I'm trying to model the location of a drunkard who starts at $x=0$ and moves towards $x=20$ with probability $0.6$ and to the left with $0.4$, when $x=20$ he moves in either direction with probability $0.5$, and when he's to the right of $x=20$ he moves to the left with probability $0.6$ and to the right with probability $0.4$.
I've already modeled simpler cases with the central limit theorem and the binomial model to get probabilities using the normal approximation and I confirmed them with simulations from a program.
Can someone hint me in the right direction? I know that Lyapunov's CLT would allow me to use random variables that aren't i.i.d. so I think I'd have to use that since the bernoulli variables aren't identically distributed but I've never used it before and I haven't done any course work for it so I don't really know what I'm doing.
Thanks