Verdict
Fold
5 outs, flop, three-quarter-pot bet
- Chance to hit by the rivertwo cards to come20.35%
- Equity the call needs$75 into a pot of $25030.00%
- Margin over the priceyour chance minus the price-9.65 points
What the numbers say
With 5 outs on the flop you hit 20.35% by the river, and a three-quarter-pot bet asks for 30.00%. A 9.65-point shortfall makes this a clear fold.
You will reach 5 outs by adding up separate draws. With 47 cards unseen, the next card helps 10.64% of the time.
Worked through on a $100 pot
- Starting pot$100
- Bet$75
- Chips you put in$75
- Pot with your call in$250
- You can win on a hit$175
- Loss on a miss$75
- Probability of a hit20.35%
- Average value of the call-$24.12
- Break-even equity30.00%
- Margin, to four decimals-9.6485 points
- Fractional outs at the price7.59 outs
- Margin measured in outs-2.59 outs
Suppose a hit wins the entire pot, a miss loses your call, and no more betting follows. The average gain is $35.62, the average loss is $59.74, and calling loses $24.12 on average, or -0.322 per dollar called.
Read as odds: 3.91 : 1 against you, 2.33 : 1 from the pot.
One easy error is to use 42.86%, the bet over the pot before your call, as the price. The right price is 30.00%, and the mistaken margin would be -22.5056 points. The bet over the starting pot, 75.00%, would claim -54.6485 points.
Implied odds that would change the answer
With 20.35% to hit, break-even sits $118.52 higher than the pot shows. Put another way, later bets must add 1.58 times your call.
If the draw had 3 more outs, for 8 in all, the chance would be 31.45% and the call would clear 30.00%.
| Future winnings | Price with them | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 30.00% | -9.65 points | -$24.12 | Fold |
| $50 | 25.00% | -4.65 points | -$13.95 | Fold |
| $100 | 21.43% | -1.08 points | -$3.77 | Fold |
| $250 | 15.00% | +5.35 points | +$26.76 | Call |
| $500 | 10.00% | +10.35 points | +$77.64 | Call |
By the river or next card
The two chances agree on the verdict. 20.35% by the river and 10.64% on one card each lead to a fold against 30.00%.
| Cards counted | Chance | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| By the river, two cards | 20.35% | -9.6485 points | -$24.12 | Fold |
| Next card only | 10.64% | -19.3617 points | -$48.40 | Fold |
One out more or less
Move up or down a few outs and watch the verdict. Every extra out is worth about 3.79 points on the flop, and the price stays at 30.00%.
The draw across every bet size
Keep 5 outs and change only the bet. The price rises from the smallest size to the largest, and the three-quarter-pot row is marked as this page.
Your draw can face a bet of up to 0.34 times the pot ($34.32 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% | +3.68 points | Call |
| third-pot | 20.00% | +0.35 points | Call |
| two-fifths-pot | 22.22% | -1.87 points | Fold |
| half-pot | 25.00% | -4.65 points | Fold |
| two-thirds-pot | 28.57% | -8.22 points | Fold |
| three-quarter-pot, this page | 30.00% | -9.65 points | Fold |
| pot-size | 33.33% | -12.98 points | Fold |
| 1.25x-pot | 35.71% | -15.36 points | Fold |
| 1.5x-pot | 37.50% | -17.15 points | Fold |
| 2x-pot | 40.00% | -19.65 points | Fold |
| 3x-pot | 42.86% | -22.51 points | Fold |
| 4x-pot | 44.44% | -24.09 points | Fold |
How this is computed
Everything is computed from the closed form. Pairs without an out: 861 of 1,081. The rest, 20.35%, hold at least one out.
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 47 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
How should you respond to a three-quarter-pot bet on the flop when you hold 5 outs?
Compare 20.35%, your chance to hit by the river, with 30.00%, the equity a three-quarter-pot bet needs. The gap is -9.65 points, so this is a fold. In dollars on a $100 pot, the call averages -$24.12 when no more betting follows.
What is the minimum number of outs for a three-quarter-pot bet on the flop?
The threshold is 8 outs. It gives 31.45%, clearing 30.00%, whereas 7 gives only 27.84%. Holding 5 puts you 3 below it, with a chance of 20.35%.
Is the by-the-river chance the right one to use on the flop?
The river figure of 20.35% assumes no further betting; the next-card figure of 10.64% assumes you pay again on the turn. Against 30.00%, both say fold, so you can use either.
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