Verdict
Fold
1 out, turn, third-pot bet
- Chance to hit by the riverone card to come2.17%
- Equity the call needs$33.33 into a pot of $166.6720.00%
- Margin over the priceyour chance minus the price-17.83 points
Chance against price
2.17% against 20.00%: the draw trails the price by 17.83 points. On this turn against a third-pot bet, that is an easy fold.
No common draw is a single card, so read this as a one-card hope: 2.17% on the next card, with 46 cards unseen.
The same spot in dollars
- The pot before betting$100
- The bet$33.33
- Chips you put in$33.33
- Total pot after calling$166.67
- You can win on a hit$133.33
- You lose on a miss$33.33
- Probability of a hit2.17%
- Expected value of a call-$29.71
- Break-even equity20.00%
- Unrounded margin-17.8261 points
- Break-even count of outs9.20 outs
- Your outs minus break-even outs-8.20 outs
Expected value says the same in dollars. Win the whole pot on a hit, lose your call on a miss, add no more betting, and the call loses $29.71 on average: $2.90 in, $32.61 out, -0.891 per dollar called.
The same comparison in odds: the odds against hitting are 45 : 1, and the pot lays 4 : 1 on a call.
One easy error is to use 25.00%, the bet over the pot before your call, as the price. The right price is 20.00%, and the mistaken margin would be -22.8261 points. The bet over the starting pot, 33.33%, would claim -31.1594 points.
What implied odds would have to do
Implied odds are the way to close the gap. You need $1,366.67 more on later streets after hitting, which is 41.00 times the call you make.
The call starts to work at 10 outs, where the chance is 21.74%. Your 1 out falls 9 outs below that.
| Future winnings | Price with them | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 20.00% | -17.83 points | -$29.71 | Fold |
| $50 | 15.38% | -13.21 points | -$28.62 | Fold |
| $100 | 12.50% | -10.33 points | -$27.54 | Fold |
| $250 | 8.00% | -5.83 points | -$24.28 | Fold |
| $500 | 5.00% | -2.83 points | -$18.84 | Fold |
The same draw on the flop
Compare the streets. With two cards left, 1 out hits 4.26% (a fold); with one card left they hit 2.17% (a fold). The difference is 2.08 points.
| Street | Chance by the river | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| Flop, two cards to come | 4.26% | -15.7447 points | -$26.24 | Fold |
| Turn, one card to come | 2.17% | -17.8261 points | -$29.71 | Fold |
Draws around this one
Draws near 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.
Other bet sizes for this draw
The same 1 out on the turn meets a different price at each bet size. The table runs from the smallest bet to the largest, and the row for this page is marked.
Your draw can face a bet of up to 0.02 times the pot ($2.27 on a $100 pot) and still break even. That is under the quarter-pot bet, so none of the 12 sizes is a call.
| Bet size | Equity needed | Margin | Verdict |
|---|---|---|---|
| quarter-pot | 16.67% | -14.49 points | Fold |
| third-pot, this page | 20.00% | -17.83 points | Fold |
| two-fifths-pot | 22.22% | -20.05 points | Fold |
| half-pot | 25.00% | -22.83 points | Fold |
| two-thirds-pot | 28.57% | -26.40 points | Fold |
| three-quarter-pot | 30.00% | -27.83 points | Fold |
| pot-size | 33.33% | -31.16 points | Fold |
| 1.25x-pot | 35.71% | -33.54 points | Fold |
| 1.5x-pot | 37.50% | -35.33 points | Fold |
| 2x-pot | 40.00% | -37.83 points | Fold |
| 3x-pot | 42.86% | -40.68 points | Fold |
| 4x-pot | 44.44% | -42.27 points | Fold |
How this is computed
No sampling is involved. On the turn there are 46 unseen cards and 1 out among them, which gives 1 / 46 = 2.17%.
The model is deliberately simple: call everything, win everything on a hit, face no more bets, deal from 46 equally likely unseen cards, and ignore an opponent's holding. With the price at $33.33 / $166.67 = 20.00%, later streets and shared outs are what change the real answer.
Computed from the closed form by the GeorgeLiPoker math library.
Updated
Questions
Call or fold with 1 out on the turn against a bet of a third of the pot?
The verdict is fold. Your chance is 2.17% and the price is 20.00%, which leaves -17.83 points. On a $100 pot with a $33.33 bet, calling is worth -$29.71 on average if the whole pot is won on a hit and nothing more is bet.
What is the fewest outs that can call a third-pot bet on the turn?
The fewest outs that call a third-pot bet on the turn is 10. With 10 outs you hit 21.74%, which reaches the 20.00% price, while 9 outs hit only 19.57%. You have 1, so you are 9 below that count.
When is the next-card chance the better comparison?
They are one number here. With a single card to come, 2.17% is both the next-card chance and the by-the-river chance, and it gives a fold against 20.00%, a margin of -17.83 points.
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