Verdict
Call
17 outs, flop, third-pot bet
- Chance to hit by the rivertwo cards to come59.76%
- Equity the call needs$33.33 into a pot of $166.6720.00%
- Margin over the priceyour chance minus the price+39.76 points
Your chance and the price
59.76% against 20.00%: the draw beats the price by 39.76 points. On this flop against a third-pot bet, that is a comfortable call.
You will reach 17 outs by adding up separate draws. With 47 cards unseen, the next card helps 36.17% of the time.
Counting the chips on a $100 pot
- Pot before the bet$100
- Bet$33.33
- Chips you put in$33.33
- Pot with your call in$166.67
- What a hit wins$133.33
- Net loss when you miss$33.33
- How often you hit59.76%
- Average value of the call+$66.27
- Equity the call needs20.00%
- Your chance minus the price, unrounded+39.7595 points
- Break-even count of outs4.91 outs
- Outs to spare, exactly+12.09 outs
Stay with simple rules: the whole pot on a hit, the call lost on a miss, no more money in. Under them calling gains $66.27 on average. The hit side averages $79.68, the miss side $13.41, and each dollar called returns +1.988.
Odds say the same thing. Hitting is 0.67 : 1 against, and the pot lays 4 : 1.
Watch the pot you divide by. Leaving your call out turns 20.00% into 25.00%, and the margin into +34.7595 points. Dividing by the starting pot gives 33.33% and a margin of +26.4261 points, further from the truth.
Where the call would flip
The threshold is 5 outs, a chance of 20.35%. With 17 in hand you are 12 outs clear of it.
Your margin is worth $110.89 in later losses. Past that, 3.33 times your call, folding would have been better.
| Given back later | Price with it | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 20.00% | +39.76 points | +$66.27 | Call |
| $10 | 21.28% | +38.48 points | +$60.29 | Call |
| $25 | 23.53% | +36.23 points | +$51.33 | Call |
| $50 | 28.57% | +31.19 points | +$36.39 | Call |
| $100 | 50.00% | +9.76 points | +$6.51 | Call |
Pricing one card at a time
The two chances agree on the verdict. 59.76% by the river and 36.17% on one card each lead to a call against 20.00%.
| Cards counted | Chance | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| By the river, two cards | 59.76% | +39.7595 points | +$66.27 | Call |
| Next card only | 36.17% | +16.1702 points | +$26.95 | Call |
The call as outs change
Same bet, same street, different draws. The row for 17 outs is marked, and every out is worth about 2.68 points.
Bigger and smaller bets
Look down the margin column to see where the draw stops paying. Every row uses 17 outs on the flop and a bet of a different size.
Nothing in the list is too big to call: 17 outs reach 59.76% on the flop, above every price on the page.
| Bet size | Equity needed | Margin | Verdict |
|---|---|---|---|
| quarter-pot | 16.67% | +43.09 points | Call |
| third-pot, this page | 20.00% | +39.76 points | Call |
| two-fifths-pot | 22.22% | +37.54 points | Call |
| half-pot | 25.00% | +34.76 points | Call |
| two-thirds-pot | 28.57% | +31.19 points | Call |
| three-quarter-pot | 30.00% | +29.76 points | Call |
| pot-size | 33.33% | +26.43 points | Call |
| 1.25x-pot | 35.71% | +24.05 points | Call |
| 1.5x-pot | 37.50% | +22.26 points | Call |
| 2x-pot | 40.00% | +19.76 points | Call |
| 3x-pot | 42.86% | +16.90 points | Call |
| 4x-pot | 44.44% | +15.32 points | Call |
How this is computed
The number is exact rather than estimated. 435 of the 1,081 pairs that could come are blanks, which leaves 59.76% for a hit.
The numbers are a baseline rather than a prediction for one hand. The price is 20.00%, from $33.33 into $166.67, 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
Call or fold with 17 outs on the flop against a bet of a third of the pot?
By the numbers it is a call. 17 outs on the flop hit 59.76% by the river, a third-pot bet needs 20.00%, and the margin is +39.76 points. That assumes you call the full $33.33 and no more betting follows, and it values the call at +$66.27 per $100 pot.
How strong must a draw be to call a third-pot bet on the flop?
A call starts to work at 5 outs: 20.35% to hit versus 20.00% needed. One out fewer drops the chance to 16.47%. You hold 17, which is 12 more than the minimum.
Which hit chance fits a third-pot bet on the flop?
Count two cards, 59.76%, when the bet is the last money going in, and one card, 36.17%, when the next street brings another bet. At a price of 20.00%, either number leads to a call.
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