Verdict
Fold
3 outs, turn, third-pot bet
- Chance to hit by the riverone card to come6.52%
- Equity the call needs$33.33 into a pot of $166.6720.00%
- Margin over the priceyour chance minus the price-13.48 points
Comparing the draw with the bet
Pay the third-pot bet and you pay more than the draw is worth. You need 20.00%, you have 6.52%, and the 13.48-point shortfall is large.
Holding one overcard to top pair gives you exactly 3 outs, out of 46 unseen cards. One card hits 6.52% of the time.
The same spot in dollars
- The pot before betting$100
- Your opponent bets$33.33
- You call$33.33
- Final pot if you call$166.67
- Net gain when you hit$133.33
- Loss on a miss$33.33
- How often you hit6.52%
- Expected value of a call-$22.46
- Equity needed to break even20.00%
- Unrounded margin-13.4783 points
- Outs at break-even9.20 outs
- Your outs minus break-even outs-6.20 outs
Price it in dollars, with no later bets: win the whole pot on a hit, lose the call on a miss. That averages $8.70 in and $31.16 out, so calling loses $22.46 on average at -0.674 per dollar called.
Put as odds, the draw is 14.33 : 1 against, and the pot offers 4 : 1 for the call.
One easy error is to use 25.00%, the bet over the pot before your call, as the price. The right price is 20.00%, and the mistaken margin would be -18.4783 points. The bet over the starting pot, 33.33%, would claim -26.8116 points.
The extra winnings a call would need
The call becomes fair only if a hit brings in $344.44 more after the draw arrives. Measured against the $33.33 you pay, that is 10.33 times your call.
The smallest count that pays for a third-pot bet is 10 outs at 21.74%. You hold 3, which is 7 outs fewer.
| Future winnings | Price with them | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 20.00% | -13.48 points | -$22.46 | Fold |
| $50 | 15.38% | -8.86 points | -$19.20 | Fold |
| $100 | 12.50% | -5.98 points | -$15.94 | Fold |
| $250 | 8.00% | -1.48 points | -$6.16 | Fold |
| $500 | 5.00% | +1.52 points | +$10.14 | Call |
The cost of waiting a street
On the turn only one card is left, so the chance by the river and the chance on the next card are the same 6.52%. Back on the flop, the same 3 outs hit 12.49%, 5.97 points more, and that would have been a fold.
| Street | Chance by the river | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| Flop, two cards to come | 12.49% | -7.5116 points | -$12.52 | Fold |
| Turn, one card to come | 6.52% | -13.4783 points | -$22.46 | Fold |
The call as outs change
One out can change the answer, so the table lists the counts on either side of 3. Each out adds roughly 2.17 points against the 20.00% price.
The draw across every bet size
Your 6.52% chance is fixed, so the only thing that moves is the price. The 12 rows below price the call at every bet size on the turn.
With 6.52% to hit, you can call a bet up to 0.07 times the pot ($7.50 on a $100 pot) and no more, which is smaller than every size listed. All 12 rows are folds.
| Bet size | Equity needed | Margin | Verdict |
|---|---|---|---|
| quarter-pot | 16.67% | -10.14 points | Fold |
| third-pot, this page | 20.00% | -13.48 points | Fold |
| two-fifths-pot | 22.22% | -15.70 points | Fold |
| half-pot | 25.00% | -18.48 points | Fold |
| two-thirds-pot | 28.57% | -22.05 points | Fold |
| three-quarter-pot | 30.00% | -23.48 points | Fold |
| pot-size | 33.33% | -26.81 points | Fold |
| 1.25x-pot | 35.71% | -29.19 points | Fold |
| 1.5x-pot | 37.50% | -30.98 points | Fold |
| 2x-pot | 40.00% | -33.48 points | Fold |
| 3x-pot | 42.86% | -36.34 points | Fold |
| 4x-pot | 44.44% | -37.92 points | Fold |
How this is computed
The hit chance comes straight from combinations. With one card left and 3 outs in 46 cards, you hit 6.52% of the time.
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 46 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 turn when you hold 3 outs?
By the numbers it is a fold. 3 outs on the turn hit 6.52% by the river, a third-pot bet needs 20.00%, and the margin is -13.48 points. That assumes you call the full $33.33 and no more betting follows, and it values the call at -$22.46 per $100 pot.
How many outs do you need to call a third-pot bet on the turn?
To call a third-pot bet on the turn you want 10 outs or more. 10 reach 21.74% and 9 reach 19.57%, with 20.00% as the bar. Your 3 outs are 7 under.
Which hit chance fits a third-pot bet on the turn?
There is no difference on the turn, because one card remains. Use 6.52% and compare it with 20.00%: the margin is -13.48 points, a fold, whichever way you phrase the question.
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