In closed loop toy models with a fixed money supply, what are the downsides of calculating probable outcomes with a binomial coefficient?
For example, given a toy economy where trades yield a profit or loss of $t$, and all participants start with wealth $W$ as expressed by:
$f(x_{n+1})=x_n \pm t$
and
$f(x_0)=W$
I would predict the probability of one participant reaching a wealth of $0$ by iteration $q$ to be :
$$ P = 1- \prod\limits_{n=1}^{q} {\left(1-\dbinom{n}{\frac{W+tn}{2t}}\frac{(n+1)\bmod 2}{2^n}\right)} $$
Are there better methods?