Verdict
Fold
2 outs, flop, half-pot bet
- Chance to hit by the rivertwo cards to come8.42%
- Equity the call needs$50 into a pot of $20025.00%
- Margin over the priceyour chance minus the price-16.58 points
Your chance and the price
Your draw is priced at 25.00% and it arrives just 8.42% of the time. A gap of 16.58 points is large, and later bets would have to be large to make up for it.
For a pocket pair that wants a set, 2 outs is the number to use, and one card hits 4.26% of the time out of 47 unseen.
The same spot in dollars
- Pot when the bet arrives$100
- The bet$50
- You call$50
- Total pot after calling$200
- You can win on a hit$150
- Net loss when you miss$50
- How often you hit8.42%
- Average value of the call-$33.16
- Equity the call needs25.00%
- Your chance minus the price, unrounded-16.5819 points
- Break-even count of outs6.23 outs
- Margin measured in outs-4.23 outs
Suppose a hit wins the entire pot, a miss loses your call, and no more betting follows. The average gain is $12.63, the average loss is $45.79, and calling loses $33.16 on average, or -0.663 per dollar called.
The same comparison in odds: the odds against hitting are 10.88 : 1, and the pot lays 3 : 1 on a call.
The price is 25.00% because your call goes into the pot too. Leave it out and you get 33.33%, a margin of -24.9152 points that does not exist; use the starting pot instead and 50.00% puts the margin at -41.5819 points.
What it would take to call
Implied odds are the way to close the gap. You need $393.96 more on later streets after hitting, which is 7.88 times the call you make.
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 5 more outs than the 2 you hold.
| Future winnings | Price with them | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 25.00% | -16.58 points | -$33.16 | Fold |
| $50 | 20.00% | -11.58 points | -$28.95 | Fold |
| $100 | 16.67% | -8.25 points | -$24.75 | Fold |
| $250 | 11.11% | -2.69 points | -$12.12 | Fold |
| $500 | 7.14% | +1.28 points | +$8.93 | Call |
Two views of the same draw
Whether you count one card or two, the answer is a fold. The river figure is 8.42%, the next-card figure is 4.26%, and both are measured against 25.00%.
| Cards counted | Chance | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| By the river, two cards | 8.42% | -16.5819 points | -$33.16 | Fold |
| Next card only | 4.26% | -20.7447 points | -$41.49 | Fold |
Nearby draws
Same bet, same street, different draws. The row for 2 outs is marked, and every out is worth about 4.07 points.
Other bet sizes for this draw
How much does bet size matter? The price climbs from 16.67% to 44.44% across the list, while 2 outs stay at 8.42%.
Break-even for this draw is a bet of 0.10 times the pot ($10.12 on a $100 pot). Every size in the table is larger than that, so each row is a fold.
| Bet size | Equity needed | Margin | Verdict |
|---|---|---|---|
| quarter-pot | 16.67% | -8.25 points | Fold |
| third-pot | 20.00% | -11.58 points | Fold |
| two-fifths-pot | 22.22% | -13.80 points | Fold |
| half-pot, this page | 25.00% | -16.58 points | Fold |
| two-thirds-pot | 28.57% | -20.15 points | Fold |
| three-quarter-pot | 30.00% | -21.58 points | Fold |
| pot-size | 33.33% | -24.92 points | Fold |
| 1.25x-pot | 35.71% | -27.30 points | Fold |
| 1.5x-pot | 37.50% | -29.08 points | Fold |
| 2x-pot | 40.00% | -31.58 points | Fold |
| 3x-pot | 42.86% | -34.44 points | Fold |
| 4x-pot | 44.44% | -36.03 points | Fold |
Pages that use the same math
How this is computed
The chance rests on counting, not on a rule of thumb. Blank pairs: 990 out of 1,081; hit chance: 8.42%.
Keep the assumptions in view: a full call ($50 into $200, or 25.00%), the whole pot on a hit, no more betting, and 47 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 does the math say about calling a bet of half the pot with 2 outs on the flop?
The verdict is fold. Your chance is 8.42% and the price is 25.00%, which leaves -16.58 points. On a $100 pot with a $50 bet, calling is worth -$33.16 on average if the whole pot is won on a hit and nothing more is bet.
How many outs do you need to call a half-pot bet on the flop?
To call a half-pot bet on the flop you want 7 outs or more. 7 reach 27.84% and 6 reach 24.14%, with 25.00% as the bar. Your 2 outs are 5 under.
Which hit chance fits a half-pot bet on the flop?
Match the number to the betting: 8.42% if all-in or checked down, 4.26% if you face another bet on the turn. The price is 25.00%, and both numbers agree on fold.
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