Verdict
Fold
10 outs, turn, three-quarter-pot bet
- Chance to hit by the riverone card to come21.74%
- Equity the call needs$75 into a pot of $25030.00%
- Margin over the priceyour chance minus the price-8.26 points
The price of the call
Your draw is priced at 30.00% and it arrives just 21.74% of the time. A gap of 8.26 points is large, and later bets would have to be large to make up for it.
A count of 10 outs is usually the sum of more than one draw. Out of 46 unseen cards, one card helps 21.74% of the time.
One hand, in dollars
- Pot when the bet arrives$100
- Your opponent bets$75
- Chips you put in$75
- Pot with your call in$250
- What a hit wins$175
- What a miss costs$75
- Chance to hit by the river21.74%
- Expected value of a call-$20.65
- Break-even equity30.00%
- Your chance minus the price, unrounded-8.2609 points
- Outs that exactly reach the price13.80 outs
- Your outs minus break-even outs-3.80 outs
Stay with simple rules: the whole pot on a hit, the call lost on a miss, no more money in. Under them calling loses $20.65 on average. The hit side averages $38.04, the miss side $58.70, and each dollar called returns -0.275.
Read as odds: 3.6 : 1 against you, 2.33 : 1 from the pot.
The price is 30.00% because your call goes into the pot too. Leave it out and you get 42.86%, a margin of -21.1180 points that does not exist; use the starting pot instead and 75.00% puts the margin at -53.2609 points.
What it would take to call
With 21.74% to hit, break-even sits $95 higher than the pot shows. Put another way, later bets must add 1.27 times your call.
The smallest count that pays for a three-quarter-pot bet is 14 outs at 30.43%. You hold 10, which is 4 outs fewer.
| Future winnings | Price with them | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 30.00% | -8.26 points | -$20.65 | Fold |
| $50 | 25.00% | -3.26 points | -$9.78 | Fold |
| $100 | 21.43% | +0.31 points | +$1.09 | Call |
| $250 | 15.00% | +6.74 points | +$33.70 | Call |
| $500 | 10.00% | +11.74 points | +$88.04 | Call |
One card to come instead of two
Waiting a street costs 16.65 points. The flop gives 10 outs two chances to hit, 38.39%, and a call against 30.00%; the turn gives one, 21.74%.
| Street | Chance by the river | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| Flop, two cards to come | 38.39% | +8.3904 points | +$20.98 | Call |
| Turn, one card to come | 21.74% | -8.2609 points | -$20.65 | Fold |
How the answer moves with outs
Move up or down a few outs and watch the verdict. Every extra out is worth about 2.17 points on the turn, and the price stays at 30.00%.
| Outs | By the river | Margin | Verdict |
|---|---|---|---|
| 8 outs | 17.39% | -12.61 points | Fold |
| 9 outs | 19.57% | -10.43 points | Fold |
| 10 outs, this page | 21.74% | -8.26 points | Fold |
| 11 outs | 23.91% | -6.09 points | Fold |
| 12 outs | 26.09% | -3.91 points | Fold |
The same draw against other bet sizes
How much does bet size matter? The price climbs from 16.67% to 44.44% across the list, while 10 outs stay at 21.74%.
Your draw can face a bet of up to 0.38 times the pot ($38.46 on a $100 pot) and still break even. 2 of the 12 sizes fall at or under that line.
| Bet size | Equity needed | Margin | Verdict |
|---|---|---|---|
| quarter-pot | 16.67% | +5.07 points | Call |
| third-pot | 20.00% | +1.74 points | Call |
| two-fifths-pot | 22.22% | -0.48 points | Fold |
| half-pot | 25.00% | -3.26 points | Fold |
| two-thirds-pot | 28.57% | -6.83 points | Fold |
| three-quarter-pot, this page | 30.00% | -8.26 points | Fold |
| pot-size | 33.33% | -11.59 points | Fold |
| 1.25x-pot | 35.71% | -13.98 points | Fold |
| 1.5x-pot | 37.50% | -15.76 points | Fold |
| 2x-pot | 40.00% | -18.26 points | Fold |
| 3x-pot | 42.86% | -21.12 points | Fold |
| 4x-pot | 44.44% | -22.71 points | Fold |
How this is computed
The chance rests on counting, not on a rule of thumb. Outs 10, unseen cards 46; hit chance: 21.74%.
The price is call / (pot + bet + call), here $75 / $250 = 30.00%, and the margin is your chance minus it. The page assumes you call the whole bet, win the whole pot whenever you hit, and see no more betting. All 46 unseen cards are equally likely and none is removed for an opponent's hand, so this is the chance to hit your outs, not your equity against one hand.
Computed from the closed form by the GeorgeLiPoker math library.
Updated
Questions
Is a call correct with 10 outs against a three-quarter-pot bet on the turn?
The answer is a fold, with a margin of -8.26 points. 10 outs on the turn reach 21.74%; a bet of $75 into $100 needs 30.00%. Win the whole pot on a hit and lose the call on a miss, and the call is worth -$20.65 on average.
How many outs are enough to continue against a bet of three quarters of the pot on the turn?
The threshold is 14 outs. It gives 30.43%, clearing 30.00%, whereas 13 gives only 28.26%. Holding 10 puts you 4 below it, with a chance of 21.74%.
Is the by-the-river chance the right one to use on the turn?
One card left means one chance: 21.74%. Set it beside the 30.00% price and you get -8.26 points, which is a fold. There is no second figure to weigh against it.
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