Verdict
Fold
3 outs, flop, third-pot bet
- Chance to hit by the rivertwo cards to come12.49%
- Equity the call needs$33.33 into a pot of $166.6720.00%
- Margin over the priceyour chance minus the price-7.51 points
The price of the call
Your draw is priced at 20.00% and it arrives just 12.49% of the time. A gap of 7.51 points is large, and later bets would have to be large to make up for it.
The usual home for 3 outs is one overcard to top pair. One card from the 47 unseen ones completes it 6.38% of the time.
A $100 pot, step by step
- Pot before the bet$100
- Size of the bet$33.33
- You call$33.33
- Final pot if you call$166.67
- Gain on a hit$133.33
- What a miss costs$33.33
- Chance to hit by the river12.49%
- Expected value of calling-$12.52
- Equity the call needs20.00%
- Exact margin over the price-7.5116 points
- Break-even count of outs4.91 outs
- Outs above the price-1.91 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 $12.52 on average: $16.65 from hits, minus $29.17 from misses, -0.376 per dollar called.
The same comparison in odds: the odds against hitting are 7.01 : 1, and the pot lays 4 : 1 on a call.
Counting the pot without your call makes the price look like 25.00%, when the real price is 20.00%. On that mistaken price the margin would read -12.5116 points; on 33.33%, the bet over the starting pot, it would read -20.8449 points.
How much more you would need to win
With 12.49% to hit, break-even sits $100.25 higher than the pot shows. Put another way, later bets must add 3.01 times your call.
Count the outs the call needs: 5 reach the 20.00% price, giving 20.35%. You have 3, so you are 2 outs short.
| Future winnings | Price with them | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 20.00% | -7.51 points | -$12.52 | Fold |
| $50 | 15.38% | -2.90 points | -$6.28 | Fold |
| $100 | 12.50% | -0.01 points | -$0.03 | Fold |
| $250 | 8.00% | +4.49 points | +$18.70 | Call |
| $500 | 5.00% | +7.49 points | +$49.92 | Call |
Which chance to use
Here the cards to come do not matter for the verdict. 6.38% on one card and 12.49% on two both say fold at a price of 20.00%.
| Cards counted | Chance | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| By the river, two cards | 12.49% | -7.5116 points | -$12.52 | Fold |
| Next card only | 6.38% | -13.6170 points | -$22.70 | Fold |
Counts close to yours
The table shows 3 outs and the draws around it on the flop, all against the same third-pot bet. Each extra out adds about 3.98 points to the chance here.
Changing the bet, keeping the draw
The same 3 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.
Even the smallest bet on the list outprices 3 outs on the flop. The break-even bet is 0.17 times the pot ($16.65 on a $100 pot), and every one of the 12 sizes is above it.
| Bet size | Equity needed | Margin | Verdict |
|---|---|---|---|
| quarter-pot | 16.67% | -4.18 points | Fold |
| third-pot, this page | 20.00% | -7.51 points | Fold |
| two-fifths-pot | 22.22% | -9.73 points | Fold |
| half-pot | 25.00% | -12.51 points | Fold |
| two-thirds-pot | 28.57% | -16.08 points | Fold |
| three-quarter-pot | 30.00% | -17.51 points | Fold |
| pot-size | 33.33% | -20.84 points | Fold |
| 1.25x-pot | 35.71% | -23.23 points | Fold |
| 1.5x-pot | 37.50% | -25.01 points | Fold |
| 2x-pot | 40.00% | -27.51 points | Fold |
| 3x-pot | 42.86% | -30.37 points | Fold |
| 4x-pot | 44.44% | -31.96 points | Fold |
How this is computed
The chance to hit is the exact closed form, with no simulation. From the flop, 946 of the 1,081 possible pairs of unseen cards hold no out, so the chance is 1 minus 946 / 1,081, which is 12.49%.
Read the verdict with its limits in mind. The call is the full bet, so the break-even equity is $33.33 / $166.67 = 20.00%. A hit takes the whole pot, no later betting happens, and the 47 unseen cards are all equally likely, with none removed for an opponent's cards.
Computed from the closed form by the GeorgeLiPoker math library.
Updated
Questions
Are 3 outs on the flop worth a call against a bet of a third of the pot?
Math says fold. The third-pot bet of $33.33 needs 20.00% equity, 3 outs on the flop give 12.49%, and the margin is -7.51 points. Assuming a whole pot won on a hit and no further bets, the call is worth -$12.52 on average.
What is the fewest outs that can call a third-pot bet on the flop?
The fewest outs that call a third-pot bet on the flop is 5. With 5 outs you hit 20.35%, which reaches the 20.00% price, while 4 outs hit only 16.47%. You have 3, so you are 2 below that count.
Should you use the chance on the next card or by the river?
It depends on what follows, but here it does not matter. If the hand ends here, count both cards: 12.49%. If another bet is coming on the turn, count one card: 6.38%. Against 20.00%, both say fold.
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