Chance to hit on the river
17.39%
8 outs, one card to come
- Odds against4.75 : 1
- Rule of 2 estimate-1.39 points from the exact chance16%
- Unseen cards46
The count behind 8 outs on the turn
Think of 17.39% as a long shot that pays when the price is right. At 4.75 : 1 against, you need the pot to be laying a generous price.
- Unseen cards46
- Your outs8
- Cards that miss38
- Chance on the river17.39%
- Chance on the next card (the river)17.39%
- Odds against hitting4.75 : 1
- Estimate from the rule of 216%
- Error of the rule of 2-1.39 points
Chance on the river = k / u, with u = 46 unseen cardsFor 8 outs: 8 / 46 = 17.39%
One card is left to come out of 46 unseen. 8 of them are outs and 38 miss, so the chance is 8 divided by 46, which is 17.39%.
16% from the quick rule sits 1.39 points under the true 17.39%, so the shortcut is pessimistic here.
Leave the adjusted rule for bigger flop draws. With 8 outs on the turn, the plain rule of 2 figure is 16%.
Which holding has 8 outs?
This count has a familiar home: an open-ended straight draw. It is worth knowing, because a quick look at the board often tells you the count.
Use the effective count, not the raw one, when a rival could be drawing too. Losing 3 outs to overlap moves 17.39% down to 10.87%.
| Shared outs | Effective outs | Chance on the river | Chance given up |
|---|---|---|---|
| 0 | 8 | 17.39% | 0.00 points |
| 1 | 7 | 15.22% | 2.17 points |
| 2 | 6 | 13.04% | 4.35 points |
| 3 | 5 | 10.87% | 6.52 points |
The bets 8 outs can call on the turn
Read the table from the top: small bets need little equity, and the requirement climbs with the bet. Your 17.39% clears 1 of the 12 bet sizes.
Past 26.67% of the pot, the price beats your 17.39%. On a $100 pot that line is $26.67.
| Bet size | Equity a call needs | Margin over it | Verdict |
|---|---|---|---|
| 1/4 pot | 16.67% | +0.72 points | Call |
| 1/3 pot | 20.00% | -2.61 points | Fold |
| 2/5 pot | 22.22% | -4.83 points | Fold |
| 1/2 pot | 25.00% | -7.61 points | Fold |
| 2/3 pot | 28.57% | -11.18 points | Fold |
| 3/4 pot | 30.00% | -12.61 points | Fold |
| full pot | 33.33% | -15.94 points | Fold |
| 1.25x pot | 35.71% | -18.32 points | Fold |
| 1.5x pot | 37.50% | -20.11 points | Fold |
| 2x pot | 40.00% | -22.61 points | Fold |
| 3x pot | 42.86% | -25.47 points | Fold |
| 4x pot | 44.44% | -27.05 points | Fold |
Nearby counts on both streets
Not sure whether to count one more out? It changes the chance by about 2.17 points. The table shows both streets for the counts around 8.
- 8 outs on the flop: 31.45% by the river.
- 7 outs on the turn: 15.22% on the river.
- 9 outs on the turn: 19.57% on the river.
The river is the last card
With 8 outs and one card to come, a single number answers both questions: 17.39%. Against the 25.00% that a half-pot call needs, the margin is -7.61 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 8 outs that is 8 / 46 = 17.39%. The next card is the river, so both chances are the same.
The rule of 2 figure is 2 x k, here 16%, and its error is that figure minus the exact chance in percentage points, here -1.39 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
How often do 8 outs hit on the turn?
With 8 outs on the turn you hit on the river 17.39% of the time, about 17 of every 100 hands, because 8 of the 46 unseen cards are outs. The odds against are 4.75 : 1.
How does the quick rule compare with the exact chance for 8 outs?
The rule of 2 gives 16% for 8 outs against an exact 17.39%, an error of -1.39 points. The shortcut sits below the true chance, so the exact figure is better for you.
How many bet sizes can 8 outs on the turn pay for?
At 17.39% on the river, you can call 1 of the 12 bet sizes. A half-pot bet needs 25.00%, a margin of -7.61 points, so against half the pot the verdict is Fold. The largest bet you can call is 26.67% of the pot, or $26.67 on a $100 pot.
Does every one of the 8 outs count in full on the turn?
Take them off the count first. With one shared out the chance on the river falls from 17.39% to 15.22%, and with 3 shared it falls to 10.87%, a loss of 6.52 points. The effective count is then 5 outs.
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