Verdict
Fold
4 outs, flop, third-pot bet
- Chance to hit by the rivertwo cards to come16.47%
- Equity the call needs$33.33 into a pot of $166.6720.00%
- Margin over the priceyour chance minus the price-3.53 points
The call in numbers
4 outs on the flop hit 16.47% by the river, but the third-pot bet needs 20.00%. You are 3.53 points short, so folding is right without more to go on.
The count matches a gutshot straight draw, so you can read this page as that draw. The very next card completes it 8.51% of the time, 4 out of 47.
The arithmetic of this call
- Pot when the bet arrives$100
- Bet$33.33
- You call$33.33
- Final pot if you call$166.67
- What a hit wins$133.33
- What a miss costs$33.33
- Your chance to hit16.47%
- Calling is worth, on average-$5.89
- Equity needed to break even20.00%
- Margin, to four decimals-3.5338 points
- Break-even count of outs4.91 outs
- Outs to spare, exactly-0.91 outs
Assume the whole pot goes to you when you hit, the call is lost when you miss, and nothing more is bet. Calling then loses $5.89 on average: $21.95 from hits, minus $27.84 from misses, -0.177 per dollar called.
The same comparison in odds: the odds against hitting are 5.07 : 1, and the pot lays 4 : 1 on a call.
Watch the pot you divide by. Leaving your call out turns 20.00% into 25.00%, and the margin into -8.5338 points. Dividing by the starting pot gives 33.33% and a margin of -16.8671 points, further from the truth.
The price with implied odds
Break-even needs $35.77 of future winnings on top of the $166.67 already in the pot, which is 1.07 times the cost of your call.
Outs are the other lever. At 5 outs you reach 20.35% by the river, enough for a third-pot bet, and you are 1 out away.
| Future winnings | Price with them | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 20.00% | -3.53 points | -$5.89 | Fold |
| $50 | 15.38% | +1.08 points | +$2.34 | Call |
| $100 | 12.50% | +3.97 points | +$10.58 | Call |
| $250 | 8.00% | +8.47 points | +$35.28 | Call |
| $500 | 5.00% | +11.47 points | +$76.44 | Call |
Two views of the same draw
One card or two, the call comes out the same way. 8.51% on the next card and 16.47% by the river both sit on the fold side of 20.00%.
| Cards counted | Chance | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| By the river, two cards | 16.47% | -3.5338 points | -$5.89 | Fold |
| Next card only | 8.51% | -11.4894 points | -$19.15 | Fold |
Counts close to yours
How fast does the margin move? About 3.89 points per out on the flop. The rows below keep the third-pot bet fixed and change only the outs.
Where the bet size flips the call
One draw, 12 bets. Each row gives the equity the call needs, the margin over it, and the verdict for 4 outs on the flop.
Even the smallest bet on the list outprices 4 outs on the flop. The break-even bet is 0.25 times the pot ($24.55 on a $100 pot), and every one of the 12 sizes is above it.
| Bet size | Equity needed | Margin | Verdict |
|---|---|---|---|
| quarter-pot | 16.67% | -0.20 points | Fold |
| third-pot, this page | 20.00% | -3.53 points | Fold |
| two-fifths-pot | 22.22% | -5.76 points | Fold |
| half-pot | 25.00% | -8.53 points | Fold |
| two-thirds-pot | 28.57% | -12.11 points | Fold |
| three-quarter-pot | 30.00% | -13.53 points | Fold |
| pot-size | 33.33% | -16.87 points | Fold |
| 1.25x-pot | 35.71% | -19.25 points | Fold |
| 1.5x-pot | 37.50% | -21.03 points | Fold |
| 2x-pot | 40.00% | -23.53 points | Fold |
| 3x-pot | 42.86% | -26.39 points | Fold |
| 4x-pot | 44.44% | -27.98 points | Fold |
How this is computed
The number is exact rather than estimated. 903 of the 1,081 pairs that could come are blanks, which leaves 16.47% for a hit.
The price is call / (pot + bet + call), here $33.33 / $166.67 = 20.00%, 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
How should you respond to a third-pot bet on the flop when you hold 4 outs?
The answer is a fold, with a margin of -3.53 points. 4 outs on the flop reach 16.47%; a bet of $33.33 into $100 needs 20.00%. Win the whole pot on a hit and lose the call on a miss, and the call is worth -$5.89 on average.
What is the minimum number of outs for a third-pot bet on the flop?
Against 20.00%, the first count that works on the flop is 5, at 20.35%. At 4 the chance is 16.47%, too low. Compared with that threshold, your 4 outs are 1 below.
Which chance should you compare with the price, the next card or the river?
It depends on what follows, but here it does not matter. If the hand ends here, count both cards: 16.47%. If another bet is coming on the turn, count one card: 8.51%. Against 20.00%, both say fold.
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