I'm actually not doing anything in that step, just rearranging the variables. Maybe you can see it better like this:

0 = -b*pC + 1 – pC  = 1 -b*pC – pC = 1 + (-b*pC – pC)    

Here nothing has been done, the parenthesis doesn't have any use there, just to show, now we take out of it the minus, as both "pC" are multiplied by -1, so:

==> 0 = 1+(-b*pC – pC) = 1 – (b*pC + pC)

Hopefully this will help 🙂

0 = -b*pC+1*(1-pC) 

0 = -b*pC + 1 - pC 

-This is where I get stuck, im not sure how you got to: 

0 = 1 - (b*pC +pC)

-I DO understand how you get from that to this:

0 = 1 - pC * (b+1)

1 = pC * (b+1)

pC = 1/(b+1) 

Thanks for the help!

Luckily not a hard one, I'll go step by step, if there's any one you don't understand let me know.

0 = -b*pC + 1*(1 – pC) = -b*pC + 1 – pC = 1 – (b*pC + pC) = 1 – pC * (b+1)  

==> 1 = pC * (b+1)

==> pC = 1 / (b+1)

I have been getting into studying GTO concepts lately, and I am bad at math and need refreshing.  I got hung up while studying last night in a spot where I was looking at the math of a toy game river scenario where V1 has air or nuts and V2 always has a med. strength hand.  Here is the equation to solve for our Calling Probability:

Variables:

 b = size of villains bet in units of % of the pot 

pC = the probability with which we call this bet as the OOP player with med. strength hand 

0 = -b*pC + 1*(1-pC)  -This is the equation for EV[check] = EV[bluff] for IP villain who acts first  

pC = 1/(b+1) -This is the equation solved for pC, our calling probability.  I don't know the algebraic steps used to get to this solved equation, can anyone help me step through solving for pC??  Thanks