Verdict
Call
14 outs, flop, third-pot bet
- Chance to hit by the rivertwo cards to come51.16%
- Equity the call needs$33.33 into a pot of $166.6720.00%
- Margin over the priceyour chance minus the price+31.16 points
Chance against price
51.16% against 20.00%: the draw beats the price by 31.16 points. On this flop against a third-pot bet, that is a comfortable call.
A total of 14 outs tends to come from stacking several ways to improve. The next card is an out 29.79% of the time, 14 in 47.
A $100 pot, step by step
- Starting pot$100
- Size of the bet$33.33
- Cost to 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
- How often you hit51.16%
- Calling is worth, on average+$51.93
- Price of the call20.00%
- Exact margin over the price+31.1563 points
- Outs at break-even4.91 outs
- Outs to spare, exactly+9.09 outs
If you win the whole pot on a hit and lose your call otherwise, with no more betting, calling gains $51.93 on average. Hits add $68.21 on average and misses cost $16.28 on average, or +1.558 per dollar called.
Written as odds, the pot lays 4 : 1 while the draw is 0.95 : 1 against.
Do not forget your own call. Dividing the bet by the pot without it gives 25.00%, not 20.00%, and would show a margin of +26.1563 points. The bet over the starting pot, 33.33%, is worse and would show +17.8230 points.
Your cushion over the price
5 outs is the line for a third-pot bet on the flop. Your 14 sit 9 outs above it, and the chance at the line is 20.35%.
If hitting means paying off a bigger hand later, the call survives a loss of $101.51. That is 3.05 times the $33.33 call.
| Given back later | Price with it | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 20.00% | +31.16 points | +$51.93 | Call |
| $10 | 21.28% | +29.88 points | +$46.81 | Call |
| $25 | 23.53% | +27.63 points | +$39.14 | Call |
| $50 | 28.57% | +22.58 points | +$26.35 | Call |
| $100 | 50.00% | +1.16 points | +$0.77 | Call |
Which chance to use
Both views point the same way. By the river you hit 51.16%, on the next card 29.79%, and the price is 20.00%, so the call holds whichever number applies.
| Cards counted | Chance | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| By the river, two cards | 51.16% | +31.1563 points | +$51.93 | Call |
| Next card only | 29.79% | +9.7872 points | +$16.31 | Call |
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 2.96 points.
Other bet sizes for this draw
Bet size sets the price, so the verdict changes as you scan the table. The third-pot bet of this page is marked in the first column.
14 outs are strong enough to call every size listed. A chance of 51.16% beats even the biggest price in the table.
| Bet size | Equity needed | Margin | Verdict |
|---|---|---|---|
| quarter-pot | 16.67% | +34.49 points | Call |
| third-pot, this page | 20.00% | +31.16 points | Call |
| two-fifths-pot | 22.22% | +28.93 points | Call |
| half-pot | 25.00% | +26.16 points | Call |
| two-thirds-pot | 28.57% | +22.58 points | Call |
| three-quarter-pot | 30.00% | +21.16 points | Call |
| pot-size | 33.33% | +17.82 points | Call |
| 1.25x-pot | 35.71% | +15.44 points | Call |
| 1.5x-pot | 37.50% | +13.66 points | Call |
| 2x-pot | 40.00% | +11.16 points | Call |
| 3x-pot | 42.86% | +8.30 points | Call |
| 4x-pot | 44.44% | +6.71 points | Call |
How this is computed
The number is exact rather than estimated. 528 of the 1,081 pairs that could come are blanks, which leaves 51.16% for a hit.
The price is call / (pot + bet + call), here $33.33 / $166.67 = 20.00%, 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
What is the right play with 14 outs when a third-pot bet comes on the flop?
By the numbers it is a call. 14 outs on the flop hit 51.16% by the river, a third-pot bet needs 20.00%, and the margin is +31.16 points. That assumes you call the full $33.33 and no more betting follows, and it values the call at +$51.93 per $100 pot.
What is the minimum number of outs for a third-pot bet 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 14 you are 9 past the minimum.
Does it matter whether you count one card or two against a third-pot bet?
Count two cards, 51.16%, when the bet is the last money going in, and one card, 29.79%, when the next street brings another bet. At a price of 20.00%, either number leads to a call.
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