Game theory: Optimal Strategy. Need help with a system of equations.

[morrowcosom]

This problem is not schoolwork, it is from "The Mathematics of Poker". I have three equations based off a 3x3 Rock, Paper, Scissors payout table where winning with scissors is given a +2 payout instead of +1.

Homework Statement

Find the solution to the system of equations

Homework Equations

-b+c
a-2c
-a+2b

The Attempt at a Solution

a=2b=2c
*This answer is stated in the book, but I do not know how the answer arrived from
the system of equations, as the book does not explain the mathematics.

It looks like this is dealing with derivatives,
but I have not worked with those.

Could somebody explain how the answer was computed?

Thanks for the help,
I want to solve more games

 

[jedishrfu]

I found this reference that goes through the analysis of making the payout matrix and reducing it to what you have which may help.

http://en.donkr.com/forum/modeling-poker---part-2-537213

 

[morrowcosom]

I just do not know how to compute that reduced system of equations that I have into the correct answer. The actual math is beyond me.

On the poker website, he is using simple EV equations, but the answer in the book for my game comes out looking like it came from some other process.

That author you pulled up has some really heady stuff on optimal play in poker (some of which I use), but ironically, I was just trying to use the simpler examples in my book to help me solve simpler day to day things with game theory for fun.