Chance to hit on the river
13.04%
6 outs, one card to come
- Odds against6.67 : 1
- Rule of 2 estimate-1.04 points from the exact chance12%
- Unseen cards46
The count behind 6 outs on the turn
A 13.04% chance is the kind of figure that makes bet size the whole question. A small bet can be called, a large one cannot, and the bets section below puts a number on the line.
- Unseen cards46
- Your outs6
- Cards that miss40
- Chance on the river13.04%
- Chance on the next card (the river)13.04%
- Odds against hitting6.67 : 1
- Estimate from the rule of 212%
- Error of the rule of 2-1.04 points
Chance on the river = k / u, with u = 46 unseen cardsFor 6 outs: 6 / 46 = 13.04%
The river is the last card, so the by-the-river chance and the next-card chance are the same number. For 6 outs it is 6 / 46, or 13.04%.
The true chance is 13.04%, which beats the 12% that the rule of 2 reports by 1.04 points.
The adjusted rule only applies from the flop above 8 outs, so 6 outs on the turn use the plain rule of 2: 2 x 6 = 12%.
Which holding has 6 outs?
Which hand has exactly 6 outs? Think of two overcards. That holding is the usual way to reach this count.
An out that also completes a better hand for a rival is a poor out. With one shared out among your 6 outs, the chance on the river falls from 13.04% to 10.87%, a loss of 2.17 points.
| Shared outs | Effective outs | Chance on the river | Chance given up |
|---|---|---|---|
| 0 | 6 | 13.04% | 0.00 points |
| 1 | 5 | 10.87% | 2.17 points |
| 2 | 4 | 8.70% | 4.35 points |
| 3 | 3 | 6.52% | 6.52 points |
The bets 6 outs can call on the turn
The table prices every bet against 13.04%. Margin is your chance minus the equity a call needs, and no bet size is a call.
Your 13.04% stretches to a bet of 17.65% of the pot. Put in dollars, that is $17.65 when the pot holds $100.
| Bet size | Equity a call needs | Margin over it | Verdict |
|---|---|---|---|
| 1/4 pot | 16.67% | -3.62 points | Fold |
| 1/3 pot | 20.00% | -6.96 points | Fold |
| 2/5 pot | 22.22% | -9.18 points | Fold |
| 1/2 pot | 25.00% | -11.96 points | Fold |
| 2/3 pot | 28.57% | -15.53 points | Fold |
| 3/4 pot | 30.00% | -16.96 points | Fold |
| full pot | 33.33% | -20.29 points | Fold |
| 1.25x pot | 35.71% | -22.67 points | Fold |
| 1.5x pot | 37.50% | -24.46 points | Fold |
| 2x pot | 40.00% | -26.96 points | Fold |
| 3x pot | 42.86% | -29.81 points | Fold |
| 4x pot | 44.44% | -31.40 points | Fold |
Nearby counts on both streets
Compare 6 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.
- 6 outs on the flop: 24.14% by the river.
- 5 outs on the turn: 10.87% on the river.
- 7 outs on the turn: 15.22% on the river.
The river is the last card
The turn call buys the last card. 13.04% is the chance, 25.00% is the price of a half-pot bet, and the margin of -11.96 points gives 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 6 outs that is 6 / 46 = 13.04%. The next card is the river, so both chances are the same.
The rule of 2 figure is 2 x k, here 12%, and its error is that figure minus the exact chance in percentage points, here -1.04 points.
The count covers every card you cannot see. All 46 unseen cards stay in it, the call is paid in full, and the pot is $100 before the bet, so the verdicts are a plain price check.
Computed from the closed form by the GeorgeLiPoker math library.
Updated
Questions
Out of 100 hands, how many hit with 6 outs on the turn?
With 6 outs on the turn you hit on the river 13.04% of the time, about 13 of every 100 hands, because 6 of the 46 unseen cards are outs. The odds against are 6.67 : 1.
Is the rule of 2 close enough for 6 outs?
The rule of 2 gives 12% for 6 outs against an exact 13.04%, an error of -1.04 points. The shortcut sits below the true chance, so the exact figure is better for you.
Are 6 outs on the turn enough to call a half-pot bet?
At 13.04% on the river, you can call none of the 12 bet sizes. A half-pot bet needs 25.00%, a margin of -11.96 points, so against half the pot the verdict is Fold. The largest bet you can call is 17.65% of the pot, or $17.65 on a $100 pot.
What if some of my 6 outs also help a better hand?
Take them off the count first. With one shared out the chance on the river falls from 13.04% to 10.87%, and with 3 shared it falls to 6.52%, a loss of 6.52 points. The effective count is then 3 outs.
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