Equity a call needs
28.57%
against a two-thirds-pot bet
- Pot oddsfor every 1 you call2.5 : 1
- Bet on a $100 pottwo thirds of the pot$66.67
- Pot after your callyou put in $66.67$233.33
The price of a two-thirds-pot bet
At 28.57% the call is neither cheap nor steep, which makes your outs count worth checking before you act.
e = f / (1 + 2f)f = 0.6667 (rounded)e = 0.6667 / (1 + 2 x 0.6667) = 28.57%Pot odds = (1 + 0.6667) / 0.6667 = 2.5 : 1
You pay $66.67 to join a pot that will hold $233.33, which is 28.57% of it. As odds, that is 2.5 : 1.
A $100 pot facing a two-thirds-pot bet
Take a pot of $100 and a two-thirds-pot bet of $66.67. The pot reads $166.67 when the action gets to you.
- Pot before the bet$100
- Opponent bets$66.67
- You call$66.67
- Pot after your call$233.33
- You risk$66.67
- You can win$166.67
- Equity needed28.57%
If you call, the pot becomes $233.33. Your $66.67 makes up 28.57% of it, so you need to win that share of the time to break even.
Which draws can call a two-thirds-pot bet
Eight draws, one price. The outs count sets your chance, and 28.57% sets the bar every row must clear.
Four draws in the table are calls on the flop. An open-ended straight draw is the first one that pays.
With one card to come the list shrinks. One of the 8 draws is still above 28.57%; it is a flush draw with an open-ended straight draw.
| 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% | -20.15 points | Fold | 4.35% | -24.22 points | Fold |
| One overcard to top pair | 3 | 12.49% | -16.08 points | Fold | 6.52% | -22.05 points | Fold |
| A gutshot straight draw | 4 | 16.47% | -12.11 points | Fold | 8.70% | -19.88 points | Fold |
| Two overcards | 6 | 24.14% | -4.43 points | Fold | 13.04% | -15.53 points | Fold |
| An open-ended straight draw | 8 | 31.45% | +2.88 points | Call | 17.39% | -11.18 points | Fold |
| A flush draw | 9 | 34.97% | +6.40 points | Call | 19.57% | -9.01 points | Fold |
| A flush draw with a gutshot | 12 | 44.96% | +16.39 points | Call | 26.09% | -2.48 points | Fold |
| A flush draw with an open-ended straight draw | 15 | 54.12% | +25.55 points | Call | 32.61% | +4.04 points | Call |
Implied odds against a two-thirds-pot bet
The price of 28.57% assumes no more betting. If you can add W to the pot on later streets, you need only $66.67 / ($233.33 + W).
Moving from nothing to $500 of future winnings lowers the bar by 19.48 points, from 28.57% down to 9.09%.
At 19.57% the turn flush draw cannot call alone. It needs $107.41 still to be won after the card hits.
Implied odds help least when the pot is already big next to the stacks, since there is not much left to win after you hit.
Weak made hands face the opposite problem. When you call with a pair that is behind, more betting costs you extra, which pushes the true price above 28.57%.
| Future winnings W | Pot after call plus W | Equity needed | Change from the plain price | Flush draw margin from the flop |
|---|---|---|---|---|
| $0 | $233.33 | 28.57% | 0.00 points | +6.40 points |
| $50 | $283.33 | 23.53% | -5.04 points | +11.44 points |
| $100 | $333.33 | 20.00% | -8.57 points | +14.97 points |
| $250 | $483.33 | 13.79% | -14.78 points | +21.17 points |
| $500 | $733.33 | 9.09% | -19.48 points | +25.88 points |
Two-thirds-pot next to the other sizes
Compared with half-pot, this bet costs you 3.57 points more in equity: 28.57% against 25.00%.
Step up to a three-quarter-pot bet and the price climbs to 30.00%, which is 1.43 points higher than 28.57%.
- Pot odds facing a half-pot bet: Needs 25.00%, 3.57 points less.
- Pot odds facing a three-quarter-pot bet: Needs 30.00%, 1.43 points more.
The outs that justify a call
On the flop the cut-off is 8 outs. That count reaches 31.45% against the 28.57% price, and the next one down falls short at 27.84%.
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 28.57%.
- 14 outs on the turn: 30.43% on the river against 28.57%.
Full call-or-fold pages exist for the two-thirds-pot bet, and each one tests a single draw against it in detail.
- Flush draw on the flop against a two-thirds-pot bet: 9 outs, 34.97% to hit, against 28.57%.
- 8 outs on the flop against a two-thirds-pot bet: The cut-off count, 31.45% to hit.
How this is computed
The computation covers one bet size. It takes $66.67 into $100, finds the pot after your call, and divides to get 28.57%, then sets draw chances beside it.
Using f = 0.6667, the formula e = f / (1 + 2f) returns 28.57%. The odds form is (1 + f) / f, which returns 2.5 : 1. The two are the same price written two ways.
Read the numbers with these limits in mind: a full call, no further bets, the pot won whole on a hit, and equal odds for each of the 47 or 46 unseen cards.
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-thirds-pot bet?
Call when your equity beats 28.57%. The figure is your $66.67 call divided by the $233.33 pot you play for, and it equals pot odds of 2.5 : 1. Use it on every street where a two-thirds-pot bet shows up.
How many outs do you need against a two-thirds-pot bet?
You need 8 outs on the flop to call, because that many outs reach 31.45% against a price of 28.57%. On the turn you need 14 outs. Use the cleaned count, after dropping outs that could lose to a better hand.
How much do implied odds help against a two-thirds-pot bet?
Each extra dollar you expect to win cuts the price. The range here runs from 28.57% with nothing extra down to 9.09% with $500, a 19.48 point swing. Hidden draws earn more implied odds than obvious ones.
Can you call a two-thirds-pot bet with a flush draw?
Flush draws hold 9 outs. On the flop its chance to hit by the river is 34.97%, which is above 28.57%, so it is a call. On the turn the chance is 19.57%, which is below 28.57%, so it is a fold. If the stacks are deep, implied odds make the call easier.
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