Chance to hit on the river
2.17%
1 out, one card to come
- Odds against45 : 1
- Rule of 2 estimate-0.17 points from the exact chance2%
- Unseen cards46
The count behind 1 out on the turn
Think of 2.17% as a long shot that pays when the price is right. At 45 : 1 against, you need the pot to be laying a generous price.
- Unseen cards46
- Your outs1
- Cards that miss45
- Chance on the river2.17%
- Chance on the next card (the river)2.17%
- Odds against hitting45 : 1
- Estimate from the rule of 22%
- Error of the rule of 2-0.17 points
Chance on the river = k / u, with u = 46 unseen cardsFor 1 out: 1 / 46 = 2.17%
The river is the last card, so the by-the-river chance and the next-card chance are the same number. For 1 out it is 1 / 46, or 2.17%.
With 1 out the rule of 2 stays near the truth: 2% estimated, 2.17% exact, 0.17 points apart.
Only flop counts above 8 call for the adjusted rule. For 1 out on the turn, 2 x 1 = 2% is the whole shortcut.
Which holding has 1 out?
A count of 1 means a single card helps. It comes from your own count of helpful cards, not from a standard draw.
Count carefully: a card that gives you the draw and gives an opponent a better hand should come off the list. One shared out takes the chance down by 2.17 points, to 0.00%.
| Shared outs | Effective outs | Chance on the river | Chance given up |
|---|---|---|---|
| 0 | 1 | 2.17% | 0.00 points |
| 1 | 0 | 0.00% | 2.17 points |
The bets 1 out can call on the turn
Compare the columns: required equity on the left, margin in the middle, verdict at the end. With 1 out you can call none of the 12 bet sizes.
Stated as a share of the pot, the largest bet you can pay is 2.27%. On a $100 pot you can call up to $2.27.
| Bet size | Equity a call needs | Margin over it | Verdict |
|---|---|---|---|
| 1/4 pot | 16.67% | -14.49 points | Fold |
| 1/3 pot | 20.00% | -17.83 points | Fold |
| 2/5 pot | 22.22% | -20.05 points | Fold |
| 1/2 pot | 25.00% | -22.83 points | Fold |
| 2/3 pot | 28.57% | -26.40 points | Fold |
| 3/4 pot | 30.00% | -27.83 points | Fold |
| full pot | 33.33% | -31.16 points | Fold |
| 1.25x pot | 35.71% | -33.54 points | Fold |
| 1.5x pot | 37.50% | -35.33 points | Fold |
| 2x pot | 40.00% | -37.83 points | Fold |
| 3x pot | 42.86% | -40.68 points | Fold |
| 4x pot | 44.44% | -42.27 points | Fold |
Nearby counts on both streets
Counts near 1 sit side by side below, on the turn and on the other street. One out is worth around 2.17 points on this page.
- 1 out on the flop: 4.26% by the river.
- 2 outs on the turn: 4.35% on the river.
The river is the last card
One card remains, so the next-card and by-the-river figures match at 2.17%. Facing half the pot, you need 25.00% and hold a margin of -22.83 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 1 out that is 1 / 46 = 2.17%. The next card is the river, so both chances are the same.
The rule of 2 figure is 2 x k, here 2%, and its error is that figure minus the exact chance in percentage points, here -0.17 points.
The model gives every one of the 46 unseen cards the same chance and removes nothing for what a rival holds. It measures hitting an out, not winning the hand. Bets are priced on a $100 pot, and a call adds one bet to the pot.
Computed from the closed form by the GeorgeLiPoker math library.
Updated
Questions
How likely is a hit with 1 out on the turn?
With 1 out on the turn you hit on the river 2.17% of the time, about 2 of every 100 hands, because 1 of the 46 unseen cards is an out. The odds against are 45 : 1.
What does the rule of 2 say for a count of 1?
The rule of 2 gives 2% for 1 out against an exact 2.17%, an error of -0.17 points. That is close enough to use at the table.
Which bets can 1 out call on the turn?
At 2.17% on the river, you can call none of the 12 bet sizes. A half-pot bet needs 25.00%, a margin of -22.83 points, so against half the pot the verdict is Fold. The largest bet you can call is 2.27% of the pot, or $2.27 on a $100 pot.
What if my out also helps a better hand?
Take it off the count first. With your one out shared, the chance on the river falls from 2.17% to 0.00%, a loss of 2.17 points, and the effective count is then 0 outs.
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