Chance to hit by the river
24.14%
6 outs, two cards to come
- Chance on the next card12.77%
- Odds against by the river3.14 : 1
- Rule of 4 estimate-0.14 points from the exact chance24%
The count behind 6 outs on the flop
One hit in about 4.1 tries is what 24.14% means. It is neither a favorite nor a long shot, so the bet you face decides the answer.
- Unseen cards47
- Your outs6
- Cards that miss41
- Pairs of cards with no out820
- Pairs with at least one out261
- Chance by the river24.14%
- Chance on the next card12.77%
- Odds against hitting3.14 : 1
- Estimate from the rule of 424%
- Error of the rule of 4-0.14 points
Chance by the river = 1 - C(u - k, 2) / C(u, 2), with u = 47 unseen cardsFor 6 outs: 1 - C(41, 2) / C(47, 2) = 1 - 820 / 1,081 = 24.14%Next card = 6 / 47 = 12.77%
The draw fails only when the turn and the river both miss. That covers 820 of the 1,081 pairs, so it lands in the other 261, or 24.14%.
With 6 outs the rule of 4 stays near the truth: 24% estimated, 24.14% exact, 0.14 points apart.
No adjustment is needed on the flop with 6 outs. The plain rule of 4 gives 4 x 6 = 24%.
Which holding has 6 outs?
Two overcards is the hand to picture here: it has exactly 6 outs, and every figure below applies to it directly.
Use the effective count, not the raw one, when a rival could be drawing too. Losing 3 outs to overlap moves 24.14% down to 12.49%.
| Shared outs | Effective outs | Chance by the river | Chance given up |
|---|---|---|---|
| 0 | 6 | 24.14% | 0.00 points |
| 1 | 5 | 20.35% | 3.79 points |
| 2 | 4 | 16.47% | 7.68 points |
| 3 | 3 | 12.49% | 11.66 points |
The bets 6 outs can call on the flop
Draw the line at 24.14%: any bet that needs less equity than that is a call. Here that covers 3 of the 12 bet sizes.
Break-even for the call falls at a bet of $46.69 into a $100 pot, or 46.69% of the pot. Anything smaller is a call.
| Bet size | Equity a call needs | Margin over it | Verdict |
|---|---|---|---|
| 1/4 pot | 16.67% | +7.48 points | Call |
| 1/3 pot | 20.00% | +4.14 points | Call |
| 2/5 pot | 22.22% | +1.92 points | Call |
| 1/2 pot | 25.00% | -0.86 points | Fold |
| 2/3 pot | 28.57% | -4.43 points | Fold |
| 3/4 pot | 30.00% | -5.86 points | Fold |
| full pot | 33.33% | -9.19 points | Fold |
| 1.25x pot | 35.71% | -11.57 points | Fold |
| 1.5x pot | 37.50% | -13.36 points | Fold |
| 2x pot | 40.00% | -15.86 points | Fold |
| 3x pot | 42.86% | -18.71 points | Fold |
| 4x pot | 44.44% | -20.30 points | Fold |
Nearby counts on both streets
Adding or losing one out moves the chance by about 3.70 points on the flop. Here are the counts next to 6, with the other street alongside.
- 6 outs on the turn: 13.04% on the river.
- 5 outs on the flop: 20.35% by the river.
- 7 outs on the flop: 27.84% by the river.
When a bet buys only one card
Check the one-card case before you call a flop bet. 12.77% against 25.00% is -12.23 points for 6 outs, and that is Fold against a half-pot bet.
Drop to the next-card chance and the number of calls goes from 3 to 0 out of 12.
How this is computed
The chance to hit by the river from the flop is 1 - C(u - k, 2) / C(u, 2), where u = 47 unseen cards and k is your effective outs. For 6 outs that is 1 - 820 / 1,081 = 24.14%. The chance on the next card is k / 47, here 12.77%.
The rule of 4 figure is 4 x k, here 24%, and its error is that figure minus the exact chance in percentage points, here -0.14 points.
The chance counts only the 47 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 6 outs on the flop?
With 6 outs on the flop you hit by the river 24.14% of the time, about 24 of every 100 hands, and on the next card 12.77%. The odds against hitting by the river are 3.14 : 1, since 820 of 1,081 pairs of unseen cards hold no out.
How accurate is the rule of 4 for 6 outs?
The rule of 4 gives 24% for 6 outs against an exact 24.14%, an error of -0.14 points. That is close enough to use at the table.
Are 6 outs on the flop enough to call a half-pot bet?
At 24.14% by the river, you can call 3 of the 12 bet sizes. A half-pot bet needs 25.00%, a margin of -0.86 points, so against half the pot the verdict is Fold. The largest bet you can call is 46.69% of the pot, or $46.69 on a $100 pot.
Should I count every out when a rival could be drawing too, with 6 outs?
Take them off the count first. With one shared out the chance by the river falls from 24.14% to 20.35%, and with 3 shared it falls to 12.49%, a loss of 11.66 points. The effective count is then 3 outs.
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