Chance to hit on the river
39.13%
18 outs, one card to come
- Odds against1.56 : 1
- Rule of 2 estimate-3.13 points from the exact chance36%
- Unseen cards46
The count behind 18 outs on the turn
With 39.13% on the river, the draw fails 60.87% of the time and lands the rest. That is enough to call a bet of up to 180.00% of the pot.
- Unseen cards46
- Your outs18
- Cards that miss28
- Chance on the river39.13%
- Chance on the next card (the river)39.13%
- Odds against hitting1.56 : 1
- Estimate from the rule of 236%
- Error of the rule of 2-3.13 points
Chance on the river = k / u, with u = 46 unseen cardsFor 18 outs: 18 / 46 = 39.13%
One card is left to come out of 46 unseen. 18 of them are outs and 28 miss, so the chance is 18 divided by 46, which is 39.13%.
36% from the quick rule sits 3.13 points under the true 39.13%, so the shortcut is pessimistic here.
The adjusted rule only applies from the flop above 8 outs, so 18 outs on the turn use the plain rule of 2: 2 x 18 = 36%.
Which holding has 18 outs?
A count of 18 is a combination, not a textbook draw. Add up the helpful cards from each part of your hand and take away any that repeat.
Suppose up to 3 of your outs also help a stronger hand. The effective count drops to 15, and the chance on the river drops to 32.61%.
| Shared outs | Effective outs | Chance on the river | Chance given up |
|---|---|---|---|
| 0 | 18 | 39.13% | 0.00 points |
| 1 | 17 | 36.96% | 2.17 points |
| 2 | 16 | 34.78% | 4.35 points |
| 3 | 15 | 32.61% | 6.52 points |
The bets 18 outs can call on the turn
Draw the line at 39.13%: any bet that needs less equity than that is a call. Here that covers 9 of the 12 bet sizes.
Your 39.13% stretches to a bet of 180.00% of the pot. Put in dollars, that is $180 when the pot holds $100.
| Bet size | Equity a call needs | Margin over it | Verdict |
|---|---|---|---|
| 1/4 pot | 16.67% | +22.46 points | Call |
| 1/3 pot | 20.00% | +19.13 points | Call |
| 2/5 pot | 22.22% | +16.91 points | Call |
| 1/2 pot | 25.00% | +14.13 points | Call |
| 2/3 pot | 28.57% | +10.56 points | Call |
| 3/4 pot | 30.00% | +9.13 points | Call |
| full pot | 33.33% | +5.80 points | Call |
| 1.25x pot | 35.71% | +3.42 points | Call |
| 1.5x pot | 37.50% | +1.63 points | Call |
| 2x pot | 40.00% | -0.87 points | Fold |
| 3x pot | 42.86% | -3.73 points | Fold |
| 4x pot | 44.44% | -5.31 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 18 on the flop and the turn.
- 18 outs on the flop: 62.44% by the river.
- 17 outs on the turn: 36.96% on the river.
- 19 outs on the turn: 41.30% on the river.
The river is the last card
You do not need a second view on the turn. The 39.13% chance is final, and against a half-pot price of 25.00% it leaves +14.13 points: 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 18 outs that is 18 / 46 = 39.13%. The next card is the river, so both chances are the same.
The rule of 2 figure is 2 x k, here 36%, and its error is that figure minus the exact chance in percentage points, here -3.13 points.
The chance counts only the 46 cards you cannot see, each equally likely. It ignores what an opponent may hold and any money still to be won. Verdicts compare your chance with the bet over the pot plus two bets, on a $100 pot.
Computed from the closed form by the GeorgeLiPoker math library.
Updated
Questions
How good is a draw with 18 outs on the turn?
With 18 outs on the turn you hit on the river 39.13% of the time, about 39 of every 100 hands, because 18 of the 46 unseen cards are outs. The odds against are 1.56 : 1.
Is the rule of 2 close enough for 18 outs?
The rule of 2 gives 36% for 18 outs against an exact 39.13%, an error of -3.13 points. The shortcut sits below the true chance, so the exact figure is better for you.
Do 18 outs on the turn justify a call, and against which bets?
At 39.13% on the river, you can call 9 of the 12 bet sizes. A half-pot bet needs 25.00%, a margin of +14.13 points, so against half the pot the verdict is Call. The largest bet you can call is 180.00% of the pot, or $180 on a $100 pot.
How do I adjust a count of 18 for outs that help an opponent?
Take them off the count first. With one shared out the chance on the river falls from 39.13% to 36.96%, and with 3 shared it falls to 32.61%, a loss of 6.52 points. The effective count is then 15 outs.
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