Verdict
Fold
3 outs, turn, two-thirds-pot bet
- Chance to hit by the riverone card to come6.52%
- Equity the call needs$66.67 into a pot of $233.3328.57%
- Margin over the priceyour chance minus the price-22.05 points
How the verdict is reached
6.52% against 28.57%: the draw trails the price by 22.05 points. On this turn against a two-thirds-pot bet, that is an easy fold.
Count one overcard to top pair and you land on 3 outs. With 46 cards unseen, the next card helps 6.52% of the time.
Counting the chips on a $100 pot
- Pot when the bet arrives$100
- Your opponent bets$66.67
- Chips you put in$66.67
- Final pot if you call$233.33
- What a hit wins$166.67
- You lose on a miss$66.67
- Probability of a hit6.52%
- Calling is worth, on average-$51.45
- Equity the call needs28.57%
- Your chance minus the price, unrounded-22.0497 points
- Outs that exactly reach the price13.14 outs
- Your outs minus break-even outs-10.14 outs
Over many identical spots, with the whole pot won on every hit, the call lost on every miss and no extra betting, calling loses $51.45 on average. Hits bring in $10.87, misses cost $62.32, and the ratio is -0.772 per dollar called.
Odds say the same thing. Hitting is 14.33 : 1 against, and the pot lays 2.5 : 1.
A common slip is to divide the bet by the pot after the bet but before your call. That gives 40.00% instead of 28.57% and would put your margin at -33.4783 points. Using the bet over the starting pot, 66.67%, is further off and would put it at -60.1449 points.
Closing the gap with future bets
With 6.52% to hit, break-even sits $788.89 higher than the pot shows. Put another way, later bets must add 11.83 times your call.
14 outs is the threshold against a two-thirds-pot bet on the turn, a chance of 30.43%. That is 11 more than your 3.
| Future winnings | Price with them | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 28.57% | -22.05 points | -$51.45 | Fold |
| $50 | 23.53% | -17.01 points | -$48.19 | Fold |
| $100 | 20.00% | -13.48 points | -$44.93 | Fold |
| $250 | 13.79% | -7.27 points | -$35.14 | Fold |
| $500 | 9.09% | -2.57 points | -$18.84 | Fold |
Flop and turn compared
Compare the streets. With two cards left, 3 outs hit 12.49% (a fold); with one card left they hit 6.52% (a fold). The difference is 5.97 points.
| Street | Chance by the river | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| Flop, two cards to come | 12.49% | -16.0830 points | -$37.53 | Fold |
| Turn, one card to come | 6.52% | -22.0497 points | -$51.45 | Fold |
Neighbors of this draw
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 28.57% price.
The same draw against other bet sizes
Bigger bets ask for more equity while your chance stays at 6.52%. Here is every bet size against the same draw, with the row for this page marked.
3 outs stop paying at 0.07 times the pot ($7.50 on a $100 pot), below the smallest size listed. The call fails at all 12 bet sizes.
| Bet size | Equity needed | Margin | Verdict |
|---|---|---|---|
| quarter-pot | 16.67% | -10.14 points | Fold |
| third-pot | 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, this page | 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 chance to hit is the exact closed form, with no simulation. From the turn, 3 of the 46 unseen cards are outs, so the chance is 3 / 46, which is 6.52%.
Keep the assumptions in view: a full call ($66.67 into $233.33, or 28.57%), the whole pot on a hit, no more betting, and 46 unseen cards that are equally likely. The math does not know what the other player holds.
Computed from the closed form by the GeorgeLiPoker math library.
Updated
Questions
What is the right play with 3 outs when a two-thirds-pot bet comes on the turn?
Math says fold. The two-thirds-pot bet of $66.67 needs 28.57% equity, 3 outs on the turn give 6.52%, and the margin is -22.05 points. Assuming a whole pot won on a hit and no further bets, the call is worth -$51.45 on average.
How many outs are enough to continue against a bet of two thirds of the pot on the turn?
To call a two-thirds-pot bet on the turn you want 14 outs or more. 14 reach 30.43% and 13 reach 28.26%, with 28.57% as the bar. Your 3 outs are 11 under.
Which hit chance fits a two-thirds-pot bet on the turn?
They are one number here. With a single card to come, 6.52% is both the next-card chance and the by-the-river chance, and it gives a fold against 28.57%, a margin of -22.05 points.
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