There might be a better way to write this out, but:
for 10% equity
Where x is their breakeven point for calling
0 = .9(-.75x)+.1(2.5)+(1-x)
when you solve for x you find out that if villain calls 74.6% or folds 25.4% our semi bluff breaks even.
The first part of the equation accounts for the times when he calls and we lost, the second accounts for the times when he calls and we win, and the third for the times that our bluff works. If you want to solve for 20 percent equity just change the .9 in the first part to .8 and the .1 in the second part to .2.

Hope this explanation is worded semi clearly.

cheers

Thanks Blackhawk,

Am I right ?

Bet 3/4 POT :

With " 0% equity " ==> 1-alpha ==> we need 42.8 % FE ( or more ) to bet profitably any two.

With 10% equity , we need 25.4% FE ( or more ) to bet profitably

With 20% equity , we need 6.25% FE ( or more ) to bet profitably.

• I checked 2times for the 20% ... it seems so low !! cant believe we just need 6% FE with 20% equity to bet profitably , something is wrong ?

0 = .9(-.75x)+.1(2.5x)+(1-x)1
You're right, I missed an x.
I think this one is better, hopefully someone can confirm this.
29.8% folds for 10% equity
9.1% folds for 20% equity

Blackhawk's formula is the right idea, but slightly off. In the second term we don't count the 0.75 pot we bet on the turn, just the money already in the pot and his call, so it should be .1(1.75x)

So then:
33.3% folds for 10% equity
20% folds for 20% equity
0% folds for 30% equity (if he never folds we're basically putting in a bet getting 1.75:0.75 or 7:3)

edit: also this ignores river betting so it's far from absolute. e.g. if your 10% equity is that you make the nuts 10% of the time then you'll need less folds but if all of your hands will have 10% equity on the river and your opponent can bet then you'll need more folds.

Depends on if your EQ is always nut equity or just EQ against villains actual holding.