Verdict
Fold
4 outs, flop, pot-size bet
- Chance to hit by the rivertwo cards to come16.47%
- Equity the call needs$100 into a pot of $30033.33%
- Margin over the priceyour chance minus the price-16.87 points
The price of the call
16.47% against 33.33%: the draw trails the price by 16.87 points. On this flop against a pot-size bet, that is an easy fold.
If you are on a gutshot straight draw, this is your count: 4 outs among 47 unseen cards, or 8.51% on a single card.
A $100 pot, step by step
- The pot before betting$100
- The bet$100
- Your call$100
- Final pot if you call$300
- What a hit wins$200
- Loss on a miss$100
- Chance to hit by the river16.47%
- Expected value of calling-$50.60
- Equity the call needs33.33%
- Margin, to four decimals-16.8671 points
- Outs that exactly reach the price8.53 outs
- Outs above the price-4.53 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 $50.60 on average. The hit side averages $32.93, the miss side $83.53, and each dollar called returns -0.506.
Put as odds, the draw is 5.07 : 1 against, and the pot offers 2 : 1 for the call.
Watch the pot you divide by. Leaving your call out turns 33.33% into 50.00%, and the margin into -33.5338 points.
The extra winnings a call would need
Implied odds are the way to close the gap. You need $307.30 more on later streets after hitting, which is 3.07 times the call you make.
The smallest count that pays for a pot-size bet is 9 outs at 34.97%. You hold 4, which is 5 outs fewer.
| Future winnings | Price with them | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 33.33% | -16.87 points | -$50.60 | Fold |
| $50 | 28.57% | -12.11 points | -$42.37 | Fold |
| $100 | 25.00% | -8.53 points | -$34.14 | Fold |
| $250 | 18.18% | -1.72 points | -$9.44 | Fold |
| $500 | 12.50% | +3.97 points | +$31.73 | Call |
By the river or next card
The two chances agree on the verdict. 16.47% by the river and 8.51% on one card each lead to a fold against 33.33%.
| Cards counted | Chance | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| By the river, two cards | 16.47% | -16.8671 points | -$50.60 | Fold |
| Next card only | 8.51% | -24.8227 points | -$74.47 | Fold |
Nearby draws
Draws close to yours, on the same street and against the same bet: the price is fixed at 33.33%, and each out moves the chance about 3.89 points.
Other bet sizes for this draw
One draw, 12 bets. Each row gives the equity the call needs, the margin over it, and the verdict for 4 outs on the flop.
Even the smallest bet on the list outprices 4 outs on the flop. The break-even bet is 0.25 times the pot ($24.55 on a $100 pot), and every one of the 12 sizes is above it.
| Bet size | Equity needed | Margin | Verdict |
|---|---|---|---|
| quarter-pot | 16.67% | -0.20 points | Fold |
| third-pot | 20.00% | -3.53 points | Fold |
| two-fifths-pot | 22.22% | -5.76 points | Fold |
| half-pot | 25.00% | -8.53 points | Fold |
| two-thirds-pot | 28.57% | -12.11 points | Fold |
| three-quarter-pot | 30.00% | -13.53 points | Fold |
| pot-size, this page | 33.33% | -16.87 points | Fold |
| 1.25x-pot | 35.71% | -19.25 points | Fold |
| 1.5x-pot | 37.50% | -21.03 points | Fold |
| 2x-pot | 40.00% | -23.53 points | Fold |
| 3x-pot | 42.86% | -26.39 points | Fold |
| 4x-pot | 44.44% | -27.98 points | Fold |
How this is computed
The chance rests on counting, not on a rule of thumb. Blank pairs: 903 out of 1,081; hit chance: 16.47%.
Keep the assumptions in view: a full call ($100 into $300, or 33.33%), the whole pot on a hit, no more betting, and 47 unseen cards that are equally likely. The math does not know what the other player holds.
Computed from the closed form by the GeorgeLiPoker math library.
Updated
Questions
What does the math say about calling a bet of the full pot with 4 outs on the flop?
Reduce the question to a comparison of two numbers: 16.47% to hit and 33.33% to break even. The first minus the second is -16.87 points, which makes this a fold, and the call averages -$50.60 on a $100 pot if no more betting follows.
How strong must a draw be to call a pot-size bet on the flop?
9 outs is the line. At 9 the chance is 34.97%, enough for 33.33%; one fewer gives 31.45%, which is not. Your 4 outs sit 5 below it on the flop, at 16.47%.
Is the by-the-river chance the right one to use on the flop?
The river figure of 16.47% assumes no further betting; the next-card figure of 8.51% assumes you pay again on the turn. Against 33.33%, both say fold, so you can use either.
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