Lets create an equation. Bonus points if you graph it.

So this is a gambling game player 1 selects any whole real positive number. Then rolls a fair dice with sides equal to the number(ex. rolls 1 to 100). What ever number they roll player 2 rolls that many sided fair dice. This repeats back and forth until whoever hits 1 first loses.

What is this probability function for the initial number chosen?
Bonus if you make a graph.