aez-notes

Player \(M\) has \(\$1\), and Player \(N\) has \(\$2\). Each play gives one of the players \(\$1\) from the other. Player \(M\) is enough better than Player \(N\) that he wins \(2/3\) of the plays. They play until one is bankrupt. What is the chance that Player \(M\) wins?

This is pretty much the same as the previous problem with a different boundary condition.

load(solve_rec)$

p[0] = 0;
p[3] = 1;
my_deq : p[n] = (2/3) * p[n+1] + (1/3) * p[n-1];

my_sol : solve_rec(my_deq, p[n], p[0] = 0, p[3] = 1);

print(ev(my_sol, n = 1));
/*
     4
p  = -
 1   7
*/