Chance to hit on the river
43.48%
20 outs, one card to come
- Odds against1.3 : 1
- Rule of 2 estimate-3.48 points from the exact chance40%
- Unseen cards46
The count behind 20 outs on the turn
With 43.48% on the river, you complete the hand about 43 times in 100. That is a draw you can often call big with.
- Unseen cards46
- Your outs20
- Cards that miss26
- Chance on the river43.48%
- Chance on the next card (the river)43.48%
- Odds against hitting1.3 : 1
- Estimate from the rule of 240%
- Error of the rule of 2-3.48 points
Chance on the river = k / u, with u = 46 unseen cardsFor 20 outs: 20 / 46 = 43.48%
No pairs to count here, just 20 helpful cards in a deck of 46 unseen ones. That is 43.48%, with 26 unhelpful cards making up the rest.
You would sell this draw short by 3.48 points if you stopped at 40%. The exact count is 43.48%.
The adjusted rule only applies from the flop above 8 outs, so 20 outs on the turn use the plain rule of 2: 2 x 20 = 40%.
Which holding has 20 outs?
A count of 20 is a combination, not a textbook draw. Add up the helpful cards from each part of your hand and take away any that repeat.
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 41.30%.
| Shared outs | Effective outs | Chance on the river | Chance given up |
|---|---|---|---|
| 0 | 20 | 43.48% | 0.00 points |
| 1 | 19 | 41.30% | 2.17 points |
| 2 | 18 | 39.13% | 4.35 points |
| 3 | 17 | 36.96% | 6.52 points |
The bets 20 outs can call on the turn
Compare the columns: required equity on the left, margin in the middle, verdict at the end. With 20 outs you can call 11 of the 12 bet sizes.
Break-even for the call falls at a bet of $333.33 into a $100 pot, or 333.33% of the pot. Anything smaller is a call.
| Bet size | Equity a call needs | Margin over it | Verdict |
|---|---|---|---|
| 1/4 pot | 16.67% | +26.81 points | Call |
| 1/3 pot | 20.00% | +23.48 points | Call |
| 2/5 pot | 22.22% | +21.26 points | Call |
| 1/2 pot | 25.00% | +18.48 points | Call |
| 2/3 pot | 28.57% | +14.91 points | Call |
| 3/4 pot | 30.00% | +13.48 points | Call |
| full pot | 33.33% | +10.14 points | Call |
| 1.25x pot | 35.71% | +7.76 points | Call |
| 1.5x pot | 37.50% | +5.98 points | Call |
| 2x pot | 40.00% | +3.48 points | Call |
| 3x pot | 42.86% | +0.62 points | Call |
| 4x pot | 44.44% | -0.97 points | Fold |
Nearby counts on both streets
Use the rows below to see what the count next door looks like. A step of one out is about 2.17 points on the turn.
- 20 outs on the flop: 67.53% by the river.
- 19 outs on the turn: 41.30% on the river.
The river is the last card
One card remains, so the next-card and by-the-river figures match at 43.48%. Facing half the pot, you need 25.00% and hold a margin of +18.48 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 20 outs that is 20 / 46 = 43.48%. The next card is the river, so both chances are the same.
The rule of 2 figure is 2 x k, here 40%, and its error is that figure minus the exact chance in percentage points, here -3.48 points.
Assumptions: every unseen card is equally likely, and no card is removed for an opponent's hand, so this is the chance to hit your outs, not your equity against a named hand. A call is paid in full, so the pot after it holds the pot plus two bets. Here the pot is $100.
Computed from the closed form by the GeorgeLiPoker math library.
Updated
Questions
How likely is a hit with 20 outs on the turn?
With 20 outs on the turn you hit on the river 43.48% of the time, about 43 of every 100 hands, because 20 of the 46 unseen cards are outs. The odds against are 1.3 : 1.
What is the error of the rule of 2 at 20 outs?
The rule of 2 gives 40% for 20 outs against an exact 43.48%, an error of -3.48 points. The shortcut sits below the true chance, so the exact figure is better for you.
How many bet sizes can 20 outs on the turn pay for?
At 43.48% on the river, you can call 11 of the 12 bet sizes. A half-pot bet needs 25.00%, a margin of +18.48 points, so against half the pot the verdict is Call. The largest bet you can call is 333.33% of the pot, or $333.33 on a $100 pot.
What is the effective count if some of the 20 outs are shared?
Take them off the count first. With one shared out the chance on the river falls from 43.48% to 41.30%, and with 3 shared it falls to 36.96%, a loss of 6.52 points. The effective count is then 17 outs.
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