Chance to hit by the river
62.44%
18 outs, two cards to come
- Chance on the next card38.30%
- Odds against by the river0.6 : 1
- Rule of 4 estimate+9.56 points from the exact chance72%
The count behind 18 outs on the flop
Plan on the draw landing often: 62.44% by the river is far above the thin draws that need a small bet.
- Unseen cards47
- Your outs18
- Cards that miss29
- Pairs of cards with no out406
- Pairs with at least one out675
- Chance by the river62.44%
- Chance on the next card38.30%
- Odds against hitting0.6 : 1
- Estimate from the rule of 472%
- Error of the rule of 4+9.56 points
- Adjusted rule 4k - (k - 8)62%
- Error of the adjusted rule-0.44 points
Chance by the river = 1 - C(u - k, 2) / C(u, 2), with u = 47 unseen cardsFor 18 outs: 1 - C(29, 2) / C(47, 2) = 1 - 406 / 1,081 = 62.44%Next card = 18 / 47 = 38.30%
Start with the cards you have not seen: 47 of them. 29 of those miss and 18 are outs. Two cards come, so there are 1,081 possible pairs, and 406 of them hold no out at all.
The rule of 4 says 72%, which is 9.56 points above the exact 62.44%. At this size of draw the shortcut runs high enough to matter.
Above 8 outs the adjusted rule applies: 4 x 18 - 10 = 62%. Against 62.44%, it is off by 0.44 points.
Which holding has 18 outs?
Many players never hold this exact count from one draw alone. 18 outs shows up when two draws overlap, once each shared card is counted a single time.
Shared outs are a quiet leak. From 62.44%, a single shared out leaves 59.76%, and 3 of them leave 54.12%.
| Shared outs | Effective outs | Chance by the river | Chance given up |
|---|---|---|---|
| 0 | 18 | 62.44% | 0.00 points |
| 1 | 17 | 59.76% | 2.68 points |
| 2 | 16 | 56.98% | 5.46 points |
| 3 | 15 | 54.12% | 8.33 points |
The bets 18 outs can call on the flop
A call is right when your chance beats what the bet asks of you. At 62.44%, that holds for all 12 bet sizes in the table.
With 62.44% you can call any size of bet. Even an enormous bet only needs a bit under 50% equity, and you hold more than that.
| Bet size | Equity a call needs | Margin over it | Verdict |
|---|---|---|---|
| 1/4 pot | 16.67% | +45.78 points | Call |
| 1/3 pot | 20.00% | +42.44 points | Call |
| 2/5 pot | 22.22% | +40.22 points | Call |
| 1/2 pot | 25.00% | +37.44 points | Call |
| 2/3 pot | 28.57% | +33.87 points | Call |
| 3/4 pot | 30.00% | +32.44 points | Call |
| full pot | 33.33% | +29.11 points | Call |
| 1.25x pot | 35.71% | +26.73 points | Call |
| 1.5x pot | 37.50% | +24.94 points | Call |
| 2x pot | 40.00% | +22.44 points | Call |
| 3x pot | 42.86% | +19.59 points | Call |
| 4x pot | 44.44% | +18.00 points | Call |
Nearby counts on both streets
Adding or losing one out moves the chance by about 2.59 points on the flop. Here are the counts next to 18, with the other street alongside.
- 18 outs on the turn: 39.13% on the river.
- 17 outs on the flop: 59.76% by the river.
- 19 outs on the flop: 65.03% by the river.
When a bet buys only one card
When more betting is still to come, the fair test is the next card alone. 38.30% against the 25.00% that a half-pot call needs is +13.30 points, which reads Call.
The one-card view cuts the bet sizes you can call to 9, from 12 in the table above.
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 18 outs that is 1 - 406 / 1,081 = 62.44%. The chance on the next card is k / 47, here 38.30%.
The rule of 4 figure is 4 x k, here 72%, and its error is that figure minus the exact chance in percentage points, here +9.56 points. The adjusted rule 4k - (k - 8) gives 62%, an error of -0.44 points.
Model notes: every unseen card among the 47 has the same chance of coming, no rival hand is removed, and each bet is matched by one call on a $100 pot, which is the whole amount a hit wins.
Computed from the closed form by the GeorgeLiPoker math library.
Updated
Questions
How likely is a hit with 18 outs on the flop?
With 18 outs on the flop you hit by the river 62.44% of the time, about 62 of every 100 hands, and on the next card 38.30%. The odds against hitting by the river are 0.6 : 1, since 406 of 1,081 pairs of unseen cards hold no out.
What does the rule of 4 say for a count of 18?
The rule of 4 gives 72% for 18 outs against an exact 62.44%, an error of +9.56 points, so it overstates the draw. The adjusted rule 4k - (k - 8) gives 62%, an error of -0.44 points, and is the closer figure.
When should I call or fold with 18 outs on the flop?
At 62.44% by the river, you can call all 12 bet sizes. A half-pot bet needs 25.00%, a margin of +37.44 points, so against half the pot the verdict is Call. Any bet size is a call, because 62.44% is above one half.
How many points do I lose if outs are shared with a better hand?
Take them off the count first. With one shared out the chance by the river falls from 62.44% to 59.76%, and with 3 shared it falls to 54.12%, a loss of 8.33 points. The effective count is then 15 outs.
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