Equity a call needs
42.86%
against a 3x-pot bet
- Pot oddsfor every 1 you call1.33 : 1
- Bet on a $100 potthree times the pot$300
- Pot after your callyou put in $300$700
The price of a 3x-pot bet
Large bets cut your odds to 1.33 : 1. Against a 3x-pot bet you need a lot of equity, or a lot of money still to win behind.
e = f / (1 + 2f)f = 3e = 3 / (1 + 2 x 3) = 42.86%Pot odds = (1 + 3) / 3 = 1.33 : 1
Odds of 1.33 : 1 and an equity bar of 42.86% say the same thing about this call.
A $100 pot facing a 3x-pot bet
Run the numbers on $100: the bet is $300, the pot is $400 and your call is $300.
- Pot before the bet$100
- Opponent bets$300
- You call$300
- Pot after your call$700
- You risk$300
- You can win$400
- Equity needed42.86%
Your call lifts the pot to $700. Dividing $300 by $700 gives 42.86%, the equity you must have.
Which draws can call a 3x-pot bet
Use this table to see which draws are above 42.86%. Positive margins are calls, negative margins are folds.
From the flop, 2 of the 8 draws clear 42.86%, and the smallest of them is a flush draw with a gutshot, with 12 outs.
A turn call needs help from future bets, since even a flush draw with an open-ended straight draw only has 32.61% against 42.86%.
| 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% | -34.44 points | Fold | 4.35% | -38.51 points | Fold |
| One overcard to top pair | 3 | 12.49% | -30.37 points | Fold | 6.52% | -36.34 points | Fold |
| A gutshot straight draw | 4 | 16.47% | -26.39 points | Fold | 8.70% | -34.16 points | Fold |
| Two overcards | 6 | 24.14% | -18.71 points | Fold | 13.04% | -29.81 points | Fold |
| An open-ended straight draw | 8 | 31.45% | -11.40 points | Fold | 17.39% | -25.47 points | Fold |
| A flush draw | 9 | 34.97% | -7.89 points | Fold | 19.57% | -23.29 points | Fold |
| A flush draw with a gutshot | 12 | 44.96% | +2.10 points | Call | 26.09% | -16.77 points | Fold |
| A flush draw with an open-ended straight draw | 15 | 54.12% | +11.26 points | Call | 32.61% | -10.25 points | Fold |
Implied odds against a 3x-pot bet
Drawing hands often win more than the pot when they hit. Add that extra, W, to the pot of $700 and divide $300 by the total.
Even the first step helps: with $50 extra, the price is 40.00%. With $500 extra it is 25.00%.
A flush draw on the turn hits 19.57% of the time, short of 42.86%. It needs about $833.33 of future winnings to break even.
When the stacks left behind are shallow, the bet of $300 may use up most of what is left, and implied odds shrink to nothing.
The mirror of implied odds is expensive: you hit, you bet, and a better hand calls. When that is likely, assume the price is higher than 42.86%.
| Future winnings W | Pot after call plus W | Equity needed | Change from the plain price | Flush draw margin from the flop |
|---|---|---|---|---|
| $0 | $700 | 42.86% | 0.00 points | -7.89 points |
| $50 | $750 | 40.00% | -2.86 points | -5.03 points |
| $100 | $800 | 37.50% | -5.36 points | -2.53 points |
| $250 | $950 | 31.58% | -11.28 points | +3.39 points |
| $500 | $1,200 | 25.00% | -17.86 points | +9.97 points |
3x-pot next to the other sizes
Look one size down and 2x-pot sets the bar at 40.00%, 2.86 points below 42.86%.
At the next size above, 4x-pot, the equity needed is 44.44%. The gap from 42.86% is 1.59 points.
- Pot odds facing a 2x-pot bet: Needs 40.00%, 2.86 points less.
- Pot odds facing a 4x-pot bet: Needs 44.44%, 1.59 points more.
The outs that justify a call
Break-even on the flop sits between 11 and 12 outs: 41.72% is too low and 44.96% is enough.
The turn cut-off is 20 outs, which hits 43.48%. The step below it, 41.30%, is not enough for 42.86%.
- 12 outs on the flop: 44.96% by the river against 42.86%.
- 20 outs on the turn: 43.48% on the river against 42.86%.
How this is computed
Here is what is computed: your call of $300, a final pot of $700, the price 42.86%, the odds 1.33 : 1, and the margin of eight common draws over that price.
Write the bet as a fraction f of the pot. Your call is f, the pot after the call is 1 + 2f, and the ratio is f / (1 + 2f). For f = 3 the ratio is 42.86%, and the pot odds are (1 + f) / f = 1.33 : 1.
The price ignores later betting and assumes a hit wins the pot whole. Draw chances use 47 unseen cards from the flop and 46 from the turn, with each card as likely as any other.
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 3x-pot bet?
Required equity is 42.86%, which is 1.33 : 1 in odds. The figure holds for any pot size, because only the size of the bet next to the pot matters: three times the pot. Scale the dollars and the percent does not move.
How many outs do you need against a 3x-pot bet?
Two cards to come mean 12 outs are enough: 44.96% beats 42.86%. On the turn you need 20 outs. Keep the count honest, since shared outs shrink your real chance.
How much do implied odds help against a 3x-pot bet?
Implied odds can help a lot. With $500 of expected future winnings, the equity you need falls from 42.86% to 25.00%. Use a number you can defend, because the extra money only arrives when your opponent pays you off after you hit.
Can you call a 3x-pot bet with a flush draw?
A flush draw has 9 outs. On the flop its chance to hit by the river is 34.97%, which is below 42.86%, so it is a fold. On the turn the chance is 19.57%, which is below 42.86%, so it is a fold. Add any implied odds on top, and subtract outs that a better hand could share.
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