Chance to hit on the river
26.09%
12 outs, one card to come
- Odds against2.83 : 1
- Rule of 2 estimate-2.09 points from the exact chance24%
- Unseen cards46
The count behind 12 outs on the turn
This is a respectable draw. Landing on the river 26.09% of the time, you can pay for a bet of up to 54.55% of the pot, and the third section shows the full table.
- Unseen cards46
- Your outs12
- Cards that miss34
- Chance on the river26.09%
- Chance on the next card (the river)26.09%
- Odds against hitting2.83 : 1
- Estimate from the rule of 224%
- Error of the rule of 2-2.09 points
Chance on the river = k / u, with u = 46 unseen cardsFor 12 outs: 12 / 46 = 26.09%
One card is left to come out of 46 unseen. 12 of them are outs and 34 miss, so the chance is 12 divided by 46, which is 26.09%.
The rule of 2 says 24%, which is 2.09 points below the exact 26.09%. At this count the shortcut runs low, so the true draw is better than it suggests.
Here the shortcut is simply 2 per out: 24% in total, with no adjustment at this count.
Which holding has 12 outs?
This count has a familiar home: a flush draw with a gutshot. It is worth knowing, because a quick look at the board often tells you the count.
An out that also completes a better hand for a rival is a poor out. With one shared out among your 12 outs, the chance on the river falls from 26.09% to 23.91%, a loss of 2.17 points.
| Shared outs | Effective outs | Chance on the river | Chance given up |
|---|---|---|---|
| 0 | 12 | 26.09% | 0.00 points |
| 1 | 11 | 23.91% | 2.17 points |
| 2 | 10 | 21.74% | 4.35 points |
| 3 | 9 | 19.57% | 6.52 points |
The bets 12 outs can call on the turn
Each row compares your 26.09% chance with the equity a call needs. You can call 4 of the 12 bet sizes with 12 outs on the turn.
Work the price backward from 26.09% and you find a limit of 54.55% of the pot: $54.55 into a $100 pot.
| Bet size | Equity a call needs | Margin over it | Verdict |
|---|---|---|---|
| 1/4 pot | 16.67% | +9.42 points | Call |
| 1/3 pot | 20.00% | +6.09 points | Call |
| 2/5 pot | 22.22% | +3.86 points | Call |
| 1/2 pot | 25.00% | +1.09 points | Call |
| 2/3 pot | 28.57% | -2.48 points | Fold |
| 3/4 pot | 30.00% | -3.91 points | Fold |
| full pot | 33.33% | -7.25 points | Fold |
| 1.25x pot | 35.71% | -9.63 points | Fold |
| 1.5x pot | 37.50% | -11.41 points | Fold |
| 2x pot | 40.00% | -13.91 points | Fold |
| 3x pot | 42.86% | -16.77 points | Fold |
| 4x pot | 44.44% | -18.36 points | Fold |
Nearby counts on both streets
A single out is worth about 2.17 points here. The table lists the counts around 12 on both streets so you can see how the other street compares.
- 12 outs on the flop: 44.96% by the river.
- 11 outs on the turn: 23.91% on the river.
- 13 outs on the turn: 28.26% on the river.
The river is the last card
With 12 outs and one card to come, a single number answers both questions: 26.09%. Against the 25.00% that a half-pot call needs, the margin is +1.09 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 12 outs that is 12 / 46 = 26.09%. The next card is the river, so both chances are the same.
The rule of 2 figure is 2 x k, here 24%, and its error is that figure minus the exact chance in percentage points, here -2.09 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 should I read the hit chance for 12 outs on the turn?
With 12 outs on the turn you hit on the river 26.09% of the time, about 26 of every 100 hands, because 12 of the 46 unseen cards are outs. The odds against are 2.83 : 1.
What does the rule of 2 say for a count of 12?
The rule of 2 gives 24% for 12 outs against an exact 26.09%, an error of -2.09 points. The shortcut sits below the true chance, so the exact figure is better for you.
How many bet sizes can 12 outs on the turn pay for?
At 26.09% on the river, you can call 4 of the 12 bet sizes. A half-pot bet needs 25.00%, a margin of +1.09 points, so against half the pot the verdict is Call. The largest bet you can call is 54.55% of the pot, or $54.55 on a $100 pot.
Should I count every out when a rival could be drawing too, with 12 outs?
Take them off the count first. With one shared out the chance on the river falls from 26.09% to 23.91%, and with 3 shared it falls to 19.57%, a loss of 6.52 points. The effective count is then 9 outs.
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