Chance to hit on the river
4.35%
2 outs, one card to come
- Odds against22 : 1
- Rule of 2 estimate-0.35 points from the exact chance4%
- Unseen cards46
The count behind 2 outs on the turn
This count leaves you empty-handed 95.65% of the time. A 4.35% chance can still be worth chasing, but only when the bet you face is a small fraction of the pot.
- Unseen cards46
- Your outs2
- Cards that miss44
- Chance on the river4.35%
- Chance on the next card (the river)4.35%
- Odds against hitting22 : 1
- Estimate from the rule of 24%
- Error of the rule of 2-0.35 points
Chance on the river = k / u, with u = 46 unseen cardsFor 2 outs: 2 / 46 = 4.35%
Divide your outs by the unseen cards: 2 / 46 = 4.35%. The other 44 cards are blanks.
With 2 outs the rule of 2 stays near the truth: 4% estimated, 4.35% exact, 0.35 points apart.
The correction for big counts belongs to the flop above 8 outs. Here the plain figure, 2 x 2 = 4%, is the one to use.
Which holding has 2 outs?
A pocket pair that wants a set fits this count exactly, with 2 outs. Memorizing counts like this lets you read the chance straight from the table on this page.
Suppose up to 2 of your outs also help a stronger hand. The effective count drops to 0, and the chance on the river drops to 0.00%.
| Shared outs | Effective outs | Chance on the river | Chance given up |
|---|---|---|---|
| 0 | 2 | 4.35% | 0.00 points |
| 1 | 1 | 2.17% | 2.17 points |
| 2 | 0 | 0.00% | 4.35 points |
The bets 2 outs can call on the turn
Here is the price list. For each bet size it shows the equity a call needs, your margin over it and the verdict, and no verdict is Call.
Stated as a share of the pot, the largest bet you can pay is 4.76%. On a $100 pot you can call up to $4.76.
| Bet size | Equity a call needs | Margin over it | Verdict |
|---|---|---|---|
| 1/4 pot | 16.67% | -12.32 points | Fold |
| 1/3 pot | 20.00% | -15.65 points | Fold |
| 2/5 pot | 22.22% | -17.87 points | Fold |
| 1/2 pot | 25.00% | -20.65 points | Fold |
| 2/3 pot | 28.57% | -24.22 points | Fold |
| 3/4 pot | 30.00% | -25.65 points | Fold |
| full pot | 33.33% | -28.99 points | Fold |
| 1.25x pot | 35.71% | -31.37 points | Fold |
| 1.5x pot | 37.50% | -33.15 points | Fold |
| 2x pot | 40.00% | -35.65 points | Fold |
| 3x pot | 42.86% | -38.51 points | Fold |
| 4x pot | 44.44% | -40.10 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 2.
- 2 outs on the flop: 8.42% by the river.
- 1 out on the turn: 2.17% on the river.
- 3 outs on the turn: 6.52% on the river.
The river is the last card
On the turn there is nothing left to separate: the river is the last card, so the by-the-river chance and the next-card chance are the same 4.35%.
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 2 outs that is 2 / 46 = 4.35%. The next card is the river, so both chances are the same.
The rule of 2 figure is 2 x k, here 4%, and its error is that figure minus the exact chance in percentage points, here -0.35 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 often do 2 outs hit on the turn?
With 2 outs on the turn you hit on the river 4.35% of the time, about 4 of every 100 hands, because 2 of the 46 unseen cards are outs. The odds against are 22 : 1.
What does the rule of 2 say for a count of 2?
The rule of 2 gives 4% for 2 outs against an exact 4.35%, an error of -0.35 points. That is close enough to use at the table.
What price can a draw with 2 outs on the turn afford?
At 4.35% on the river, you can call none of the 12 bet sizes. A half-pot bet needs 25.00%, a margin of -20.65 points, so against half the pot the verdict is Fold. The largest bet you can call is 4.76% of the pot, or $4.76 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 4.35% to 2.17%, and with 2 shared it falls to 0.00%, a loss of 4.35 points. The effective count is then 0 outs.
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