Verdict
Call
17 outs, turn, three-quarter-pot bet
- Chance to hit by the riverone card to come36.96%
- Equity the call needs$75 into a pot of $25030.00%
- Margin over the priceyour chance minus the price+6.96 points
Your chance and the price
17 outs on the turn hit 36.96% by the river, and the three-quarter-pot bet needs 30.00%. You are 6.96 points above the price, a real edge, so calling is right.
Think of 17 outs as a running total of every card that improves you. 17 of the 46 unseen cards qualify, which is 36.96% on one card.
Counting the chips on a $100 pot
- Pot when the bet arrives$100
- Your opponent bets$75
- Cost to call$75
- Total pot after calling$250
- Net gain when you hit$175
- Loss on a miss$75
- Chance to hit by the river36.96%
- Average value of the call+$17.39
- Equity the call needs30.00%
- Exact margin over the price+6.9565 points
- Outs that exactly reach the price13.80 outs
- Outs to spare, exactly+3.20 outs
Over many identical spots, with the whole pot won on every hit, the call lost on every miss and no extra betting, calling gains $17.39 on average. Hits bring in $64.67, misses cost $47.28, and the ratio is +0.232 per dollar called.
Stated as odds, you are 1.71 : 1 against hitting and the call gets 2.33 : 1 from the pot.
Skipping your own call in the pot gives a price of 42.86% where 30.00% is correct, and a margin of -5.9006 points instead of +6.96 points. The starting pot gives 75.00% and a margin of -38.0435 points, which is wrong by even more.
How much room the call has
14 outs is the line for a three-quarter-pot bet on the turn. Your 17 sit 3 outs above it, and the chance at the line is 30.43%.
If hitting means paying off a bigger hand later, the call survives a loss of $47.06. That is 0.63 times the $75 call.
| Given back later | Price with it | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 30.00% | +6.96 points | +$17.39 | Call |
| $10 | 31.25% | +5.71 points | +$13.70 | Call |
| $25 | 33.33% | +3.62 points | +$8.15 | Call |
| $50 | 37.50% | -0.54 points | -$1.09 | Fold |
| $100 | 50.00% | -13.04 points | -$19.57 | Fold |
Flop and turn compared
The turn card has already fallen, and a draw that hit 59.76% from the flop is down to 36.96%. That drop of 22.80 points leaves the verdict a call, as it was on the flop.
| Street | Chance by the river | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| Flop, two cards to come | 59.76% | +29.7595 points | +$74.40 | Call |
| Turn, one card to come | 36.96% | +6.9565 points | +$17.39 | Call |
Neighbors of this draw
A few outs either way, against a three-quarter-pot bet that needs 30.00%. The chance climbs about 2.17 points with each extra out.
| Outs | By the river | Margin | Verdict |
|---|---|---|---|
| 15 outs | 32.61% | +2.61 points | Call |
| 16 outs | 34.78% | +4.78 points | Call |
| 17 outs, this page | 36.96% | +6.96 points | Call |
| 18 outs | 39.13% | +9.13 points | Call |
| 19 outs | 41.30% | +11.30 points | Call |
Bigger and smaller bets
How much does bet size matter? The price climbs from 16.67% to 44.44% across the list, while 17 outs stay at 36.96%.
Past 1.42 times the pot ($141.67 on a $100 pot) the price outruns your chance. Of the 12 sizes, 8 are calls for 17 outs on the turn.
| Bet size | Equity needed | Margin | Verdict |
|---|---|---|---|
| quarter-pot | 16.67% | +20.29 points | Call |
| third-pot | 20.00% | +16.96 points | Call |
| two-fifths-pot | 22.22% | +14.73 points | Call |
| half-pot | 25.00% | +11.96 points | Call |
| two-thirds-pot | 28.57% | +8.39 points | Call |
| three-quarter-pot, this page | 30.00% | +6.96 points | Call |
| pot-size | 33.33% | +3.62 points | Call |
| 1.25x-pot | 35.71% | +1.24 points | Call |
| 1.5x-pot | 37.50% | -0.54 points | Fold |
| 2x-pot | 40.00% | -3.04 points | Fold |
| 3x-pot | 42.86% | -5.90 points | Fold |
| 4x-pot | 44.44% | -7.49 points | Fold |
How this is computed
The chance to hit is the exact closed form, with no simulation. From the turn, 17 of the 46 unseen cards are outs, so the chance is 17 / 46, which is 36.96%.
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 46 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 is the right play with 17 outs when a three-quarter-pot bet comes on the turn?
Math says call. The three-quarter-pot bet of $75 needs 30.00% equity, 17 outs on the turn give 36.96%, and the margin is +6.96 points. Assuming a whole pot won on a hit and no further bets, the call is worth +$17.39 on average.
What is the fewest outs that can call a three-quarter-pot bet on the turn?
Against 30.00%, the first count that works on the turn is 14, at 30.43%. At 13 the chance is 28.26%, too low. Compared with that threshold, your 17 outs are 3 above.
When is the next-card chance the better comparison?
On the turn only one card is left, so the by-the-river chance and the next-card chance are the same, 36.96%. Against the 30.00% price that is a call, with a margin of +6.96 points.
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