Verdict
Fold
5 outs, flop, pot-size bet
- Chance to hit by the rivertwo cards to come20.35%
- Equity the call needs$100 into a pot of $30033.33%
- Margin over the priceyour chance minus the price-12.98 points
Reading the verdict
20.35% against 33.33%: the draw trails the price by 12.98 points. On this flop against a pot-size bet, that is an easy fold.
A count of 5 outs is usually the sum of more than one draw. Out of 47 unseen cards, one card helps 10.64% of the time.
A $100 pot, step by step
- Pot when the bet arrives$100
- Bet$100
- You call$100
- Final pot if you call$300
- Net gain when you hit$200
- Net loss when you miss$100
- Chance to hit by the river20.35%
- Calling is worth, on average-$38.95
- Break-even equity33.33%
- Unrounded margin-12.9818 points
- Outs at break-even8.53 outs
- Outs above the price-3.53 outs
If you win the whole pot on a hit and lose your call otherwise, with no more betting, calling loses $38.95 on average. Hits add $40.70 on average and misses cost $79.65 on average, or -0.389 per dollar called.
In odds, you face 3.91 : 1 against you and the pot pays 2 : 1.
The price is 33.33% because your call goes into the pot too. Leave it out and you get 50.00%, a margin of -29.6485 points that does not exist.
The extra winnings a call would need
Think of it as a missing $191.36. When the draw hits you must collect that much beyond the pot for the $100 call to pay for itself, 1.91 times your call.
Another way to close the gap is more outs. The fewest outs that call a pot-size bet on the flop is 9; with 9 outs you would hit 34.97%. That is 4 more outs than the 5 you hold.
| Future winnings | Price with them | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 33.33% | -12.98 points | -$38.95 | Fold |
| $50 | 28.57% | -8.22 points | -$28.77 | Fold |
| $100 | 25.00% | -4.65 points | -$18.59 | Fold |
| $250 | 18.18% | +2.17 points | +$11.93 | Call |
| $500 | 12.50% | +7.85 points | +$62.81 | Call |
One card or two
You can skip the usual debate over one card versus two, because 10.64% and 20.35% both give a fold against 33.33%.
| Cards counted | Chance | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| By the river, two cards | 20.35% | -12.9818 points | -$38.95 | Fold |
| Next card only | 10.64% | -22.6950 points | -$68.09 | Fold |
Counts close to yours
The table shows 5 outs and the draws around it on the flop, all against the same pot-size bet. Each extra out adds about 3.79 points to the chance here.
The draw across every bet size
Bigger bets ask for more equity while your chance stays at 20.35%. Here is every bet size against the same draw, with the row for this page marked.
5 outs stop paying at 0.34 times the pot ($34.32 on a $100 pot). The call holds up against 2 of the 12 bet sizes.
| Bet size | Equity needed | Margin | Verdict |
|---|---|---|---|
| quarter-pot | 16.67% | +3.68 points | Call |
| third-pot | 20.00% | +0.35 points | Call |
| two-fifths-pot | 22.22% | -1.87 points | Fold |
| half-pot | 25.00% | -4.65 points | Fold |
| two-thirds-pot | 28.57% | -8.22 points | Fold |
| three-quarter-pot | 30.00% | -9.65 points | Fold |
| pot-size, this page | 33.33% | -12.98 points | Fold |
| 1.25x-pot | 35.71% | -15.36 points | Fold |
| 1.5x-pot | 37.50% | -17.15 points | Fold |
| 2x-pot | 40.00% | -19.65 points | Fold |
| 3x-pot | 42.86% | -22.51 points | Fold |
| 4x-pot | 44.44% | -24.09 points | Fold |
How this is computed
Here is how 20.35% was found. Deal every pair of the 47 unseen cards: 861 of 1,081 pairs contain no out.
The numbers are a baseline rather than a prediction for one hand. The price is 33.33%, from $100 into $300, and the chance assumes a whole pot won on a hit, no more betting, 47 equally likely unseen cards, and no cards removed for the other player.
Computed from the closed form by the GeorgeLiPoker math library.
Updated
Questions
Does the math favor calling a pot-size bet with 5 outs on the flop?
By the numbers it is a fold. 5 outs on the flop hit 20.35% by the river, a pot-size bet needs 33.33%, and the margin is -12.98 points. That assumes you call the full $100 and no more betting follows, and it values the call at -$38.95 per $100 pot.
What is the minimum number of outs for a pot-size bet on the flop?
To call a pot-size bet on the flop you want 9 outs or more. 9 reach 34.97% and 8 reach 31.45%, with 33.33% as the bar. Your 5 outs are 4 under.
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: 20.35%. If another bet is coming on the turn, count one card: 10.64%. Against 33.33%, both say fold.
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