Chance to hit on the river
34.78%
16 outs, one card to come
- Odds against1.88 : 1
- Rule of 2 estimate-2.78 points from the exact chance32%
- Unseen cards46
The count behind 16 outs on the turn
This is a respectable draw. Landing on the river 34.78% of the time, you can pay for a bet of up to 114.29% of the pot, and the third section shows the full table.
- Unseen cards46
- Your outs16
- Cards that miss30
- Chance on the river34.78%
- Chance on the next card (the river)34.78%
- Odds against hitting1.88 : 1
- Estimate from the rule of 232%
- Error of the rule of 2-2.78 points
Chance on the river = k / u, with u = 46 unseen cardsFor 16 outs: 16 / 46 = 34.78%
Divide your outs by the unseen cards: 16 / 46 = 34.78%. The other 30 cards are blanks.
You would sell this draw short by 2.78 points if you stopped at 32%. The exact count is 34.78%.
The adjusted rule only applies from the flop above 8 outs, so 16 outs on the turn use the plain rule of 2: 2 x 16 = 32%.
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.
A shared out has a price: 2.17 points for the first, and 6.52 points in all with 3 shared. Subtract any shared outs before you compare with a bet.
| Shared outs | Effective outs | Chance on the river | Chance given up |
|---|---|---|---|
| 0 | 16 | 34.78% | 0.00 points |
| 1 | 15 | 32.61% | 2.17 points |
| 2 | 14 | 30.43% | 4.35 points |
| 3 | 13 | 28.26% | 6.52 points |
The bets 16 outs can call on the turn
Draw the line at 34.78%: any bet that needs less equity than that is a call. Here that covers 7 of the 12 bet sizes.
Stated as a share of the pot, the largest bet you can pay is 114.29%. On a $100 pot you can call up to $114.29.
| Bet size | Equity a call needs | Margin over it | Verdict |
|---|---|---|---|
| 1/4 pot | 16.67% | +18.12 points | Call |
| 1/3 pot | 20.00% | +14.78 points | Call |
| 2/5 pot | 22.22% | +12.56 points | Call |
| 1/2 pot | 25.00% | +9.78 points | Call |
| 2/3 pot | 28.57% | +6.21 points | Call |
| 3/4 pot | 30.00% | +4.78 points | Call |
| full pot | 33.33% | +1.45 points | Call |
| 1.25x pot | 35.71% | -0.93 points | Fold |
| 1.5x pot | 37.50% | -2.72 points | Fold |
| 2x pot | 40.00% | -5.22 points | Fold |
| 3x pot | 42.86% | -8.07 points | Fold |
| 4x pot | 44.44% | -9.66 points | Fold |
Nearby counts on both streets
If your count is off by one, the chance moves by about 2.17 points. These rows show the counts near 16 on the flop and the turn.
- 16 outs on the flop: 56.98% by the river.
- 15 outs on the turn: 32.61% on the river.
- 17 outs on the turn: 36.96% on the river.
The river is the last card
The turn call buys the last card. 34.78% is the chance, 25.00% is the price of a half-pot bet, and the margin of +9.78 points gives Call.
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 16 outs that is 16 / 46 = 34.78%. The next card is the river, so both chances are the same.
The rule of 2 figure is 2 x k, here 32%, and its error is that figure minus the exact chance in percentage points, here -2.78 points.
Two assumptions sit behind the page. First, all 46 unseen cards are equally likely, with no cards taken out for an opponent. Second, each bet is called in full on a $100 pot, so you pay one bet to play for a pot that holds the pot and both bets.
Computed from the closed form by the GeorgeLiPoker math library.
Updated
Questions
What is the chance to hit with 16 outs on the turn?
With 16 outs on the turn you hit on the river 34.78% of the time, about 35 of every 100 hands, because 16 of the 46 unseen cards are outs. The odds against are 1.88 : 1.
What is the error of the rule of 2 at 16 outs?
The rule of 2 gives 32% for 16 outs against an exact 34.78%, an error of -2.78 points. The shortcut sits below the true chance, so the exact figure is better for you.
What price can a draw with 16 outs on the turn afford?
At 34.78% on the river, you can call 7 of the 12 bet sizes. A half-pot bet needs 25.00%, a margin of +9.78 points, so against half the pot the verdict is Call. The largest bet you can call is 114.29% of the pot, or $114.29 on a $100 pot.
How do I adjust a count of 16 for outs that help an opponent?
Take them off the count first. With one shared out the chance on the river falls from 34.78% to 32.61%, and with 3 shared it falls to 28.26%, a loss of 6.52 points. The effective count is then 13 outs.
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