Chance to hit by the river
59.76%
17 outs, two cards to come
- Chance on the next card36.17%
- Odds against by the river0.67 : 1
- Rule of 4 estimate+8.24 points from the exact chance68%
The count behind 17 outs on the flop
This is a very large draw. You miss 40.24% of the time, and most bet sizes in the table below are calls.
- Unseen cards47
- Your outs17
- Cards that miss30
- Pairs of cards with no out435
- Pairs with at least one out646
- Chance by the river59.76%
- Chance on the next card36.17%
- Odds against hitting0.67 : 1
- Estimate from the rule of 468%
- Error of the rule of 4+8.24 points
- Adjusted rule 4k - (k - 8)59%
- Error of the adjusted rule-0.76 points
Chance by the river = 1 - C(u - k, 2) / C(u, 2), with u = 47 unseen cardsFor 17 outs: 1 - C(30, 2) / C(47, 2) = 1 - 435 / 1,081 = 59.76%Next card = 17 / 47 = 36.17%
Start with the cards you have not seen: 47 of them. 30 of those miss and 17 are outs. Two cards come, so there are 1,081 possible pairs, and 435 of them hold no out at all.
A 68% estimate against a true 59.76% is an overstatement of 8.24 points, more than the 2 points that make a shortcut safe to use unchecked.
Above 8 outs the adjusted rule applies: 4 x 17 - 9 = 59%. Against 59.76%, it is off by 0.76 points.
Which holding has 17 outs?
A count of 17 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 2.78 points, to 56.98%.
| Shared outs | Effective outs | Chance by the river | Chance given up |
|---|---|---|---|
| 0 | 17 | 59.76% | 0.00 points |
| 1 | 16 | 56.98% | 2.78 points |
| 2 | 15 | 54.12% | 5.64 points |
| 3 | 14 | 51.16% | 8.60 points |
The bets 17 outs can call on the flop
Bet sizes run from 1/4 pot to 4x pot. Against 59.76% by the river, all 12 bet sizes are calls.
There is no limit to find here. Holding 59.76%, you can call a bet of any size, from 1/4 pot up and beyond 4x pot.
| Bet size | Equity a call needs | Margin over it | Verdict |
|---|---|---|---|
| 1/4 pot | 16.67% | +43.09 points | Call |
| 1/3 pot | 20.00% | +39.76 points | Call |
| 2/5 pot | 22.22% | +37.54 points | Call |
| 1/2 pot | 25.00% | +34.76 points | Call |
| 2/3 pot | 28.57% | +31.19 points | Call |
| 3/4 pot | 30.00% | +29.76 points | Call |
| full pot | 33.33% | +26.43 points | Call |
| 1.25x pot | 35.71% | +24.05 points | Call |
| 1.5x pot | 37.50% | +22.26 points | Call |
| 2x pot | 40.00% | +19.76 points | Call |
| 3x pot | 42.86% | +16.90 points | Call |
| 4x pot | 44.44% | +15.32 points | Call |
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 2.68 points on the flop.
- 17 outs on the turn: 36.96% on the river.
- 16 outs on the flop: 56.98% by the river.
- 18 outs on the flop: 62.44% by the river.
When a bet buys only one card
Two views, one draw: 59.76% if you see both cards and 36.17% if you see one. Against 25.00%, the one-card view has a margin of +11.17 points and reads Call.
On one card, 17 outs clear 8 of the 12 bet sizes. On two cards they clear all 12 bet sizes.
How this is computed
The chance to hit by the river from the flop is 1 - C(u - k, 2) / C(u, 2), where u = 47 unseen cards and k is your effective outs. For 17 outs that is 1 - 435 / 1,081 = 59.76%. The chance on the next card is k / 47, here 36.17%.
The rule of 4 figure is 4 x k, here 68%, and its error is that figure minus the exact chance in percentage points, here +8.24 points. The adjusted rule 4k - (k - 8) gives 59%, an error of -0.76 points.
The count covers every card you cannot see. All 47 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
Out of 100 hands, how many hit with 17 outs on the flop?
With 17 outs on the flop you hit by the river 59.76% of the time, about 60 of every 100 hands, and on the next card 36.17%. The odds against hitting by the river are 0.67 : 1, since 435 of 1,081 pairs of unseen cards hold no out.
What is the error of the rule of 4 at 17 outs?
The rule of 4 gives 68% for 17 outs against an exact 59.76%, an error of +8.24 points, so it overstates the draw. The adjusted rule 4k - (k - 8) gives 59%, an error of -0.76 points, and is the closer figure.
Do 17 outs on the flop justify a call, and against which bets?
At 59.76% by the river, you can call all 12 bet sizes. A half-pot bet needs 25.00%, a margin of +34.76 points, so against half the pot the verdict is Call. Any bet size is a call, because 59.76% is above one half.
How do I adjust a count of 17 for outs that help an opponent?
Take them off the count first. With one shared out the chance by the river falls from 59.76% to 56.98%, and with 3 shared it falls to 51.16%, a loss of 8.60 points. The effective count is then 14 outs.
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