Verdict
Call
5 outs, flop, third-pot bet
- Chance to hit by the rivertwo cards to come20.35%
- Equity the call needs$33.33 into a pot of $166.6720.00%
- Margin over the priceyour chance minus the price+0.35 points
Comparing the draw with the bet
You are only 0.35 points above break-even here: 20.35% to hit, 20.00% to call. It is a thin call, and it depends on every out being clean.
You will reach 5 outs by adding up separate draws. With 47 cards unseen, the next card helps 10.64% of the time.
A $100 pot, step by step
- Pot when the bet arrives$100
- Bet$33.33
- Your call$33.33
- Pot with your call in$166.67
- You can win on a hit$133.33
- Net loss when you miss$33.33
- Probability of a hit20.35%
- Average value of the call+$0.59
- Equity needed to break even20.00%
- Your chance minus the price, unrounded+0.3515 points
- Break-even count of outs4.91 outs
- Outs to spare, exactly+0.09 outs
Stay with simple rules: the whole pot on a hit, the call lost on a miss, no more money in. Under them calling gains $0.59 on average. The hit side averages $27.14, the miss side $26.55, and each dollar called returns +0.018.
Stated as odds, you are 3.91 : 1 against hitting and the call gets 4 : 1 from the pot.
The price is 20.00% because your call goes into the pot too. Leave it out and you get 25.00%, a margin of -4.6485 points that does not exist; use the starting pot instead and 33.33% puts the margin at -12.9818 points.
Where the call would flip
With 5 outs you sit exactly at the minimum of 5 that a third-pot bet requires on the flop, so there is no room to give up an out.
The call keeps its edge until you lose $2.88 on later streets after hitting. That is 0.09 times the $33.33 you pay now.
| Given back later | Price with it | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 20.00% | +0.35 points | +$0.59 | Call |
| $10 | 21.28% | -0.93 points | -$1.45 | Fold |
| $25 | 23.53% | -3.18 points | -$4.50 | Fold |
| $50 | 28.57% | -8.22 points | -$9.59 | Fold |
| $100 | 50.00% | -29.65 points | -$19.77 | Fold |
Two views of the same draw
The two figures land on opposite sides, or on the line. 20.35% gives a call and 10.64% gives a fold against 20.00%, so check whether more betting is likely before you rely on the river number.
| Cards counted | Chance | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| By the river, two cards | 20.35% | +0.3515 points | +$0.59 | Call |
| Next card only | 10.64% | -9.3617 points | -$15.60 | Fold |
Neighbors of this draw
Draws close to yours, on the same street and against the same bet: the price is fixed at 20.00%, and each out moves the chance about 3.79 points.
The same draw against other bet sizes
The same 5 outs on the flop meet 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.
Break-even for this draw is a bet of 0.34 times the pot ($34.32 on a $100 pot). Sizes below it call, sizes above it fold, and 2 of the 12 sizes are calls in the table.
| Bet size | Equity needed | Margin | Verdict |
|---|---|---|---|
| quarter-pot | 16.67% | +3.68 points | Call |
| third-pot, this page | 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 | 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.
These figures describe a clean spot. You pay the whole bet, which costs $33.33 of a $166.67 pot (20.00%), collect the whole pot on a hit, meet no more bets, and draw from 47 equally likely cards, with no adjustment for an opponent's hand.
Computed from the closed form by the GeorgeLiPoker math library.
Updated
Questions
What is the right play with 5 outs when a third-pot bet comes on the flop?
Compare 20.35%, your chance to hit by the river, with 20.00%, the equity a third-pot bet needs. The gap is +0.35 points, so this is a call. In dollars on a $100 pot, the call averages +$0.59 when no more betting follows.
How many outs are enough to continue against a bet of a third of the pot on the flop?
You need at least 5 outs against a third-pot bet on the flop. That count hits 20.35% against 20.00% needed, and 4 falls short at 16.47%. With 5 you are exactly at the minimum.
When is the next-card chance the better comparison?
Count two cards, 20.35%, when the bet is the last money going in, and one card, 10.64%, when the next street brings another bet. At a price of 20.00%, the two numbers give a call and a fold.
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