Equity a call needs
22.22%
against a two-fifths-pot bet
- Pot oddsfor every 1 you call3.5 : 1
- Bet on a $100 pottwo fifths of the pot$40
- Pot after your callyou put in $40$180
The price of a two-fifths-pot bet
The bet is $40 into $100, so you risk little: 22.22% equity is all it takes to break even on the call.
e = f / (1 + 2f)f = 0.4e = 0.4 / (1 + 2 x 0.4) = 22.22%Pot odds = (1 + 0.4) / 0.4 = 3.5 : 1
Pot odds of 3.5 : 1 mean the pot, bet included, is 3.5 times what you pay.
A $100 pot facing a two-fifths-pot bet
A two-fifths-pot bet into $100 is $40, and with the money in the middle the pot stands at $140.
- Pot before the bet$100
- Opponent bets$40
- You call$40
- Pot after your call$180
- You risk$40
- You can win$140
- Equity needed22.22%
With your $40 in, the pot is $180. You are paying 22.22% of the pot for the right to see the next card.
Which draws can call a two-fifths-pot bet
The table below puts eight common draws against this 22.22% price. Each row gives the chance to hit by the river from the flop, and the chance to hit on the turn with one card to come.
Counting the flop rows above 22.22% gives 5. The lowest draw among them is two overcards, with 6 outs.
With a single card left, 2 of the 8 draws clear the bar of 22.22%; the smallest is a flush draw with a gutshot.
| Draw | Outs | Flop: hit by the river | Flop margin | Flop verdict | Turn: hit on the river | Turn margin | Turn verdict |
|---|---|---|---|---|---|---|---|
| A pocket pair that wants a set | 2 | 8.42% | -13.80 points | Fold | 4.35% | -17.87 points | Fold |
| One overcard to top pair | 3 | 12.49% | -9.73 points | Fold | 6.52% | -15.70 points | Fold |
| A gutshot straight draw | 4 | 16.47% | -5.76 points | Fold | 8.70% | -13.53 points | Fold |
| Two overcards | 6 | 24.14% | +1.92 points | Call | 13.04% | -9.18 points | Fold |
| An open-ended straight draw | 8 | 31.45% | +9.23 points | Call | 17.39% | -4.83 points | Fold |
| A flush draw | 9 | 34.97% | +12.75 points | Call | 19.57% | -2.66 points | Fold |
| A flush draw with a gutshot | 12 | 44.96% | +22.74 points | Call | 26.09% | +3.86 points | Call |
| A flush draw with an open-ended straight draw | 15 | 54.12% | +31.89 points | Call | 32.61% | +10.39 points | Call |
Implied odds against a two-fifths-pot bet
The price of 22.22% assumes no more betting. If you can add W to the pot on later streets, you need only $40 / ($180 + W).
From 22.22% to 5.88% is the full range this table covers, a change of 16.34 points between no implied odds and $500 of them.
For a turn flush draw the break-even future winnings are $24.44, because 19.57% falls under 22.22%.
Ask two questions before counting on them: how much can your opponent still put in, and will they pay when your card comes?
A two-fifths-pot bet leaves little room to be wrong about your outs. If a card makes you second best, you can lose more than $40 on later streets.
| Future winnings W | Pot after call plus W | Equity needed | Change from the plain price | Flush draw margin from the flop |
|---|---|---|---|---|
| $0 | $180 | 22.22% | 0.00 points | +12.75 points |
| $50 | $230 | 17.39% | -4.83 points | +17.58 points |
| $100 | $280 | 14.29% | -7.94 points | +20.68 points |
| $250 | $430 | 9.30% | -12.92 points | +25.67 points |
| $500 | $680 | 5.88% | -16.34 points | +29.09 points |
Two-fifths-pot next to the other sizes
Going from third-pot (20.00%) to two-fifths-pot (22.22%) raises the bar by 2.22 points.
At the next size above, half-pot, the equity needed is 25.00%. The gap from 22.22% is 2.78 points.
- Pot odds facing a third-pot bet: Needs 20.00%, 2.22 points less.
- Pot odds facing a half-pot bet: Needs 25.00%, 2.78 points more.
The outs that justify a call
The fewest outs that justify a flop call here is 6, which hits 24.14% by the river. One out fewer hits 20.35%.
The turn is stricter: 11 outs give 23.91% on the river, against 21.74% for one out fewer.
- 6 outs on the flop: 24.14% by the river against 22.22%.
- 11 outs on the turn: 23.91% on the river against 22.22%.
How this is computed
This page works out the equity a call needs when a $100 pot faces a bet of two fifths of the pot, and it compares that price with the chance to hit common draws on the flop and on the turn.
Using f = 0.4, the formula e = f / (1 + 2f) returns 22.22%. The odds form is (1 + f) / f, which returns 3.5 : 1. The two are the same price written two ways.
Three assumptions sit under every number: you call the whole bet, nobody bets again, and a hit wins the pot outright. Each of the 47 unseen cards on the flop, or 46 on the turn, is equally likely.
Method: the closed form f / (1 + 2f) computed by the GeorgeLiPoker math library, with draw chances counted from the unseen cards.
Updated
Questions
What equity do you need to call a two-fifths-pot bet?
Call when your equity beats 22.22%. The figure is your $40 call divided by the $180 pot you play for, and it equals pot odds of 3.5 : 1. Use it on every street where a two-fifths-pot bet shows up.
How many outs do you need against a two-fifths-pot bet?
Against a bet of two fifths of the pot, the fewest outs that reach 22.22% on the flop is 6, with 24.14% to hit by the river. On the turn you need 11 outs. Always check that your outs are clean before relying on the count.
How much do implied odds help against a two-fifths-pot bet?
Plenty, if the money is real. At $50 of future winnings the price is 17.39%, and at $500 it is 5.88%, compared with 22.22% with none. Be realistic about what your opponent will pay.
Can you call a two-fifths-pot bet with a flush draw?
Start with the count of 9 outs. On the flop its chance to hit by the river is 34.97%, which is above 22.22%, so it is a call. On the turn the chance is 19.57%, which is below 22.22%, so it is a fold. A bet of two fifths of the pot sets the line at 22.22% in both cases.
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