Equity a call needs
37.50%
against a 1.5x-pot bet
- Pot oddsfor every 1 you call1.67 : 1
- Bet on a $100 potone and a half times the pot$150
- Pot after your callyou put in $150$400
The price of a 1.5x-pot bet
The pot lays you only 1.67 : 1. Expect to fold most of the time unless your hand is already strong.
e = f / (1 + 2f)f = 1.5e = 1.5 / (1 + 2 x 1.5) = 37.50%Pot odds = (1 + 1.5) / 1.5 = 1.67 : 1
The odds are 1.67 : 1, and the two forms agree: $150 divided by $400 is 37.50%.
A $100 pot facing a 1.5x-pot bet
Take a pot of $100 and a 1.5x-pot bet of $150. The pot reads $250 when the action gets to you.
- Pot before the bet$100
- Opponent bets$150
- You call$150
- Pot after your call$400
- You risk$150
- You can win$250
- Equity needed37.50%
You put in $150 and the pot grows to $400. Below 37.50% equity the call loses money over time, and above it the call gains.
Which draws can call a 1.5x-pot bet
Each draw below is compared with the 37.50% price. Two chances are shown: two cards to come from the flop, and one card to come from the turn.
On the flop the line of 37.50% is cleared by 2 of the 8 draws, and the lightest to clear it is a flush draw with a gutshot.
The turn columns hold no calls at this price: a flush draw with an open-ended straight draw comes closest at 32.61%, below 37.50%.
| 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% | -29.08 points | Fold | 4.35% | -33.15 points | Fold |
| One overcard to top pair | 3 | 12.49% | -25.01 points | Fold | 6.52% | -30.98 points | Fold |
| A gutshot straight draw | 4 | 16.47% | -21.03 points | Fold | 8.70% | -28.80 points | Fold |
| Two overcards | 6 | 24.14% | -13.36 points | Fold | 13.04% | -24.46 points | Fold |
| An open-ended straight draw | 8 | 31.45% | -6.05 points | Fold | 17.39% | -20.11 points | Fold |
| A flush draw | 9 | 34.97% | -2.53 points | Fold | 19.57% | -17.93 points | Fold |
| A flush draw with a gutshot | 12 | 44.96% | +7.46 points | Call | 26.09% | -11.41 points | Fold |
| A flush draw with an open-ended straight draw | 15 | 54.12% | +16.62 points | Call | 32.61% | -4.89 points | Fold |
Implied odds against a 1.5x-pot bet
Future bets can lower the price. The rule is C / (T + W), where C is your call of $150, T is $400, and W is what you expect to win later.
Even the first step helps: with $50 extra, the price is 33.33%. With $500 extra it is 16.67%.
A flush draw on the turn hits 19.57% of the time, short of 37.50%. It needs about $366.67 of future winnings to break even.
Strong draws that sit above 37.50% do not need implied odds at all. They are for the hands that fall a little short.
Some outs are poisoned: they make your hand, and also make a better one for your opponent. Count those cards at less than full value against a 1.5x-pot bet.
| Future winnings W | Pot after call plus W | Equity needed | Change from the plain price | Flush draw margin from the flop |
|---|---|---|---|---|
| $0 | $400 | 37.50% | 0.00 points | -2.53 points |
| $50 | $450 | 33.33% | -4.17 points | +1.63 points |
| $100 | $500 | 30.00% | -7.50 points | +4.97 points |
| $250 | $650 | 23.08% | -14.42 points | +11.89 points |
| $500 | $900 | 16.67% | -20.83 points | +18.30 points |
1.5x-pot next to the other sizes
A smaller 1.25x-pot bet asks for only 35.71%; that is 1.79 points less than the 37.50% here.
The next larger size is 2x-pot, at 40.00%. Moving there from 1.5x-pot adds 2.50 points to the price.
- Pot odds facing a 1.25x-pot bet: Needs 35.71%, 1.79 points less.
- Pot odds facing a 2x-pot bet: Needs 40.00%, 2.50 points more.
The outs that justify a call
From the flop you need at least 10 outs: 10 outs hit 38.39% by the river, while one fewer gives only 34.97%.
Only one card is left on the turn, so 18 outs are needed: 39.13% clears the price and 36.96% does not.
- 10 outs on the flop: 38.39% by the river against 37.50%.
- 18 outs on the turn: 39.13% on the river against 37.50%.
How this is computed
This page prices one bet, one and a half times the pot into $100, and measures eight draws against it. The price, the odds and the margins all come from the same two inputs.
The price comes from a single line of algebra, e = f / (1 + 2f). With f = 1.5 it returns 37.50%, and flipping it into odds gives 1.67 : 1.
The figures assume you call the full bet, no more betting follows, you win the whole pot when you hit, and every unseen card is equally likely. The flop leaves 47 unseen cards and the turn leaves 46.
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 1.5x-pot bet?
A 1.5x-pot bet needs 37.50% equity from the caller. Put $150 in, see the pot reach $400, and your break-even chance is 37.50%. This is the same price as 1.67 : 1 pot odds, just written as a percent.
How many outs do you need against a 1.5x-pot bet?
Flop first: 10 outs give you 38.39% by the river, enough for 37.50%. On the turn you need 18 outs. If some outs also make a better hand for your opponent, shave the count before you compare.
How much do implied odds help against a 1.5x-pot bet?
Plenty, if the money is real. At $50 of future winnings the price is 33.33%, and at $500 it is 16.67%, compared with 37.50% with none. Be realistic about what your opponent will pay.
Can you call a 1.5x-pot bet with a flush draw?
Look at each street. On the flop its chance to hit by the river is 34.97%, which is below 37.50%, so it is a fold. On the turn the chance is 19.57%, which is below 37.50%, so it is a fold. Hidden outs and deep stacks lean toward calling, and shared outs lean away.
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