Verdict
Fold
5 outs, flop, two-thirds-pot bet
- Chance to hit by the rivertwo cards to come20.35%
- Equity the call needs$66.67 into a pot of $233.3328.57%
- Margin over the priceyour chance minus the price-8.22 points
Chance against price
Your draw is priced at 28.57% and it arrives just 20.35% of the time. A gap of 8.22 points is large, and later bets would have to be large to make up for it.
You will reach 5 outs by adding up separate draws. With 47 cards unseen, the next card helps 10.64% of the time.
Counting the chips on a $100 pot
- Pot before the bet$100
- The bet$66.67
- Your call$66.67
- Final pot if you call$233.33
- Gain on a hit$166.67
- Net loss when you miss$66.67
- Chance to hit by the river20.35%
- Average value of the call-$19.18
- Equity needed to break even28.57%
- Margin, to four decimals-8.2199 points
- Break-even count of outs7.20 outs
- Outs above the price-2.20 outs
Over many identical spots, with the whole pot won on every hit, the call lost on every miss and no extra betting, calling loses $19.18 on average. Hits bring in $33.92, misses cost $53.10, and the ratio is -0.288 per dollar called.
Stated as odds, you are 3.91 : 1 against hitting and the call gets 2.5 : 1 from the pot.
Do not forget your own call. Dividing the bet by the pot without it gives 40.00%, not 28.57%, and would show a margin of -19.6485 points. The bet over the starting pot, 66.67%, is worse and would show -46.3151 points.
Implied odds that would change the answer
With 20.35% to hit, break-even sits $94.24 higher than the pot shows. Put another way, later bets must add 1.41 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 28.57%.
| Future winnings | Price with them | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 28.57% | -8.22 points | -$19.18 | Fold |
| $50 | 23.53% | -3.18 points | -$9 | Fold |
| $100 | 20.00% | +0.35 points | +$1.17 | Call |
| $250 | 13.79% | +6.56 points | +$31.70 | Call |
| $500 | 9.09% | +11.26 points | +$82.58 | Call |
Which chance to use
Whether you count one card or two, the answer is a fold. The river figure is 20.35%, the next-card figure is 10.64%, and both are measured against 28.57%.
| Cards counted | Chance | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| By the river, two cards | 20.35% | -8.2199 points | -$19.18 | Fold |
| Next card only | 10.64% | -17.9331 points | -$41.84 | Fold |
Nearby draws
Same bet, same street, different draws. The row for 5 outs is marked, and every out is worth about 3.79 points.
Every bet size, one draw
Bigger bets ask for more equity while your chance stays at 20.35%. Here is every bet size against the same draw, with the row for this page marked.
5 outs stop paying at 0.34 times the pot ($34.32 on a $100 pot). The call holds up against 2 of the 12 bet sizes.
| 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, this page | 28.57% | -8.22 points | Fold |
| three-quarter-pot | 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.
Read the verdict with its limits in mind. The call is the full bet, so the break-even equity is $66.67 / $233.33 = 28.57%. A hit takes the whole pot, no later betting happens, and the 47 unseen cards are all equally likely, with none removed for an opponent's cards.
Computed from the closed form by the GeorgeLiPoker math library.
Updated
Questions
What does the math say about calling a bet of two thirds of the pot with 5 outs on the flop?
Verdict: fold. A two-thirds-pot bet asks for 28.57% and you have 20.35%, a margin of -8.22 points. For a $66.67 call into a $100 pot, with no later bets and the whole pot won on a hit, the average is -$19.18.
How many outs are enough to continue against a bet of two thirds of the pot on the flop?
Look for 8 outs. That is the smallest count whose chance, 31.45%, reaches the 28.57% price; 7 manages 27.84%. You have 5, so you are 3 behind the minimum.
How many cards should you count when a two-thirds-pot bet arrives on the flop?
It depends on what follows, but here it does not matter. If the hand ends here, count both cards: 20.35%. If another bet is coming on the turn, count one card: 10.64%. Against 28.57%, both say fold.
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