Verdict
Fold
4 outs, flop, half-pot bet
- Chance to hit by the rivertwo cards to come16.47%
- Equity the call needs$50 into a pot of $20025.00%
- Margin over the priceyour chance minus the price-8.53 points
Comparing the draw with the bet
The price is 25.00% and your chance is 16.47%. You sit 8.53 points below the line, which is a wide gap, so you fold.
If you are on a gutshot straight draw, this is your count: 4 outs among 47 unseen cards, or 8.51% on a single card.
The $100 pot example
- Starting pot$100
- Bet$50
- You call$50
- Pot with your call in$200
- Net gain when you hit$150
- What a miss costs$50
- Probability of a hit16.47%
- Calling is worth, on average-$17.07
- Price of the call25.00%
- Exact margin over the price-8.5338 points
- Outs at break-even6.23 outs
- Margin measured in outs-2.23 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 $17.07 on average: $24.70 in, $41.77 out, -0.341 per dollar called.
The same comparison in odds: the odds against hitting are 5.07 : 1, and the pot lays 3 : 1 on a call.
One easy error is to use 33.33%, the bet over the pot before your call, as the price. The right price is 25.00%, and the mistaken margin would be -16.8671 points. The bet over the starting pot, 50.00%, would claim -33.5338 points.
Implied odds that would change the answer
To make the call break even you would need to win another $103.65 after you hit, which is 2.07 times your call. Anything above that makes the call a good one.
Outs are the other lever. At 7 outs you reach 27.84% by the river, enough for a half-pot bet, and you are 3 outs away.
| Future winnings | Price with them | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 25.00% | -8.53 points | -$17.07 | Fold |
| $50 | 20.00% | -3.53 points | -$8.83 | Fold |
| $100 | 16.67% | -0.20 points | -$0.60 | Fold |
| $250 | 11.11% | +5.36 points | +$24.10 | Call |
| $500 | 7.14% | +9.32 points | +$65.26 | Call |
Pricing one card at a time
Whether you count one card or two, the answer is a fold. The river figure is 16.47%, the next-card figure is 8.51%, and both are measured against 25.00%.
| Cards counted | Chance | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| By the river, two cards | 16.47% | -8.5338 points | -$17.07 | Fold |
| Next card only | 8.51% | -16.4894 points | -$32.98 | Fold |
How the answer moves with outs
The table shows 4 outs and the draws around it on the flop, all against the same half-pot bet. Each extra out adds about 3.89 points to the chance here.
Changing the bet, keeping the draw
The same 4 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.
The ceiling for a call is a bet of 0.25 times the pot ($24.55 on a $100 pot), smaller than anything in the table. All 12 sizes ask for more than 16.47%.
| Bet size | Equity needed | Margin | Verdict |
|---|---|---|---|
| quarter-pot | 16.67% | -0.20 points | Fold |
| third-pot | 20.00% | -3.53 points | Fold |
| two-fifths-pot | 22.22% | -5.76 points | Fold |
| half-pot, this page | 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
Everything is computed from the closed form. Pairs without an out: 903 of 1,081. The rest, 16.47%, 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
What does the math say about calling a bet of half the pot with 4 outs on the flop?
Math says fold. The half-pot bet of $50 needs 25.00% equity, 4 outs on the flop give 16.47%, and the margin is -8.53 points. Assuming a whole pot won on a hit and no further bets, the call is worth -$17.07 on average.
How many outs do you need to call a half-pot bet on the flop?
The fewest outs that call a half-pot bet on the flop is 7. With 7 outs you hit 27.84%, which reaches the 25.00% price, while 6 outs hit only 24.14%. You have 4, so you are 3 below that count.
Does it matter whether you count one card or two against a half-pot bet?
Count two cards, 16.47%, when the bet is the last money going in, and one card, 8.51%, when the next street brings another bet. At a price of 25.00%, either number leads to a fold.
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