Verdict
Fold
3 outs, flop, half-pot bet
- Chance to hit by the rivertwo cards to come12.49%
- Equity the call needs$50 into a pot of $20025.00%
- Margin over the priceyour chance minus the price-12.51 points
How the verdict is reached
This is one of the easier spots. 3 outs on the flop reach 12.49% by the river, the half-pot bet asks for 25.00%, and the 12.51-point gap favors folding.
Count one overcard to top pair and you land on 3 outs. With 47 cards unseen, the next card helps 6.38% of the time.
The same spot in dollars
- Pot when the bet arrives$100
- Bet$50
- Cost to call$50
- Pot with your call in$200
- Net gain when you hit$150
- You lose on a miss$50
- Chance to hit by the river12.49%
- Expected value of calling-$25.02
- Equity needed to break even25.00%
- Margin, to four decimals-12.5116 points
- Break-even count of outs6.23 outs
- Outs above the price-3.23 outs
Expected value says the same in dollars. Win the whole pot on a hit, lose your call on a miss, add no more betting, and the call loses $25.02 on average: $18.73 in, $43.76 out, -0.500 per dollar called.
Read as odds: 7.01 : 1 against you, 3 : 1 from the pot.
A common slip is to divide the bet by the pot after the bet but before your call. That gives 33.33% instead of 25.00% and would put your margin at -20.8449 points. Using the bet over the starting pot, 50.00%, is further off and would put it at -37.5116 points.
Implied odds that would change the answer
Think of it as a missing $200.37. When the draw hits you must collect that much beyond the pot for the $50 call to pay for itself, 4.01 times your call.
Another way to close the gap is more outs. The fewest outs that call a half-pot bet on the flop is 7; with 7 outs you would hit 27.84%. That is 4 more outs than the 3 you hold.
| Future winnings | Price with them | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 25.00% | -12.51 points | -$25.02 | Fold |
| $50 | 20.00% | -7.51 points | -$18.78 | Fold |
| $100 | 16.67% | -4.18 points | -$12.53 | Fold |
| $250 | 11.11% | +1.38 points | +$6.20 | Call |
| $500 | 7.14% | +5.35 points | +$37.42 | Call |
Which chance to use
Both views point the same way. By the river you hit 12.49%, on the next card 6.38%, and the price is 25.00%, so the fold holds whichever number applies.
| Cards counted | Chance | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| By the river, two cards | 12.49% | -12.5116 points | -$25.02 | Fold |
| Next card only | 6.38% | -18.6170 points | -$37.23 | Fold |
Neighbors of this draw
Move up or down a few outs and watch the verdict. Every extra out is worth about 3.98 points on the flop, and the price stays at 25.00%.
Changing the bet, keeping the draw
One draw, 12 bets. Each row gives the equity the call needs, the margin over it, and the verdict for 3 outs on the flop.
Your draw can face a bet of up to 0.17 times the pot ($16.65 on a $100 pot) and still break even. That is under the quarter-pot bet, so none of the 12 sizes is a call.
| Bet size | Equity needed | Margin | Verdict |
|---|---|---|---|
| quarter-pot | 16.67% | -4.18 points | Fold |
| third-pot | 20.00% | -7.51 points | Fold |
| two-fifths-pot | 22.22% | -9.73 points | Fold |
| half-pot, this page | 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
Everything is computed from the closed form. Pairs without an out: 946 of 1,081. The rest, 12.49%, hold at least one out.
What is held fixed: the call equals the bet, so the price is $50 / $200 = 25.00%; the pot is won whole on a hit; there is no further betting; and each of the 47 unseen cards is as likely as any other. Opponent cards are not removed.
Computed from the closed form by the GeorgeLiPoker math library.
Updated
Questions
Is a call correct with 3 outs against a half-pot bet on the flop?
Math says fold. The half-pot bet of $50 needs 25.00% equity, 3 outs on the flop give 12.49%, and the margin is -12.51 points. Assuming a whole pot won on a hit and no further bets, the call is worth -$25.02 on average.
How many outs do you need to call a half-pot bet on the flop?
A call starts to work at 7 outs: 27.84% to hit versus 25.00% needed. One out fewer drops the chance to 24.14%. You hold 3, which is 4 fewer than the minimum.
How many cards should you count when a half-pot bet arrives on the flop?
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 25.00%, both say fold.
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