Verdict
Call
17 outs, flop, pot-size bet
- Chance to hit by the rivertwo cards to come59.76%
- Equity the call needs$100 into a pot of $30033.33%
- Margin over the priceyour chance minus the price+26.43 points
What the numbers say
Pay the pot-size bet and you get a better deal than the draw needs. You need 33.33%, you have 59.76%, and the 26.43-point difference is large.
You will reach 17 outs by adding up separate draws. With 47 cards unseen, the next card helps 36.17% of the time.
One hand, in dollars
- Starting pot$100
- The bet$100
- Chips you put in$100
- Final pot if you call$300
- You can win on a hit$200
- Loss on a miss$100
- Chance to hit by the river59.76%
- Average value of the call+$79.28
- Equity needed to break even33.33%
- Margin, to four decimals+26.4261 points
- Fractional outs at the price8.53 outs
- Margin measured in outs+8.47 outs
If you win the whole pot on a hit and lose your call otherwise, with no more betting, calling gains $79.28 on average. Hits add $119.52 on average and misses cost $40.24 on average, or +0.793 per dollar called.
As odds, 0.67 : 1 against hitting meets pot odds of 2 : 1.
Skipping your own call in the pot gives a price of 50.00% where 33.33% is correct, and a margin of +9.7595 points instead of +26.43 points.
Slack in the call
9 outs is the line for a pot-size bet on the flop. Your 17 sit 8 outs above it, and the chance at the line is 34.97%.
The call keeps its edge until you lose $132.66 on later streets after hitting. That is 1.33 times the $100 you pay now.
| Given back later | Price with it | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 33.33% | +26.43 points | +$79.28 | Call |
| $10 | 34.48% | +25.28 points | +$73.30 | Call |
| $25 | 36.36% | +23.40 points | +$64.34 | Call |
| $50 | 40.00% | +19.76 points | +$49.40 | Call |
| $100 | 50.00% | +9.76 points | +$19.52 | Call |
The next card against the whole runout
No conflict here: 59.76% for two cards and 36.17% for one both give a call against the 33.33% price, so you need not decide which view applies.
| Cards counted | Chance | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| By the river, two cards | 59.76% | +26.4261 points | +$79.28 | Call |
| Next card only | 36.17% | +2.8369 points | +$8.51 | Call |
A few outs either way
Here are the neighbors of 17 outs, priced against the same 33.33%. One more out lifts your chance by about 2.68 points.
Every bet size, one draw
The same 17 outs on the flop meet a different price at each bet size. The table runs from the smallest bet to the largest, and the row for this page is marked.
No bet size here outprices a 59.76% chance. The call works at all 12 sizes, since the highest price is 44.44%.
| 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 | 28.57% | +31.19 points | Call |
| three-quarter-pot | 30.00% | +29.76 points | Call |
| pot-size, this page | 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
The chance to hit is the exact closed form, with no simulation. From the flop, 435 of the 1,081 possible pairs of unseen cards hold no out, so the chance is 1 minus 435 / 1,081, which is 59.76%.
The price is call / (pot + bet + call), here $100 / $300 = 33.33%, and the margin is your chance minus it. The page assumes you call the whole bet, win the whole pot whenever you hit, and see no more betting. All 47 unseen cards are equally likely and none is removed for an opponent's hand, so this is the chance to hit your outs, not your equity against one hand.
Computed from the closed form by the GeorgeLiPoker math library.
Updated
Questions
Does the math favor calling a pot-size bet with 17 outs on the flop?
Math says call. The pot-size bet of $100 needs 33.33% equity, 17 outs on the flop give 59.76%, and the margin is +26.43 points. Assuming a whole pot won on a hit and no further bets, the call is worth +$79.28 on average.
How strong must a draw be to call a pot-size bet on the flop?
A call starts to work at 9 outs: 34.97% to hit versus 33.33% needed. One out fewer drops the chance to 31.45%. You hold 17, which is 8 more than 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 33.33%, and the verdict is call either way.
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