Chance to hit on the river
41.30%
19 outs, one card to come
- Odds against1.42 : 1
- Rule of 2 estimate-3.30 points from the exact chance38%
- Unseen cards46
The count behind 19 outs on the turn
Plan on the draw landing often: 41.30% on the river is far above the thin draws that need a small bet.
- Unseen cards46
- Your outs19
- Cards that miss27
- Chance on the river41.30%
- Chance on the next card (the river)41.30%
- Odds against hitting1.42 : 1
- Estimate from the rule of 238%
- Error of the rule of 2-3.30 points
Chance on the river = k / u, with u = 46 unseen cardsFor 19 outs: 19 / 46 = 41.30%
No pairs to count here, just 19 helpful cards in a deck of 46 unseen ones. That is 41.30%, with 27 unhelpful cards making up the rest.
38% from the quick rule sits 3.30 points under the true 41.30%, so the shortcut is pessimistic here.
Stay with the rule of 2 for this count: 19 outs times 2 is 38%. The adjusted version is for larger flop counts.
Which holding has 19 outs?
Look at the board and your hand, count each card that helps once, and reach 19. No single named draw has this count by itself.
Suppose up to 3 of your outs also help a stronger hand. The effective count drops to 16, and the chance on the river drops to 34.78%.
| Shared outs | Effective outs | Chance on the river | Chance given up |
|---|---|---|---|
| 0 | 19 | 41.30% | 0.00 points |
| 1 | 18 | 39.13% | 2.17 points |
| 2 | 17 | 36.96% | 4.35 points |
| 3 | 16 | 34.78% | 6.52 points |
The bets 19 outs can call on the turn
A call is right when your chance beats what the bet asks of you. At 41.30%, that holds for 10 of the 12 bet sizes in the table.
Work the price backward from 41.30% and you find a limit of 237.50% of the pot: $237.50 into a $100 pot.
| Bet size | Equity a call needs | Margin over it | Verdict |
|---|---|---|---|
| 1/4 pot | 16.67% | +24.64 points | Call |
| 1/3 pot | 20.00% | +21.30 points | Call |
| 2/5 pot | 22.22% | +19.08 points | Call |
| 1/2 pot | 25.00% | +16.30 points | Call |
| 2/3 pot | 28.57% | +12.73 points | Call |
| 3/4 pot | 30.00% | +11.30 points | Call |
| full pot | 33.33% | +7.97 points | Call |
| 1.25x pot | 35.71% | +5.59 points | Call |
| 1.5x pot | 37.50% | +3.80 points | Call |
| 2x pot | 40.00% | +1.30 points | Call |
| 3x pot | 42.86% | -1.55 points | Fold |
| 4x pot | 44.44% | -3.14 points | Fold |
Nearby counts on both streets
Adding or losing one out moves the chance by about 2.17 points on the turn. Here are the counts next to 19, with the other street alongside.
- 19 outs on the flop: 65.03% by the river.
- 18 outs on the turn: 39.13% on the river.
- 20 outs on the turn: 43.48% on the river.
The river is the last card
Only the river is left to come, so the price you face now is the price of the last card. 41.30% against 25.00% is +16.30 points for a half-pot bet, and that reads Call.
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 19 outs that is 19 / 46 = 41.30%. The next card is the river, so both chances are the same.
The rule of 2 figure is 2 x k, here 38%, and its error is that figure minus the exact chance in percentage points, here -3.30 points.
Seen as a pure card count, the 46 unseen cards are all equally likely and an opponent's hand removes none of them. Prices use a $100 pot and a call equal to the bet, so the equity needed is the bet over the pot plus two bets.
Computed from the closed form by the GeorgeLiPoker math library.
Updated
Questions
How good is a draw with 19 outs on the turn?
With 19 outs on the turn you hit on the river 41.30% of the time, about 41 of every 100 hands, because 19 of the 46 unseen cards are outs. The odds against are 1.42 : 1.
How far off is the rule of 2 with 19 outs on the turn?
The rule of 2 gives 38% for 19 outs against an exact 41.30%, an error of -3.30 points. The shortcut sits below the true chance, so the exact figure is better for you.
What price can a draw with 19 outs on the turn afford?
At 41.30% on the river, you can call 10 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 Call. The largest bet you can call is 237.50% of the pot, or $237.50 on a $100 pot.
What if some of my 19 outs also help a better hand?
Take them off the count first. With one shared out the chance on the river falls from 41.30% to 39.13%, and with 3 shared it falls to 34.78%, a loss of 6.52 points. The effective count is then 16 outs.
Related pages
Check your own hands against the numbers
Bring a hand you played and we will work through the price, the chance to hit and the decision together.
Book a session