Verdict
Call
13 outs, flop, three-quarter-pot bet
- Chance to hit by the rivertwo cards to come48.10%
- Equity the call needs$75 into a pot of $25030.00%
- Margin over the priceyour chance minus the price+18.10 points
Chance against price
48.10% against 30.00%: the draw beats the price by 18.10 points. On this flop against a three-quarter-pot bet, that is a comfortable call.
Think of 13 outs as a running total of every card that improves you. 13 of the 47 unseen cards qualify, which is 27.66% on one card.
Putting dollars on the call
- Starting pot$100
- Your opponent bets$75
- Your call$75
- Final pot if you call$250
- Gain on a hit$175
- Loss on a miss$75
- Your chance to hit48.10%
- Average value of the call+$45.26
- Equity needed to break even30.00%
- Your chance minus the price, unrounded+18.1036 points
- Outs that exactly reach the price7.59 outs
- Outs to spare, exactly+5.41 outs
If you win the whole pot on a hit and lose your call otherwise, with no more betting, calling gains $45.26 on average. Hits add $84.18 on average and misses cost $38.92 on average, or +0.603 per dollar called.
The same comparison in odds: the odds against hitting are 1.08 : 1, and the pot lays 2.33 : 1 on a call.
One easy error is to use 42.86%, the bet over the pot before your call, as the price. The right price is 30.00%, and the mistaken margin would be +5.2465 points. The bet over the starting pot, 75.00%, would claim -26.8964 points.
Slack in the call
Against this bet the draw needs 8 outs at the least. You have 5 outs more than that, so the call has some room.
After a hit you could give back up to $94.09 on later streets, 1.25 times your call, before the call stops paying.
| Given back later | Price with it | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 30.00% | +18.10 points | +$45.26 | Call |
| $10 | 31.25% | +16.85 points | +$40.45 | Call |
| $25 | 33.33% | +14.77 points | +$33.23 | Call |
| $50 | 37.50% | +10.60 points | +$21.21 | Call |
| $100 | 50.00% | -1.90 points | -$2.84 | Fold |
Two views of the same draw
48.10% for two cards says call, while 27.66% for one card says fold, both against 30.00%. If you will have to pay again on the turn, trust the one-card number.
| Cards counted | Chance | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| By the river, two cards | 48.10% | +18.1036 points | +$45.26 | Call |
| Next card only | 27.66% | -2.3404 points | -$5.85 | Fold |
Neighbors of this draw
Same bet, same street, different draws. The row for 13 outs is marked, and every out is worth about 3.05 points.
Other bet sizes for this draw
Bigger bets ask for more equity while your chance stays at 48.10%. Here is every bet size against the same draw, with the row for this page marked.
Your chance is high enough that any bet in the table is a call. All 12 sizes clear with 48.10%.
| Bet size | Equity needed | Margin | Verdict |
|---|---|---|---|
| quarter-pot | 16.67% | +31.44 points | Call |
| third-pot | 20.00% | +28.10 points | Call |
| two-fifths-pot | 22.22% | +25.88 points | Call |
| half-pot | 25.00% | +23.10 points | Call |
| two-thirds-pot | 28.57% | +19.53 points | Call |
| three-quarter-pot, this page | 30.00% | +18.10 points | Call |
| pot-size | 33.33% | +14.77 points | Call |
| 1.25x-pot | 35.71% | +12.39 points | Call |
| 1.5x-pot | 37.50% | +10.60 points | Call |
| 2x-pot | 40.00% | +8.10 points | Call |
| 3x-pot | 42.86% | +5.25 points | Call |
| 4x-pot | 44.44% | +3.66 points | Call |
How this is computed
The number is exact rather than estimated. 561 of the 1,081 pairs that could come are blanks, which leaves 48.10% for a hit.
What is held fixed: the call equals the bet, so the price is $75 / $250 = 30.00%; 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 three quarters of the pot with 13 outs on the flop?
Your chance, 48.10%, set against the 30.00% price gives +18.10 points and a call. With a $100 pot, a $75 call and no more betting, the average value of the call is +$45.26.
What is the fewest outs that can call a three-quarter-pot bet on the flop?
A call starts to work at 8 outs: 31.45% to hit versus 30.00% needed. One out fewer drops the chance to 27.84%. You hold 13, which is 5 more than the minimum.
Which chance should you compare with the price, the next card or the river?
Pick the number that matches the street plan: 48.10% for seeing both cards for one bet, 27.66% for paying card by card. Both face 30.00%, and they lead to call and fold in that order.
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