Chance to hit by the river
65.03%
19 outs, two cards to come
- Chance on the next card40.43%
- Odds against by the river0.54 : 1
- Rule of 4 estimate+10.97 points from the exact chance76%
The count behind 19 outs on the flop
Counts this high behave differently. At 65.03%, the equity a call needs is below your chance for most bet sizes, and sometimes for all of them.
- Unseen cards47
- Your outs19
- Cards that miss28
- Pairs of cards with no out378
- Pairs with at least one out703
- Chance by the river65.03%
- Chance on the next card40.43%
- Odds against hitting0.54 : 1
- Estimate from the rule of 476%
- Error of the rule of 4+10.97 points
- Adjusted rule 4k - (k - 8)65%
- Error of the adjusted rule-0.03 points
Chance by the river = 1 - C(u - k, 2) / C(u, 2), with u = 47 unseen cardsFor 19 outs: 1 - C(28, 2) / C(47, 2) = 1 - 378 / 1,081 = 65.03%Next card = 19 / 47 = 40.43%
Work it from the miss side: 378 of 1,081 pairs hold no out, which is 34.97%. The draw lands in the rest, 65.03%.
A 76% estimate against a true 65.03% is an overstatement of 10.97 points, more than the 2 points that make a shortcut safe to use unchecked.
Above 8 outs the adjusted rule applies: 4 x 19 - 11 = 65%. Against 65.03%, it is off by 0.03 points.
Which holding has 19 outs?
A count of 19 is a combination, not a textbook draw. Add up the helpful cards from each part of your hand and take away any that repeat.
Use the effective count, not the raw one, when a rival could be drawing too. Losing 3 outs to overlap moves 65.03% down to 56.98%.
| Shared outs | Effective outs | Chance by the river | Chance given up |
|---|---|---|---|
| 0 | 19 | 65.03% | 0.00 points |
| 1 | 18 | 62.44% | 2.59 points |
| 2 | 17 | 59.76% | 5.27 points |
| 3 | 16 | 56.98% | 8.05 points |
The bets 19 outs can call on the flop
Read the table from the top: small bets need little equity, and the requirement climbs with the bet. Your 65.03% clears all 12 bet sizes.
No bet size beats 65.03%. The equity a call needs climbs toward one half as bets grow but never gets there, so the answer is any size.
| Bet size | Equity a call needs | Margin over it | Verdict |
|---|---|---|---|
| 1/4 pot | 16.67% | +48.37 points | Call |
| 1/3 pot | 20.00% | +45.03 points | Call |
| 2/5 pot | 22.22% | +42.81 points | Call |
| 1/2 pot | 25.00% | +40.03 points | Call |
| 2/3 pot | 28.57% | +36.46 points | Call |
| 3/4 pot | 30.00% | +35.03 points | Call |
| full pot | 33.33% | +31.70 points | Call |
| 1.25x pot | 35.71% | +29.32 points | Call |
| 1.5x pot | 37.50% | +27.53 points | Call |
| 2x pot | 40.00% | +25.03 points | Call |
| 3x pot | 42.86% | +22.18 points | Call |
| 4x pot | 44.44% | +20.59 points | Call |
Nearby counts on both streets
Neighboring counts help you judge a close draw. One out more or less shifts the chance by roughly 2.50 points on this street.
- 19 outs on the turn: 41.30% on the river.
- 18 outs on the flop: 62.44% by the river.
- 20 outs on the flop: 67.53% by the river.
When a bet buys only one card
Two views, one draw: 65.03% if you see both cards and 40.43% if you see one. Against 25.00%, the one-card view has a margin of +15.43 points and reads Call.
Only 10 bet sizes stay calls on the next card alone, against 12 on the two-card figure.
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 19 outs that is 1 - 378 / 1,081 = 65.03%. The chance on the next card is k / 47, here 40.43%.
The rule of 4 figure is 4 x k, here 76%, and its error is that figure minus the exact chance in percentage points, here +10.97 points. The adjusted rule 4k - (k - 8) gives 65%, an error of -0.03 points.
The count covers every card you cannot see. All 47 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
How should I read the hit chance for 19 outs on the flop?
With 19 outs on the flop you hit by the river 65.03% of the time, about 65 of every 100 hands, and on the next card 40.43%. The odds against hitting by the river are 0.54 : 1, since 378 of 1,081 pairs of unseen cards hold no out.
What number does the rule of 4 give for 19 outs, and is it right?
The rule of 4 gives 76% for 19 outs against an exact 65.03%, an error of +10.97 points, so it overstates the draw. The adjusted rule 4k - (k - 8) gives 65%, an error of -0.03 points, and is the closer figure.
Which bets can 19 outs call on the flop?
At 65.03% by the river, you can call all 12 bet sizes. A half-pot bet needs 25.00%, a margin of +40.03 points, so against half the pot the verdict is Call. Any bet size is a call, because 65.03% is above one half.
What is the effective count if some of the 19 outs are shared?
Take them off the count first. With one shared out the chance by the river falls from 65.03% to 62.44%, and with 3 shared it falls to 56.98%, a loss of 8.05 points. The effective count is then 16 outs.
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