So my question is, how are you dealing with the initial condition?
Suppose there were [1,k] spots. You are assigned an intial value from [1,k] and you then have to reach 0 before time t=k. Here's my code to solve the general case
object particle {
def main(args:Array[String]) = {
val simulations = args(0).toInt
val rng = new util.Random
(2 to 1000).foreach(spots=>{
val reachedZero = (1 to simulations).map(_=> {
var t = 0
var z = 1+rng.nextInt(spots)
do {
z += {if (rng.nextBoolean) 1 else -1}
t +=1
} while( z != 0 && t<spots)
z==0
})
val prob = reachedZero.count(_==true)*1.0d/simulations
printf("%4d spots: %.4f\n",spots,prob )
})
}
}
>scala particle 1000000
2 0.3773
3 0.329
4 0.292
5 0.2714
6 0.2624
7 0.2428
8 0.2247
9 0.222
10 0.2157
....