Verdict
Fold
6 outs, turn, third-pot bet
- Chance to hit by the riverone card to come13.04%
- Equity the call needs$33.33 into a pot of $166.6720.00%
- Margin over the priceyour chance minus the price-6.96 points
Comparing the draw with the bet
The odds you are given are worse than the odds you need: 20.00% needed, 13.04% held, 6.96 points missing.
Holding two overcards gives you exactly 6 outs, out of 46 unseen cards. One card hits 13.04% of the time.
The $100 pot example
- Pot before the bet$100
- Your opponent bets$33.33
- Chips you put in$33.33
- Total pot after calling$166.67
- What a hit wins$133.33
- What a miss costs$33.33
- Chance to hit by the river13.04%
- Average value of the call-$11.59
- Equity the call needs20.00%
- Your chance minus the price, unrounded-6.9565 points
- Outs at break-even9.20 outs
- Outs above the price-3.20 outs
Price it in dollars, with no later bets: win the whole pot on a hit, lose the call on a miss. That averages $17.39 in and $28.99 out, so calling loses $11.59 on average at -0.348 per dollar called.
The same comparison in odds: the odds against hitting are 6.67 : 1, and the pot lays 4 : 1 on a 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 -11.9565 points; on 33.33%, the bet over the starting pot, it would read -20.2899 points.
What implied odds would have to do
Think of it as a missing $88.89. When the draw hits you must collect that much beyond the pot for the $33.33 call to pay for itself, 2.67 times your call.
Another way to close the gap is more outs. The fewest outs that call a third-pot bet on the turn is 10; with 10 outs you would hit 21.74%. That is 4 more outs than the 6 you hold.
| Future winnings | Price with them | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 20.00% | -6.96 points | -$11.59 | Fold |
| $50 | 15.38% | -2.34 points | -$5.07 | Fold |
| $100 | 12.50% | +0.54 points | +$1.45 | Call |
| $250 | 8.00% | +5.04 points | +$21.01 | Call |
| $500 | 5.00% | +8.04 points | +$53.62 | Call |
The same draw on the flop
Only the river remains, so there is just one number: 13.04%. For reference, the same draw on the flop was 24.14%, 11.10 points higher, which against 20.00% is a call.
| Street | Chance by the river | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| Flop, two cards to come | 24.14% | +4.1443 points | +$6.91 | Call |
| Turn, one card to come | 13.04% | -6.9565 points | -$11.59 | Fold |
Counts close to yours
Draws close to yours, on the same street and against the same bet: the price is fixed at 20.00%, and each out moves the chance about 2.17 points.
| Outs | By the river | Margin | Verdict |
|---|---|---|---|
| 4 outs | 8.70% | -11.30 points | Fold |
| 5 outs | 10.87% | -9.13 points | Fold |
| 6 outs, this page | 13.04% | -6.96 points | Fold |
| 7 outs | 15.22% | -4.78 points | Fold |
| 8 outs | 17.39% | -2.61 points | Fold |
Changing the bet, keeping the draw
Bet size sets the price, so the verdict changes as you scan the table. The third-pot bet of this page is marked in the first column.
With 13.04% to hit, you can call a bet up to 0.18 times the pot ($17.65 on a $100 pot) and no more, which is smaller than every size listed. All 12 rows are folds.
| Bet size | Equity needed | Margin | Verdict |
|---|---|---|---|
| quarter-pot | 16.67% | -3.62 points | Fold |
| third-pot, this page | 20.00% | -6.96 points | Fold |
| two-fifths-pot | 22.22% | -9.18 points | Fold |
| half-pot | 25.00% | -11.96 points | Fold |
| two-thirds-pot | 28.57% | -15.53 points | Fold |
| three-quarter-pot | 30.00% | -16.96 points | Fold |
| pot-size | 33.33% | -20.29 points | Fold |
| 1.25x-pot | 35.71% | -22.67 points | Fold |
| 1.5x-pot | 37.50% | -24.46 points | Fold |
| 2x-pot | 40.00% | -26.96 points | Fold |
| 3x-pot | 42.86% | -29.81 points | Fold |
| 4x-pot | 44.44% | -31.40 points | Fold |
How this is computed
Counting is exact: one card is left, 6 of 46 unseen cards help, and the chance is 13.04%.
What is held fixed: the call equals the bet, so the price is $33.33 / $166.67 = 20.00%; 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 does the math say about calling a bet of a third of the pot with 6 outs on the turn?
Math says fold. The third-pot bet of $33.33 needs 20.00% equity, 6 outs on the turn give 13.04%, and the margin is -6.96 points. Assuming a whole pot won on a hit and no further bets, the call is worth -$11.59 on average.
At what count of outs does a third-pot bet on the turn become a call?
Look for 10 outs. That is the smallest count whose chance, 21.74%, reaches the 20.00% price; 9 manages 19.57%. You have 6, so you are 4 behind the minimum.
Which hit chance fits a third-pot bet on the turn?
The question belongs to the flop. On the turn, 6 outs among 46 cards give 13.04% either way, and against 20.00% that is a fold by 6.96 points.
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