Equity a call needs
30.00%
against a three-quarter-pot bet
- Pot oddsfor every 1 you call2.33 : 1
- Bet on a $100 potthree quarters of the pot$75
- Pot after your callyou put in $75$250
The price of a three-quarter-pot bet
The pot lays you 2.33 : 1. That is a fair price: strong draws go on, weak ones stop.
e = f / (1 + 2f)f = 0.75e = 0.75 / (1 + 2 x 0.75) = 30.00%Pot odds = (1 + 0.75) / 0.75 = 2.33 : 1
You pay $75 to join a pot that will hold $250, which is 30.00% of it. As odds, that is 2.33 : 1.
A $100 pot facing a three-quarter-pot bet
With $100 in the middle, a bet of $75 makes the pot $175. Calling costs $75.
- Pot before the bet$100
- Opponent bets$75
- You call$75
- Pot after your call$250
- You risk$75
- You can win$175
- Equity needed30.00%
Call, and $250 sits in the pot. Since you paid $75, your break-even chance is 30.00%.
Which draws can call a three-quarter-pot bet
Use this table to see which draws are above 30.00%. Positive margins are calls, negative margins are folds.
Two cards to come make draws stronger: 4 rows show a call from the flop, starting with an open-ended straight draw.
Drop to the turn and the count falls to 1 of 8. A flush draw with an open-ended straight draw is the first draw that still clears 30.00%, and it needs 15 outs.
| 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% | -21.58 points | Fold | 4.35% | -25.65 points | Fold |
| One overcard to top pair | 3 | 12.49% | -17.51 points | Fold | 6.52% | -23.48 points | Fold |
| A gutshot straight draw | 4 | 16.47% | -13.53 points | Fold | 8.70% | -21.30 points | Fold |
| Two overcards | 6 | 24.14% | -5.86 points | Fold | 13.04% | -16.96 points | Fold |
| An open-ended straight draw | 8 | 31.45% | +1.45 points | Call | 17.39% | -12.61 points | Fold |
| A flush draw | 9 | 34.97% | +4.97 points | Call | 19.57% | -10.43 points | Fold |
| A flush draw with a gutshot | 12 | 44.96% | +14.96 points | Call | 26.09% | -3.91 points | Fold |
| A flush draw with an open-ended straight draw | 15 | 54.12% | +24.12 points | Call | 32.61% | +2.61 points | Call |
Implied odds against a three-quarter-pot bet
Start from $75 over $250, which is 30.00%, then add W to the bottom. Every extra dollar you can win later cuts the equity you need.
Moving from nothing to $500 of future winnings lowers the bar by 20.00 points, from 30.00% down to 10.00%.
With 9 outs and one card to come you have 19.57%. To call a three-quarter-pot bet you would need to expect $133.33 more when the card arrives.
Ask two questions before counting on them: how much can your opponent still put in, and will they pay when your card comes?
Do not forget that you pay at the call and may pay again later. If your outs can lose to a bigger draw, you may pay more than $75 in all.
| Future winnings W | Pot after call plus W | Equity needed | Change from the plain price | Flush draw margin from the flop |
|---|---|---|---|---|
| $0 | $250 | 30.00% | 0.00 points | +4.97 points |
| $50 | $300 | 25.00% | -5.00 points | +9.97 points |
| $100 | $350 | 21.43% | -8.57 points | +13.54 points |
| $250 | $500 | 15.00% | -15.00 points | +19.97 points |
| $500 | $750 | 10.00% | -20.00 points | +24.97 points |
Three-quarter-pot next to the other sizes
Compared with two-thirds-pot, this bet costs you 1.43 points more in equity: 30.00% against 28.57%.
One size up, pot-size sets the bar at 33.33%, 3.33 points above 30.00%.
- Pot odds facing a two-thirds-pot bet: Needs 28.57%, 1.43 points less.
- Pot odds facing a pot-size bet: Needs 33.33%, 3.33 points more.
The outs that justify a call
Count your outs on the flop. With 8 outs you get 31.45%, enough for 30.00%; with fewer, you fall to 27.84% or less.
For a turn call the fewest outs is 14, hitting 30.43%. Take one away and the chance drops to 28.26%.
- 8 outs on the flop: 31.45% by the river against 30.00%.
- 14 outs on the turn: 30.43% on the river against 30.00%.
Single-draw pages are available for a bet of three quarters of the pot, each comparing your outs with 30.00%.
- Flush draw on the flop against a three-quarter-pot bet: 9 outs, 34.97% to hit, against 30.00%.
- 8 outs on the flop against a three-quarter-pot bet: The cut-off count, 31.45% to hit.
How this is computed
For a $100 pot and a three-quarter-pot bet, the page computes your call, the pot after it, the equity you need and the pot odds ratio. Draw chances come from counting unseen cards.
Let f be the bet as a share of the pot. Calling adds f to a pot that already holds 1 + f, so the final pot is 1 + 2f and the price is f / (1 + 2f) = 30.00% at f = 0.75.
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 three-quarter-pot bet?
A three-quarter-pot bet needs 30.00% equity from the caller. Put $75 in, see the pot reach $250, and your break-even chance is 30.00%. This is the same price as 2.33 : 1 pot odds, just written as a percent.
How many outs do you need against a three-quarter-pot bet?
From the flop you need 8 outs: that count hits 31.45% by the river and clears the 30.00% price. On the turn you need 14 outs. Count only outs that make the best hand, and remove any that also help your opponent.
How much do implied odds help against a three-quarter-pot bet?
Think of them as extra pot you collect later. The drop is 20.00 points at $500, which is large for hidden draws and small when your opponent can easily get away from the hand.
Can you call a three-quarter-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 above 30.00%, so it is a call. On the turn the chance is 19.57%, which is below 30.00%, so it is a fold. Add any implied odds on top, and subtract outs that a better hand could share.
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