math help on a semi bluff

[livedonk36]

hi guys,

how do you figure out the math when you are doing a semibluff?

i have 35% equity when called.

he folds 20% of the time.

if the pot were 100bb's how many bb could i risk to win the pot before it is -ev?

more importantly, what is the formula to figure that out?

if it's weird to figure out the exact break even point could someone please tell me how to do it if they bet size were some arbitrary amount, say 60bb's?

here is my attempt, please correct me where i am wrong.

pot 100bb

amount i am risking 60bb

when he folds i win 100bb x 20% = 20bb

when he calls and i win. i win 240bb x .35% = 84bb

when he calls and i lose. i lose 160bb x 65% = 104bb

if the above is correct i guess i just add up what i win and subtract what i lose.

that means my bluff would be break even at 60bb.

if the above is correct it's very weird that i randomly picked the break even point on the bluff. hopefully this is correct and i am a math wiz.

cheers guys.

[Donkadocus]

DON'T CALCULATE WHAT YOU LOSE - you just lose 60bb when you lose in your example.
____________________

You bet x.

He folds 20% the time and you win 100
(0.2 * 100)

He calls 80% of the time. You have 35% equity. You win (0.35 * (100+2x)).

So you risk x to win (0.2 * 100) + (0.8 * (0.35 * (100+2x)))

If they are equal x = (0.2 * 100) + (0.8 *(0.35 * (100+2x)))

x = 20 + 28 + 0.56x
0.44 x = 48
x = 109

You can bet 109bb and break even. If you bet less you make money.

[livedonk36]

first, let me say this is great. thank you so much!

but...

can you make your math a little longer i dont get a couple things...

So you risk x to win (0.2 * 100) + (0.8 * (0.35 * (100+2x)))

If they are equal x = (0.2 * 100) + (0.8 *(0.35 * (100+2x))

what does the bolded part above mean?

x = 20 + 28 + 0.56x
0.44 x = 48
x = 109

where do these numbers come from?

[livedonk36]

adjusted attempt...

pot 100bb

amount i am risking 60bb

when he folds i win 100bb x 20% = 20bb

when he calls and i win. i win 240bb x .35% = 84bb

when he calls and i lose. i lose 60bb x 65% = 39bb

if the above is correct i guess i just add up what i win and subtract what i lose.

that means my bluff would be profitable by 65bb

and to try and get it BE with a 109bb bet size...

pot 100bb

amount i am risking 109bb

when he folds i win 100bb x 20% = 20bb

when he calls and i win. i win 318bb x .35% = 111bb

when he calls and i lose. i lose 109bb x 65% = 71bb

if the above is correct i guess i just add up what i win and subtract what i lose.

that means my bluff would be profitable by 60bb

so the way i am doing the math is obv very wrong. can you please pretend i have no idea how to do math and write it out like you would for a 3rd grader?

[Donkadocus]

100+2x is the size of the pot after you have bet x into a pot of 100 and he has called.

[livedonk36]

i am still lost on this guys.

if anyone can come in and clear up the math that would be great.

[Donkadocus]

At work but I'll write more later

[dougiedan678]

Its hard to understand because you never gave an example in you original question.

Lets say there is a 100$ pot, and you are looking to go all in for $50 on the turn, villian folds 20% as you said, and when he calls, we have 35% equity.

When he folds : we win $100 - this happens 20% of the time
When he calls: we win 35% of $200 = $70 - this happens 80% of the time.

so 0.2(100) + 0.8(70) = $76

hence you would make $26 every time you made this bet of $50.

[AKmaert]

When he folds : we win $100 - this happens 20% of the time
When he calls: we win 35% of $200 = $70 - this happens 80% of the time.

so 0.2(100) + 0.8(70) = $76

hence you would make $26 every time you made this bet of $50.

Pretty sure this is wrong as you cant take the $50 investment off at the end because we only "invest" this $50 80% of the time. the calculation should be:

When he folds : we win $100 - this happens 20% of the time
When he calls: we win 35% of $200 = $70 - $50 we put in = $20 this happens 80% of the time.

so 0.2(100) + 0.8(20) = $36

hence you would make $36 every time you made this bet of $50.

[AKmaert]

Its also noteworthy that in this case it would be +EV to shove even if we knew he never folded due to our equity and the pot odds. Playing around with numbers were we have lesser equity gives more of a feel for the importance of FE in spots like this.