question on how often my opponent needs to fold to make a semi bluff +ev

Originally Posted by grumpy64

using some diff numbers to show that i do understand u up to a point
stacks=100xbb
ott pot before action=30xbb 2/3s pot bluff
30x.66=19.8

Let's solve your equation step-by-step.
30−30x−19.8x+2.66x+3.8x=0
30−30x−19.8x+2.66x+3.8x=0
−43.34x+30=0
−43.34x+30−30=0−30
−43.34x=−30
−43.34x
−43.34
=
−30
−43.34
x=0.692201

thing is if x doesn't actually tell me how often they need to fold i don't see how it helps me

This tells you that, assuming those frequencies, your line is +EV so long as villain folds less than 69.2%. If Villain folds exactly 69.2201%, then this is a 0EV line.


You need to go back and see where the 2.66 comes from. You've changed the value of that outcome by changing the pot and bet sizes.

In your first example, you had a pot of 10 and you bet 7.5, which villain called OTT, so the amount you stand to gain if Villain folds OTR is 17.5. In this example, that should be 30 + 19.8 = 49.8. Then multiply that value by the probability that it occurs. Here, there is an 19% chance Hero makes his draw and a 80% chance that Villain folds to the shove. So 49.8*0.19*0.8 = 7.5696 ~= 7.57

Always list out every possible outcome with the value of that outcome and the chance of that outcome happening. Then multiply the value by the chance to that part of the total EV calculation.
This is actually a very easy thing to create a spreadsheet for, and it will allow you to just change the significant numbers while it does all the calculations instantly.


EDIT: The -19.8 in your example is incorrect, too. That is the amount you lose when you bet OTT, and Villain calls, but you brick OTR and x/f. You will only brick OTR ~89% of the time, so that -19.8 should be multiplied by 0.89 to get -17.622.

The 3.8x is hard to evaluate because your statement of 100bb ESS. Do you mean that you started the hand with that ESS, or that there is 100 ESS in the hand at the point of your decision OTT. Either way... I didn't pay too much attention to it the first time through, and it does matter.


So

30 - 30x - 17.62x - 7.57x + 3.8x >= 0

Note that we want the EV of the line to be greater than or equal to 0

x <= -30/(-30-17.62-7.57+3.8) = 0.508 = 50.8%

When we divide by a negative number the inequality switches direction. We now have that x should be less than or equal to ~51%.