Verdict
Fold
4 outs, turn, third-pot bet
- Chance to hit by the riverone card to come8.70%
- Equity the call needs$33.33 into a pot of $166.6720.00%
- Margin over the priceyour chance minus the price-11.30 points
Comparing the draw with the bet
With 4 outs on the turn you hit 8.70% by the river, and a third-pot bet asks for 20.00%. A 11.30-point shortfall makes this a clear fold.
For a gutshot straight draw, 4 outs is the number to use, and one card hits 8.70% of the time out of 46 unseen.
The arithmetic of this call
- Starting pot$100
- Your opponent bets$33.33
- Cost to call$33.33
- Pot after your call$166.67
- You can win on a hit$133.33
- Net loss when you miss$33.33
- Your chance to hit8.70%
- Calling is worth, on average-$18.84
- Price of the call20.00%
- Your chance minus the price, unrounded-11.3043 points
- Outs that exactly reach the price9.20 outs
- Outs to spare, exactly-5.20 outs
Price it in dollars, with no later bets: win the whole pot on a hit, lose the call on a miss. That averages $11.59 in and $30.43 out, so calling loses $18.84 on average at -0.565 per dollar called.
Put as odds, the draw is 10.5 : 1 against, and the pot offers 4 : 1 for the call.
Counting the pot without your call makes the price look like 25.00%, when the real price is 20.00%. On that mistaken price the margin would read -16.3043 points; on 33.33%, the bet over the starting pot, it would read -24.6377 points.
What implied odds would have to do
Your chance is 8.70%, so a hit has to pay $383.33 in all, or $216.67 more than the pot you can see. That extra is 6.50 times what you call.
Outs are the other lever. At 10 outs you reach 21.74% by the river, enough for a third-pot bet, and you are 6 outs away.
| Future winnings | Price with them | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 20.00% | -11.30 points | -$18.84 | Fold |
| $50 | 15.38% | -6.69 points | -$14.49 | Fold |
| $100 | 12.50% | -3.80 points | -$10.14 | Fold |
| $250 | 8.00% | +0.70 points | +$2.90 | Call |
| $500 | 5.00% | +3.70 points | +$24.64 | Call |
How the turn changes the draw
You have lost a card to come. From the flop 4 outs reach 16.47%; from the turn they reach 8.70%, 7.77 points less. Against 20.00% the flop version is a fold.
| Street | Chance by the river | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| Flop, two cards to come | 16.47% | -3.5338 points | -$5.89 | Fold |
| Turn, one card to come | 8.70% | -11.3043 points | -$18.84 | Fold |
One out more or less
A few outs either way, against a third-pot bet that needs 20.00%. The chance climbs about 2.17 points with each extra out.
Bigger and smaller bets
How much does bet size matter? The price climbs from 16.67% to 44.44% across the list, while 4 outs stay at 8.70%.
4 outs stop paying at 0.11 times the pot ($10.53 on a $100 pot), below the smallest size listed. The call fails at all 12 bet sizes.
| Bet size | Equity needed | Margin | Verdict |
|---|---|---|---|
| quarter-pot | 16.67% | -7.97 points | Fold |
| third-pot, this page | 20.00% | -11.30 points | Fold |
| two-fifths-pot | 22.22% | -13.53 points | Fold |
| half-pot | 25.00% | -16.30 points | Fold |
| two-thirds-pot | 28.57% | -19.88 points | Fold |
| three-quarter-pot | 30.00% | -21.30 points | Fold |
| pot-size | 33.33% | -24.64 points | Fold |
| 1.25x-pot | 35.71% | -27.02 points | Fold |
| 1.5x-pot | 37.50% | -28.80 points | Fold |
| 2x-pot | 40.00% | -31.30 points | Fold |
| 3x-pot | 42.86% | -34.16 points | Fold |
| 4x-pot | 44.44% | -35.75 points | Fold |
How this is computed
Everything is computed from the closed form. The river chance is 4 outs over 46 unseen cards, 8.70%.
These figures describe a clean spot. You pay the whole bet, which costs $33.33 of a $166.67 pot (20.00%), collect the whole pot on a hit, meet no more bets, and draw from 46 equally likely cards, with no adjustment for an opponent's hand.
Computed from the closed form by the GeorgeLiPoker math library.
Updated
Questions
What does the math say about calling a bet of a third of the pot with 4 outs on the turn?
Reduce the question to a comparison of two numbers: 8.70% to hit and 20.00% to break even. The first minus the second is -11.30 points, which makes this a fold, and the call averages -$18.84 on a $100 pot if no more betting follows.
How many outs make a call correct against a third of the pot on the turn?
Against 20.00%, the first count that works on the turn is 10, at 21.74%. At 9 the chance is 19.57%, too low. Compared with that threshold, your 4 outs are 6 below.
Which hit chance fits a third-pot bet on the turn?
They are one number here. With a single card to come, 8.70% is both the next-card chance and the by-the-river chance, and it gives a fold against 20.00%, a margin of -11.30 points.
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