Chance to hit on the river
15.22%
7 outs, one card to come
- Odds against5.57 : 1
- Rule of 2 estimate-1.22 points from the exact chance14%
- Unseen cards46
The count behind 7 outs on the turn
Under one chance in five is thin. 15.22% on the river means the miss is the usual outcome, and the price has to reflect that.
- Unseen cards46
- Your outs7
- Cards that miss39
- Chance on the river15.22%
- Chance on the next card (the river)15.22%
- Odds against hitting5.57 : 1
- Estimate from the rule of 214%
- Error of the rule of 2-1.22 points
Chance on the river = k / u, with u = 46 unseen cardsFor 7 outs: 7 / 46 = 15.22%
Divide your outs by the unseen cards: 7 / 46 = 15.22%. The other 39 cards are blanks.
The rule of 2 says 14%, which is 1.22 points below the exact 15.22%. At this count the shortcut runs low, so the true draw is better than it suggests.
Leave the adjusted rule for bigger flop draws. With 7 outs on the turn, the plain rule of 2 figure is 14%.
Which holding has 7 outs?
Look at the board and your hand, count each card that helps once, and reach 7. No single named draw has this count by itself.
Shared outs are a quiet leak. From 15.22%, a single shared out leaves 13.04%, and 3 of them leave 8.70%.
| Shared outs | Effective outs | Chance on the river | Chance given up |
|---|---|---|---|
| 0 | 7 | 15.22% | 0.00 points |
| 1 | 6 | 13.04% | 2.17 points |
| 2 | 5 | 10.87% | 4.35 points |
| 3 | 4 | 8.70% | 6.52 points |
The bets 7 outs can call on the turn
A call is right when your chance beats what the bet asks of you. At 15.22%, that holds for none of the 12 bet sizes in the table.
The biggest bet you can call is 21.88% of the pot, which is $21.88 on a $100 pot.
| Bet size | Equity a call needs | Margin over it | Verdict |
|---|---|---|---|
| 1/4 pot | 16.67% | -1.45 points | Fold |
| 1/3 pot | 20.00% | -4.78 points | Fold |
| 2/5 pot | 22.22% | -7.00 points | Fold |
| 1/2 pot | 25.00% | -9.78 points | Fold |
| 2/3 pot | 28.57% | -13.35 points | Fold |
| 3/4 pot | 30.00% | -14.78 points | Fold |
| full pot | 33.33% | -18.12 points | Fold |
| 1.25x pot | 35.71% | -20.50 points | Fold |
| 1.5x pot | 37.50% | -22.28 points | Fold |
| 2x pot | 40.00% | -24.78 points | Fold |
| 3x pot | 42.86% | -27.64 points | Fold |
| 4x pot | 44.44% | -29.23 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 7.
- 7 outs on the flop: 27.84% by the river.
- 6 outs on the turn: 13.04% on the river.
- 8 outs on the turn: 17.39% on the river.
The river is the last card
One card remains, so the next-card and by-the-river figures match at 15.22%. Facing half the pot, you need 25.00% and hold a margin of -9.78 points, which is Fold.
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 7 outs that is 7 / 46 = 15.22%. The next card is the river, so both chances are the same.
The rule of 2 figure is 2 x k, here 14%, and its error is that figure minus the exact chance in percentage points, here -1.22 points.
Two assumptions sit behind the page. First, all 46 unseen cards are equally likely, with no cards taken out for an opponent. Second, each bet is called in full on a $100 pot, so you pay one bet to play for a pot that holds the pot and both bets.
Computed from the closed form by the GeorgeLiPoker math library.
Updated
Questions
What are the odds of hitting with 7 outs on the turn?
With 7 outs on the turn you hit on the river 15.22% of the time, about 15 of every 100 hands, because 7 of the 46 unseen cards are outs. The odds against are 5.57 : 1.
What does the rule of 2 say for a count of 7?
The rule of 2 gives 14% for 7 outs against an exact 15.22%, an error of -1.22 points. The shortcut sits below the true chance, so the exact figure is better for you.
What price can a draw with 7 outs on the turn afford?
At 15.22% on the river, you can call none of the 12 bet sizes. A half-pot bet needs 25.00%, a margin of -9.78 points, so against half the pot the verdict is Fold. The largest bet you can call is 21.88% of the pot, or $21.88 on a $100 pot.
Does every one of the 7 outs count in full on the turn?
Take them off the count first. With one shared out the chance on the river falls from 15.22% to 13.04%, and with 3 shared it falls to 8.70%, a loss of 6.52 points. The effective count is then 4 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