Verdict
Call
18 outs, flop, three-quarter-pot bet
- Chance to hit by the rivertwo cards to come62.44%
- Equity the call needs$75 into a pot of $25030.00%
- Margin over the priceyour chance minus the price+32.44 points
What the numbers say
62.44% against 30.00%: the draw beats the price by 32.44 points. On this flop against a three-quarter-pot bet, that is a comfortable call.
You will reach 18 outs by adding up separate draws. With 47 cards unseen, the next card helps 38.30% of the time.
Counting the chips on a $100 pot
- Starting pot$100
- Your opponent bets$75
- Cost to call$75
- Final pot if you call$250
- What a hit wins$175
- You lose on a miss$75
- Chance to hit by the river62.44%
- Expected value of a call+$81.11
- Break-even equity30.00%
- Your chance minus the price, unrounded+32.4422 points
- Outs at break-even7.59 outs
- Your outs minus break-even outs+10.41 outs
If you win the whole pot on a hit and lose your call otherwise, with no more betting, calling gains $81.11 on average. Hits add $109.27 on average and misses cost $28.17 on average, or +1.081 per dollar called.
The same comparison in odds: the odds against hitting are 0.6 : 1, and the pot lays 2.33 : 1 on a call.
Watch the pot you divide by. Leaving your call out turns 30.00% into 42.86%, and the margin into +19.5850 points. Dividing by the starting pot gives 75.00% and a margin of -12.5578 points, further from the truth.
What could go wrong before the call flips
Against this bet the draw needs 8 outs at the least. You have 10 outs more than that, so the call has some room.
Your margin is worth $129.89 in later losses. Past that, 1.73 times your call, folding would have been better.
| Given back later | Price with it | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 30.00% | +32.44 points | +$81.11 | Call |
| $10 | 31.25% | +31.19 points | +$74.86 | Call |
| $25 | 33.33% | +29.11 points | +$65.49 | Call |
| $50 | 37.50% | +24.94 points | +$49.88 | Call |
| $100 | 50.00% | +12.44 points | +$18.66 | Call |
Two views of the same draw
Whether you count one card or two, the answer is a call. The river figure is 62.44%, the next-card figure is 38.30%, and both are measured against 30.00%.
| Cards counted | Chance | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| By the river, two cards | 62.44% | +32.4422 points | +$81.11 | Call |
| Next card only | 38.30% | +8.2979 points | +$20.74 | Call |
Counts close to yours
How fast does the margin move? About 2.59 points per out on the flop. The rows below keep the three-quarter-pot bet fixed and change only the outs.
Where the bet size flips the call
Keep 18 outs and change only the bet. The price rises from the smallest size to the largest, and the three-quarter-pot row is marked as this page.
Your chance is high enough that any bet in the table is a call. All 12 sizes clear with 62.44%.
| 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 | 28.57% | +33.87 points | Call |
| three-quarter-pot, this page | 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
Here is how 62.44% was found. Deal every pair of the 47 unseen cards: 406 of 1,081 pairs contain no out.
The numbers are a baseline rather than a prediction for one hand. The price is 30.00%, from $75 into $250, and the chance assumes a whole pot won on a hit, no more betting, 47 equally likely unseen cards, and no cards removed for the other player.
Computed from the closed form by the GeorgeLiPoker math library.
Updated
Questions
Are 18 outs on the flop worth a call against a bet of three quarters of the pot?
Compare 62.44%, your chance to hit by the river, with 30.00%, the equity a three-quarter-pot bet needs. The gap is +32.44 points, so this is a call. In dollars on a $100 pot, the call averages +$81.11 when no more betting follows.
At what count of outs does a three-quarter-pot bet on the flop become a call?
The threshold is 8 outs. It gives 31.45%, clearing 30.00%, whereas 7 gives only 27.84%. Holding 18 puts you 10 above it, with a chance of 62.44%.
How many cards should you count when a three-quarter-pot bet arrives on the flop?
Match the number to the betting: 62.44% if all-in or checked down, 38.30% if you face another bet on the turn. The price is 30.00%, and both numbers agree on call.
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