Chance to hit on the river
8.70%
4 outs, one card to come
- Odds against10.5 : 1
- Rule of 2 estimate-0.70 points from the exact chance8%
- Unseen cards46
The count behind 4 outs on the turn
Under one chance in five is thin. 8.70% on the river means the miss is the usual outcome, and the price has to reflect that.
- Unseen cards46
- Your outs4
- Cards that miss42
- Chance on the river8.70%
- Chance on the next card (the river)8.70%
- Odds against hitting10.5 : 1
- Estimate from the rule of 28%
- Error of the rule of 2-0.70 points
Chance on the river = k / u, with u = 46 unseen cardsFor 4 outs: 4 / 46 = 8.70%
No pairs to count here, just 4 helpful cards in a deck of 46 unseen ones. That is 8.70%, with 42 unhelpful cards making up the rest.
Being 0.70 points low, 8% still points the right way, but the exact 8.70% is the number to put against a bet.
2 x 4 = 8% is all the shortcut asks of you with 4 outs on the turn. The adjusted rule is kept for flop counts above 8.
Which holding has 4 outs?
Common holding with this count: a gutshot straight draw. This page tells you how often it gets there.
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 | 4 | 8.70% | 0.00 points |
| 1 | 3 | 6.52% | 2.17 points |
| 2 | 2 | 4.35% | 4.35 points |
| 3 | 1 | 2.17% | 6.52 points |
The bets 4 outs can call on the turn
Each row compares your 8.70% chance with the equity a call needs. You can call none of the 12 bet sizes with 4 outs on the turn.
The line between call and fold is a bet of 10.53% of the pot, or $10.53 on a $100 pot. Stay at or under it and the draw pays for itself.
| Bet size | Equity a call needs | Margin over it | Verdict |
|---|---|---|---|
| 1/4 pot | 16.67% | -7.97 points | Fold |
| 1/3 pot | 20.00% | -11.30 points | Fold |
| 2/5 pot | 22.22% | -13.53 points | Fold |
| 1/2 pot | 25.00% | -16.30 points | Fold |
| 2/3 pot | 28.57% | -19.88 points | Fold |
| 3/4 pot | 30.00% | -21.30 points | Fold |
| full pot | 33.33% | -24.64 points | Fold |
| 1.25x pot | 35.71% | -27.02 points | Fold |
| 1.5x pot | 37.50% | -28.80 points | Fold |
| 2x pot | 40.00% | -31.30 points | Fold |
| 3x pot | 42.86% | -34.16 points | Fold |
| 4x pot | 44.44% | -35.75 points | Fold |
Nearby counts on both streets
Compare 4 outs with the counts on either side. Each step is worth near 2.17 points on the turn, and the other street is shown next to it.
- 4 outs on the flop: 16.47% by the river.
- 3 outs on the turn: 6.52% on the river.
- 5 outs on the turn: 10.87% on the river.
The river is the last card
Nothing is hidden behind a second card here. Your 8.70% is the full draw, and a half-pot bet asks for 25.00%, which makes the verdict 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 4 outs that is 4 / 46 = 8.70%. The next card is the river, so both chances are the same.
The rule of 2 figure is 2 x k, here 8%, and its error is that figure minus the exact chance in percentage points, here -0.70 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 4 outs hit on the turn?
With 4 outs on the turn you hit on the river 8.70% of the time, about 9 of every 100 hands, because 4 of the 46 unseen cards are outs. The odds against are 10.5 : 1.
What is the error of the rule of 2 at 4 outs?
The rule of 2 gives 8% for 4 outs against an exact 8.70%, an error of -0.70 points. The shortcut sits below the true chance, so the exact figure is better for you.
Which bets can 4 outs call on the turn?
At 8.70% on the river, you can call none of the 12 bet sizes. A half-pot bet needs 25.00%, a margin of -16.30 points, so against half the pot the verdict is Fold. The largest bet you can call is 10.53% of the pot, or $10.53 on a $100 pot.
Should I count every out when a rival could be drawing too, with 4 outs?
Take them off the count first. With one shared out the chance on the river falls from 8.70% to 6.52%, and with 3 shared it falls to 2.17%, a loss of 6.52 points. The effective count is then 1 out.
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