Chance to hit on the river
21.74%
10 outs, one card to come
- Odds against3.6 : 1
- Rule of 2 estimate-1.74 points from the exact chance20%
- Unseen cards46
The count behind 10 outs on the turn
Between one chance in five and two in five, 21.74% is a draw worth playing when the bet is not oversized.
- Unseen cards46
- Your outs10
- Cards that miss36
- Chance on the river21.74%
- Chance on the next card (the river)21.74%
- Odds against hitting3.6 : 1
- Estimate from the rule of 220%
- Error of the rule of 2-1.74 points
Chance on the river = k / u, with u = 46 unseen cardsFor 10 outs: 10 / 46 = 21.74%
There is only the river to come. Of the 46 cards you have not seen, 10 help, so you land the draw 10 times in 46: 21.74%.
You would sell this draw short by 1.74 points if you stopped at 20%. The exact count is 21.74%.
Leave the adjusted rule for bigger flop draws. With 10 outs on the turn, the plain rule of 2 figure is 20%.
Which holding has 10 outs?
Look at the board and your hand, count each card that helps once, and reach 10. No single named draw has this count by itself.
An out that also completes a better hand for a rival is a poor out. With one shared out among your 10 outs, the chance on the river falls from 21.74% to 19.57%, a loss of 2.17 points.
| Shared outs | Effective outs | Chance on the river | Chance given up |
|---|---|---|---|
| 0 | 10 | 21.74% | 0.00 points |
| 1 | 9 | 19.57% | 2.17 points |
| 2 | 8 | 17.39% | 4.35 points |
| 3 | 7 | 15.22% | 6.52 points |
The bets 10 outs can call on the turn
Each row compares your 21.74% chance with the equity a call needs. You can call 2 of the 12 bet sizes with 10 outs on the turn.
Stated as a share of the pot, the largest bet you can pay is 38.46%. On a $100 pot you can call up to $38.46.
| Bet size | Equity a call needs | Margin over it | Verdict |
|---|---|---|---|
| 1/4 pot | 16.67% | +5.07 points | Call |
| 1/3 pot | 20.00% | +1.74 points | Call |
| 2/5 pot | 22.22% | -0.48 points | Fold |
| 1/2 pot | 25.00% | -3.26 points | Fold |
| 2/3 pot | 28.57% | -6.83 points | Fold |
| 3/4 pot | 30.00% | -8.26 points | Fold |
| full pot | 33.33% | -11.59 points | Fold |
| 1.25x pot | 35.71% | -13.98 points | Fold |
| 1.5x pot | 37.50% | -15.76 points | Fold |
| 2x pot | 40.00% | -18.26 points | Fold |
| 3x pot | 42.86% | -21.12 points | Fold |
| 4x pot | 44.44% | -22.71 points | Fold |
Nearby counts on both streets
Use the rows below to see what the count next door looks like. A step of one out is about 2.17 points on the turn.
- 10 outs on the flop: 38.39% by the river.
- 9 outs on the turn: 19.57% on the river.
- 11 outs on the turn: 23.91% on the river.
The river is the last card
You do not need a second view on the turn. The 21.74% chance is final, and against a half-pot price of 25.00% it leaves -3.26 points: Fold.
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 10 outs that is 10 / 46 = 21.74%. The next card is the river, so both chances are the same.
The rule of 2 figure is 2 x k, here 20%, and its error is that figure minus the exact chance in percentage points, here -1.74 points.
Seen as a pure card count, the 46 unseen cards are all equally likely and an opponent's hand removes none of them. Prices use a $100 pot and a call equal to the bet, so the equity needed is the bet over the pot plus two bets.
Computed from the closed form by the GeorgeLiPoker math library.
Updated
Questions
What percent chance does a count of 10 give you on the turn?
With 10 outs on the turn you hit on the river 21.74% of the time, about 22 of every 100 hands, because 10 of the 46 unseen cards are outs. The odds against are 3.6 : 1.
How accurate is the rule of 2 for 10 outs?
The rule of 2 gives 20% for 10 outs against an exact 21.74%, an error of -1.74 points. The shortcut sits below the true chance, so the exact figure is better for you.
How many bet sizes can 10 outs on the turn pay for?
At 21.74% on the river, you can call 2 of the 12 bet sizes. A half-pot bet needs 25.00%, a margin of -3.26 points, so against half the pot the verdict is Fold. The largest bet you can call is 38.46% of the pot, or $38.46 on a $100 pot.
Should I count every out when a rival could be drawing too, with 10 outs?
Take them off the count first. With one shared out the chance on the river falls from 21.74% to 19.57%, and with 3 shared it falls to 15.22%, a loss of 6.52 points. The effective count is then 7 outs.
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