Chance to hit on the river
36.96%
17 outs, one card to come
- Odds against1.71 : 1
- Rule of 2 estimate-2.96 points from the exact chance34%
- Unseen cards46
The count behind 17 outs on the turn
Between one chance in five and two in five, 36.96% is a draw worth playing when the bet is not oversized.
- Unseen cards46
- Your outs17
- Cards that miss29
- Chance on the river36.96%
- Chance on the next card (the river)36.96%
- Odds against hitting1.71 : 1
- Estimate from the rule of 234%
- Error of the rule of 2-2.96 points
Chance on the river = k / u, with u = 46 unseen cardsFor 17 outs: 17 / 46 = 36.96%
Divide your outs by the unseen cards: 17 / 46 = 36.96%. The other 29 cards are blanks.
Being 2.96 points low, 34% still points the right way, but the exact 36.96% is the number to put against a bet.
Here the shortcut is simply 2 per out: 34% in total, with no adjustment at this count.
Which holding has 17 outs?
You will not find a standard named draw for this number. Reach 17 by adding the outs of separate draws and subtracting any card that appears in both.
Shared outs are a quiet leak. From 36.96%, a single shared out leaves 34.78%, and 3 of them leave 30.43%.
| Shared outs | Effective outs | Chance on the river | Chance given up |
|---|---|---|---|
| 0 | 17 | 36.96% | 0.00 points |
| 1 | 16 | 34.78% | 2.17 points |
| 2 | 15 | 32.61% | 4.35 points |
| 3 | 14 | 30.43% | 6.52 points |
The bets 17 outs can call on the turn
Read the table from the top: small bets need little equity, and the requirement climbs with the bet. Your 36.96% clears 8 of the 12 bet sizes.
The line between call and fold is a bet of 141.67% of the pot, or $141.67 on a $100 pot. Stay at or under it and the draw pays for itself.
| Bet size | Equity a call needs | Margin over it | Verdict |
|---|---|---|---|
| 1/4 pot | 16.67% | +20.29 points | Call |
| 1/3 pot | 20.00% | +16.96 points | Call |
| 2/5 pot | 22.22% | +14.73 points | Call |
| 1/2 pot | 25.00% | +11.96 points | Call |
| 2/3 pot | 28.57% | +8.39 points | Call |
| 3/4 pot | 30.00% | +6.96 points | Call |
| full pot | 33.33% | +3.62 points | Call |
| 1.25x pot | 35.71% | +1.24 points | Call |
| 1.5x pot | 37.50% | -0.54 points | Fold |
| 2x pot | 40.00% | -3.04 points | Fold |
| 3x pot | 42.86% | -5.90 points | Fold |
| 4x pot | 44.44% | -7.49 points | Fold |
Nearby counts on both streets
Not sure whether to count one more out? It changes the chance by about 2.17 points. The table shows both streets for the counts around 17.
- 17 outs on the flop: 59.76% by the river.
- 16 outs on the turn: 34.78% on the river.
- 18 outs on the turn: 39.13% on the river.
The river is the last card
You do not need a second view on the turn. The 36.96% chance is final, and against a half-pot price of 25.00% it leaves +11.96 points: 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 17 outs that is 17 / 46 = 36.96%. The next card is the river, so both chances are the same.
The rule of 2 figure is 2 x k, here 34%, and its error is that figure minus the exact chance in percentage points, here -2.96 points.
Read the figures as a card count. All 46 unseen cards stay in, including any your opponent holds, so the figures describe your outs, not a matchup. Bets are called in full against a $100 pot with no extra money assumed.
Computed from the closed form by the GeorgeLiPoker math library.
Updated
Questions
How often do 17 outs hit on the turn?
With 17 outs on the turn you hit on the river 36.96% of the time, about 37 of every 100 hands, because 17 of the 46 unseen cards are outs. The odds against are 1.71 : 1.
How far off is the rule of 2 with 17 outs on the turn?
The rule of 2 gives 34% for 17 outs against an exact 36.96%, an error of -2.96 points. The shortcut sits below the true chance, so the exact figure is better for you.
Do 17 outs on the turn justify a call, and against which bets?
At 36.96% on the river, you can call 8 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 Call. The largest bet you can call is 141.67% of the pot, or $141.67 on a $100 pot.
What is the effective count if some of the 17 outs are shared?
Take them off the count first. With one shared out the chance on the river falls from 36.96% to 34.78%, and with 3 shared it falls to 30.43%, a loss of 6.52 points. The effective count is then 14 outs.
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