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HELP! Need basic algebra help for a simple GTO river equation
Douggyfr3sh
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August 27, 2015 - 8:05 pm
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Hey TPE, 

 

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

Thomps
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August 28, 2015 - 3:41 am
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Hi,

 

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)

Douggyfr3sh
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August 29, 2015 - 8:12 pm
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Thanks Thomps!

 

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!

The Riceman
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August 30, 2015 - 9:27 pm
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I dont understand any of it…you might as well be talking an ancient Chinese-Hebrew mix as interpreted by an Austro-Hungarian at the outbreak of World War Two.

Thomps
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August 31, 2015 - 3:02 am
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Hey Douggy,

 

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 🙂

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