Verdict
Call
18 outs, flop, two-thirds-pot bet
- Chance to hit by the rivertwo cards to come62.44%
- Equity the call needs$66.67 into a pot of $233.3328.57%
- Margin over the priceyour chance minus the price+33.87 points
The price of the call
This is one of the easier spots. 18 outs on the flop reach 62.44% by the river, the two-thirds-pot bet asks for just 28.57%, and the 33.87-point margin favors the call.
Few single draws land on exactly 18 outs, so add up each way to improve and check the total. One card hits 38.30% of the time here.
Worked through on a $100 pot
- Pot before the bet$100
- Bet$66.67
- You call$66.67
- Final pot if you call$233.33
- You can win on a hit$166.67
- You lose on a miss$66.67
- Chance to hit by the river62.44%
- Expected value of a call+$79.03
- Equity needed to break even28.57%
- Exact margin over the price+33.8708 points
- Break-even count of outs7.20 outs
- Outs above the price+10.80 outs
Over many identical spots, with the whole pot won on every hit, the call lost on every miss and no extra betting, calling gains $79.03 on average. Hits bring in $104.07, misses cost $25.04, and the ratio is +1.185 per dollar called.
Put as odds, the draw is 0.6 : 1 against, and the pot offers 2.5 : 1 for the call.
One easy error is to use 40.00%, the bet over the pot before your call, as the price. The right price is 28.57%, and the mistaken margin would be +22.4422 points. The bet over the starting pot, 66.67%, would claim -4.2245 points.
Your cushion over the price
The threshold is 8 outs, a chance of 31.45%. With 18 in hand you are 10 outs clear of it.
Reverse implied odds are the risk here. A hit that costs you $126.57 later, 1.90 times your call, is where the call stops being worth it.
| Given back later | Price with it | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 28.57% | +33.87 points | +$79.03 | Call |
| $10 | 29.85% | +32.59 points | +$72.79 | Call |
| $25 | 32.00% | +30.44 points | +$63.42 | Call |
| $50 | 36.36% | +26.08 points | +$47.81 | Call |
| $100 | 50.00% | +12.44 points | +$16.59 | Call |
Two views of the same draw
Use either number and the verdict is a call. The next card is 38.30%, the full runout is 62.44%, and the price is 28.57%.
| Cards counted | Chance | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| By the river, two cards | 62.44% | +33.8708 points | +$79.03 | Call |
| Next card only | 38.30% | +9.7264 points | +$22.70 | Call |
How the answer moves with outs
The table shows 18 outs and the draws around it on the flop, all against the same two-thirds-pot bet. Each extra out adds about 2.59 points to the chance here.
The same draw against other bet sizes
The same 18 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.
Nothing in the list is too big to call: 18 outs reach 62.44% on the flop, above every price on the page.
| Bet size | Equity needed | Margin | Verdict |
|---|---|---|---|
| quarter-pot | 16.67% | +45.78 points | Call |
| third-pot | 20.00% | +42.44 points | Call |
| two-fifths-pot | 22.22% | +40.22 points | Call |
| half-pot | 25.00% | +37.44 points | Call |
| two-thirds-pot, this page | 28.57% | +33.87 points | Call |
| three-quarter-pot | 30.00% | +32.44 points | Call |
| pot-size | 33.33% | +29.11 points | Call |
| 1.25x-pot | 35.71% | +26.73 points | Call |
| 1.5x-pot | 37.50% | +24.94 points | Call |
| 2x-pot | 40.00% | +22.44 points | Call |
| 3x-pot | 42.86% | +19.59 points | Call |
| 4x-pot | 44.44% | +18.00 points | Call |
How this is computed
Counting is exact: the pairs of unseen cards with no out number 406 out of 1,081, so hitting by the river has chance 62.44%.
The model is deliberately simple: call everything, win everything on a hit, face no more bets, deal from 47 equally likely unseen cards, and ignore an opponent's holding. With the price at $66.67 / $233.33 = 28.57%, later streets and shared outs are what change the real answer.
Computed from the closed form by the GeorgeLiPoker math library.
Updated
Questions
How should you respond to a two-thirds-pot bet on the flop when you hold 18 outs?
The verdict is call. Your chance is 62.44% and the price is 28.57%, which leaves +33.87 points. On a $100 pot with a $66.67 bet, calling is worth +$79.03 on average if the whole pot is won on a hit and nothing more is bet.
At what count of outs does a two-thirds-pot bet on the flop become a call?
Against 28.57%, the first count that works on the flop is 8, at 31.45%. At 7 the chance is 27.84%, too low. Compared with that threshold, your 18 outs are 10 above.
Should you use the chance on the next card or by the river?
Use the by-the-river chance, 62.44%, when no more betting follows, and the next-card chance, 38.30%, when you must pay again on the turn. Against the 28.57% price both give a call, so the choice does not change the play here.
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