Chance to hit by the river
56.98%
16 outs, two cards to come
- Chance on the next card34.04%
- Odds against by the river0.75 : 1
- Rule of 4 estimate+7.02 points from the exact chance64%
The count behind 16 outs on the flop
Counts this high behave differently. At 56.98%, the equity a call needs is below your chance for most bet sizes, and sometimes for all of them.
- Unseen cards47
- Your outs16
- Cards that miss31
- Pairs of cards with no out465
- Pairs with at least one out616
- Chance by the river56.98%
- Chance on the next card34.04%
- Odds against hitting0.75 : 1
- Estimate from the rule of 464%
- Error of the rule of 4+7.02 points
- Adjusted rule 4k - (k - 8)56%
- Error of the adjusted rule-0.98 points
Chance by the river = 1 - C(u - k, 2) / C(u, 2), with u = 47 unseen cardsFor 16 outs: 1 - C(31, 2) / C(47, 2) = 1 - 465 / 1,081 = 56.98%Next card = 16 / 47 = 34.04%
Work it from the miss side: 465 of 1,081 pairs hold no out, which is 43.02%. The draw lands in the rest, 56.98%.
The quick rule is generous here, by 7.02 points. Use 56.98% when a bet is close to the line.
The fix for a large count is to subtract 8, the number of outs over 8. That moves 64% down to 56%, which is -0.98 points against the exact figure.
Which holding has 16 outs?
No single common draw has exactly 16 outs. A count like this comes from combining draws and removing the cards that count twice.
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 2.87 points, to 54.12%.
| Shared outs | Effective outs | Chance by the river | Chance given up |
|---|---|---|---|
| 0 | 16 | 56.98% | 0.00 points |
| 1 | 15 | 54.12% | 2.87 points |
| 2 | 14 | 51.16% | 5.83 points |
| 3 | 13 | 48.10% | 8.88 points |
The bets 16 outs can call on the flop
Read the table from the top: small bets need little equity, and the requirement climbs with the bet. Your 56.98% clears all 12 bet sizes.
Every row of the table above is a call, and any bigger bet would be one too. At 56.98%, the largest bet you can call is any size.
| Bet size | Equity a call needs | Margin over it | Verdict |
|---|---|---|---|
| 1/4 pot | 16.67% | +40.32 points | Call |
| 1/3 pot | 20.00% | +36.98 points | Call |
| 2/5 pot | 22.22% | +34.76 points | Call |
| 1/2 pot | 25.00% | +31.98 points | Call |
| 2/3 pot | 28.57% | +28.41 points | Call |
| 3/4 pot | 30.00% | +26.98 points | Call |
| full pot | 33.33% | +23.65 points | Call |
| 1.25x pot | 35.71% | +21.27 points | Call |
| 1.5x pot | 37.50% | +19.48 points | Call |
| 2x pot | 40.00% | +16.98 points | Call |
| 3x pot | 42.86% | +14.13 points | Call |
| 4x pot | 44.44% | +12.54 points | Call |
Nearby counts on both streets
Adding or losing one out moves the chance by about 2.78 points on the flop. Here are the counts next to 16, with the other street alongside.
- 16 outs on the turn: 34.78% on the river.
- 15 outs on the flop: 54.12% by the river.
- 17 outs on the flop: 59.76% by the river.
When a bet buys only one card
Check the one-card case before you call a flop bet. 34.04% against 25.00% is +9.04 points for 16 outs, and that is Call against a half-pot bet.
Counting the next card alone, you can call 7 of the 12 bet sizes, compared with all 12 bet sizes when you see both cards.
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 16 outs that is 1 - 465 / 1,081 = 56.98%. The chance on the next card is k / 47, here 34.04%.
The rule of 4 figure is 4 x k, here 64%, and its error is that figure minus the exact chance in percentage points, here +7.02 points. The adjusted rule 4k - (k - 8) gives 56%, an error of -0.98 points.
The model gives every one of the 47 unseen cards the same chance and removes nothing for what a rival holds. It measures hitting an out, not winning the hand. Bets are priced on a $100 pot, and a call adds one bet to the pot.
Computed from the closed form by the GeorgeLiPoker math library.
Updated
Questions
How should I read the hit chance for 16 outs on the flop?
With 16 outs on the flop you hit by the river 56.98% of the time, about 57 of every 100 hands, and on the next card 34.04%. The odds against hitting by the river are 0.75 : 1, since 465 of 1,081 pairs of unseen cards hold no out.
What does the rule of 4 say for a count of 16?
The rule of 4 gives 64% for 16 outs against an exact 56.98%, an error of +7.02 points, so it overstates the draw. The adjusted rule 4k - (k - 8) gives 56%, an error of -0.98 points, and is the closer figure.
Are 16 outs on the flop enough to call a half-pot bet?
At 56.98% by the river, you can call all 12 bet sizes. A half-pot bet needs 25.00%, a margin of +31.98 points, so against half the pot the verdict is Call. Any bet size is a call, because 56.98% is above one half.
What if some of my 16 outs also help a better hand?
Take them off the count first. With one shared out the chance by the river falls from 56.98% to 54.12%, and with 3 shared it falls to 48.10%, a loss of 8.88 points. The effective count is then 13 outs.
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