Verdict
Call
17 outs, flop, two-thirds-pot bet
- Chance to hit by the rivertwo cards to come59.76%
- Equity the call needs$66.67 into a pot of $233.3328.57%
- Margin over the priceyour chance minus the price+31.19 points
Reading the verdict
Pay the two-thirds-pot bet and you get a better deal than the draw needs. You need 28.57%, you have 59.76%, and the 31.19-point difference is large.
A total of 17 outs tends to come from stacking several ways to improve. The next card is an out 36.17% of the time, 17 in 47.
The same spot in dollars
- Pot before the bet$100
- The bet$66.67
- Your call$66.67
- Pot after your call$233.33
- You can win on a hit$166.67
- You lose on a miss$66.67
- How often you hit59.76%
- Calling is worth, on average+$72.77
- Equity the call needs28.57%
- Your chance minus the price, unrounded+31.1881 points
- Outs at break-even7.20 outs
- Your outs minus break-even outs+9.80 outs
Suppose a hit wins the entire pot, a miss loses your call, and no more betting follows. The average gain is $99.60, the average loss is $26.83, and calling gains $72.77 on average, or +1.092 per dollar called.
Stated as odds, you are 0.67 : 1 against hitting and the call gets 2.5 : 1 from the pot.
The price is 28.57% because your call goes into the pot too. Leave it out and you get 40.00%, a margin of +19.7595 points that does not exist; use the starting pot instead and 66.67% puts the margin at -6.9072 points.
Your cushion over the price
The threshold is 8 outs, a chance of 31.45%. With 17 in hand you are 9 outs clear of it.
Break-even on later streets sits at $121.78 given back, or 1.83 times your call.
| Given back later | Price with it | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 28.57% | +31.19 points | +$72.77 | Call |
| $10 | 29.85% | +29.91 points | +$66.80 | Call |
| $25 | 32.00% | +27.76 points | +$57.83 | Call |
| $50 | 36.36% | +23.40 points | +$42.89 | Call |
| $100 | 50.00% | +9.76 points | +$13.01 | Call |
The next card against the whole runout
You can skip the usual debate over one card versus two, because 36.17% and 59.76% both give a call against 28.57%.
| Cards counted | Chance | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| By the river, two cards | 59.76% | +31.1881 points | +$72.77 | Call |
| Next card only | 36.17% | +7.5988 points | +$17.73 | Call |
One out more or less
Move up or down a few outs and watch the verdict. Every extra out is worth about 2.68 points on the flop, and the price stays at 28.57%.
Every bet size, one draw
Bigger bets ask for more equity while your chance stays at 59.76%. Here is every bet size against the same draw, with the row for this page marked.
With 59.76% to hit, no bet on the list is too big. 17 outs call all 12 sizes on the flop.
| Bet size | Equity needed | Margin | Verdict |
|---|---|---|---|
| quarter-pot | 16.67% | +43.09 points | Call |
| third-pot | 20.00% | +39.76 points | Call |
| two-fifths-pot | 22.22% | +37.54 points | Call |
| half-pot | 25.00% | +34.76 points | Call |
| two-thirds-pot, this page | 28.57% | +31.19 points | Call |
| three-quarter-pot | 30.00% | +29.76 points | Call |
| pot-size | 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 |
How this is computed
Here is how 59.76% was found. Deal every pair of the 47 unseen cards: 435 of 1,081 pairs contain no out.
What is held fixed: the call equals the bet, so the price is $66.67 / $233.33 = 28.57%; the pot is won whole on a hit; there is no further betting; and each of the 47 unseen cards is as likely as any other. Opponent cards are not removed.
Computed from the closed form by the GeorgeLiPoker math library.
Updated
Questions
Are 17 outs on the flop worth a call against a bet of two thirds of the pot?
By the numbers it is a call. 17 outs on the flop hit 59.76% by the river, a two-thirds-pot bet needs 28.57%, and the margin is +31.19 points. That assumes you call the full $66.67 and no more betting follows, and it values the call at +$72.77 per $100 pot.
How strong must a draw be to call a two-thirds-pot bet on the flop?
You need at least 8 outs against a two-thirds-pot bet on the flop. That count hits 31.45% against 28.57% needed, and 7 falls short at 27.84%. With 17 you are 9 past the minimum.
Should you use the chance on the next card or by the river?
Pick the number that matches the street plan: 59.76% for seeing both cards for one bet, 36.17% for paying card by card. Both face 28.57%, and the verdict is call either way.
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