2) / C(u, 2), with u = 47 unseen cardsFor 14 outs: 1 - C(33, 2) / C(47, 2) = 1 - 528 / 1,081 = 51.16%Next card = 14 / 47 = 29.79%
Here is the arithmetic for 14 outs. Both cards must miss for the draw to fail: that is 528 pairs out of 1,081. The remaining 553 pairs give you 51.16%.
The quick rule is generous here, by 4.84 points. Use 51.16% when a bet is close to the line.
The adjusted rule 4k - (k - 8) gives 50% for 14 outs, 1.16 points from the exact 51.16%. It trims the shortcut back toward the truth.
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.
Suppose up to 3 of your outs also help a stronger hand. The effective count drops to 11, and the chance by the river drops to 41.72%.
| Shared outs | Effective outs | Chance by the river | Chance given up |
|---|---|---|---|
| 0 | 14 | 51.16% | 0.00 points |
| 1 | 13 | 48.10% | 3.05 points |
| 2 | 12 | 44.96% | 6.20 points |
| 3 | 11 | 41.72% | 9.44 points |
The bets 14 outs can call on the flop
Bet sizes run from 1/4 pot to 4x pot. Against 51.16% by the river, all 12 bet sizes are calls.
The largest bet you can call is any size. At 51.16%, you clear the price of a bet of any number of pots.
| Bet size | Equity a call needs | Margin over it | Verdict |
|---|---|---|---|
| 1/4 pot | 16.67% | +34.49 points | Call |
| 1/3 pot | 20.00% | +31.16 points | Call |
| 2/5 pot | 22.22% | +28.93 points | Call |
| 1/2 pot | 25.00% | +26.16 points | Call |
| 2/3 pot | 28.57% | +22.58 points | Call |
| 3/4 pot | 30.00% | +21.16 points | Call |
| full pot | 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 |
Nearby counts on both streets
Adding or losing one out moves the chance by about 2.96 points on the flop. Here are the counts next to 14, with the other street alongside.
- 14 outs on the turn: 30.43% on the river.
- 13 outs on the flop: 48.10% by the river.
- 15 outs on the flop: 54.12% by the river.
When a bet buys only one card
When another bet is coming on the turn, a call on the flop buys you one card, not two. Your next-card chance is 29.79%, against 25.00% needed to call a half-pot bet, a margin of +4.79 points, so the next-card verdict is Call.
5 of 12 sizes survive the one-card test, where the two-card test passed all 12.
How this is computed
The chance to hit by the river from the flop is 1 - C(u - k, 2) / C(u, 2), where u = 47 unseen cards and k is your effective outs. For 14 outs that is 1 - 528 / 1,081 = 51.16%. The chance on the next card is k / 47, here 29.79%.
The rule of 4 figure is 4 x k, here 56%, and its error is that figure minus the exact chance in percentage points, here +4.84 points. The adjusted rule 4k - (k - 8) gives 50%, an error of -1.16 points.
Assumptions: every unseen card is equally likely, and no card is removed for an opponent's hand, so this is the chance to hit your outs, not your equity against a named hand. A call is paid in full, so the pot after it holds the pot plus two bets. Here the pot is $100.
Computed from the closed form by the GeorgeLiPoker math library.
Updated
Questions
How likely is a hit with 14 outs on the flop?
With 14 outs on the flop you hit by the river 51.16% of the time, about 51 of every 100 hands, and on the next card 29.79%. The odds against hitting by the river are 0.95 : 1, since 528 of 1,081 pairs of unseen cards hold no out.
What does the rule of 4 say for a count of 14?
The rule of 4 gives 56% for 14 outs against an exact 51.16%, an error of +4.84 points, so it overstates the draw. The adjusted rule 4k - (k - 8) gives 50%, an error of -1.16 points, and is the closer figure.
How many bet sizes can 14 outs on the flop pay for?
At 51.16% by the river, you can call all 12 bet sizes. A half-pot bet needs 25.00%, a margin of +26.16 points, so against half the pot the verdict is Call. Any bet size is a call, because 51.16% is above one half.
What is the effective count if some of the 14 outs are shared?
Take them off the count first. With one shared out the chance by the river falls from 51.16% to 48.10%, and with 3 shared it falls to 41.72%, a loss of 9.44 points. The effective count is then 11 outs.
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