Chance to hit on the river
28.26%
13 outs, one card to come
- Odds against2.54 : 1
- Rule of 2 estimate-2.26 points from the exact chance26%
- Unseen cards46
The count behind 13 outs on the turn
This is a respectable draw. Landing on the river 28.26% of the time, you can pay for a bet of up to 65.00% of the pot, and the third section shows the full table.
- Unseen cards46
- Your outs13
- Cards that miss33
- Chance on the river28.26%
- Chance on the next card (the river)28.26%
- Odds against hitting2.54 : 1
- Estimate from the rule of 226%
- Error of the rule of 2-2.26 points
Chance on the river = k / u, with u = 46 unseen cardsFor 13 outs: 13 / 46 = 28.26%
There is only the river to come. Of the 46 cards you have not seen, 13 help, so you land the draw 13 times in 46: 28.26%.
You would sell this draw short by 2.26 points if you stopped at 26%. The exact count is 28.26%.
Stay with the rule of 2 for this count: 13 outs times 2 is 26%. The adjusted version is for larger flop counts.
Which holding has 13 outs?
A count of 13 is a combination, not a textbook draw. Add up the helpful cards from each part of your hand and take away any that repeat.
The table removes shared outs one at a time. The first costs 2.17 points; with 3 shared you are at 21.74%, 6.52 points lower than the clean count.
| Shared outs | Effective outs | Chance on the river | Chance given up |
|---|---|---|---|
| 0 | 13 | 28.26% | 0.00 points |
| 1 | 12 | 26.09% | 2.17 points |
| 2 | 11 | 23.91% | 4.35 points |
| 3 | 10 | 21.74% | 6.52 points |
The bets 13 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 28.26% clears 4 of the 12 bet sizes.
The biggest bet you can call is 65.00% of the pot, which is $65 on a $100 pot.
| Bet size | Equity a call needs | Margin over it | Verdict |
|---|---|---|---|
| 1/4 pot | 16.67% | +11.59 points | Call |
| 1/3 pot | 20.00% | +8.26 points | Call |
| 2/5 pot | 22.22% | +6.04 points | Call |
| 1/2 pot | 25.00% | +3.26 points | Call |
| 2/3 pot | 28.57% | -0.31 points | Fold |
| 3/4 pot | 30.00% | -1.74 points | Fold |
| full pot | 33.33% | -5.07 points | Fold |
| 1.25x pot | 35.71% | -7.45 points | Fold |
| 1.5x pot | 37.50% | -9.24 points | Fold |
| 2x pot | 40.00% | -11.74 points | Fold |
| 3x pot | 42.86% | -14.60 points | Fold |
| 4x pot | 44.44% | -16.18 points | Fold |
Nearby counts on both streets
Counts near 13 sit side by side below, on the turn and on the other street. One out is worth around 2.17 points on this page.
- 13 outs on the flop: 48.10% by the river.
- 12 outs on the turn: 26.09% on the river.
- 14 outs on the turn: 30.43% on the river.
The river is the last card
One card remains, so the next-card and by-the-river figures match at 28.26%. Facing half the pot, you need 25.00% and hold a margin of +3.26 points, which is 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 13 outs that is 13 / 46 = 28.26%. The next card is the river, so both chances are the same.
The rule of 2 figure is 2 x k, here 26%, and its error is that figure minus the exact chance in percentage points, here -2.26 points.
The count covers every card you cannot see. All 46 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
What are the odds of hitting with 13 outs on the turn?
With 13 outs on the turn you hit on the river 28.26% of the time, about 28 of every 100 hands, because 13 of the 46 unseen cards are outs. The odds against are 2.54 : 1.
What does the rule of 2 say for a count of 13?
The rule of 2 gives 26% for 13 outs against an exact 28.26%, an error of -2.26 points. The shortcut sits below the true chance, so the exact figure is better for you.
What is the largest bet worth calling with a count of 13 on the turn?
At 28.26% on the river, you can call 4 of the 12 bet sizes. A half-pot bet needs 25.00%, a margin of +3.26 points, so against half the pot the verdict is Call. The largest bet you can call is 65.00% of the pot, or $65 on a $100 pot.
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 on the river falls from 28.26% to 26.09%, and with 3 shared it falls to 21.74%, a loss of 6.52 points. The effective count is then 10 outs.
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