RW = function (k, N, p = 0.5) 
{
    pos <- k
    rw <- pos
    status <- 0
    if (pos == N) 
        status <- "win"
    if (pos == 0) 
        status <- "ruin"
    while (status == 0) {
        x <- rbinom(1, 1, p)
        if (x == 1) 
            pos <- pos + 1
        if (x == 0) 
            pos <- pos - 1
        rw <- c(rw, pos)
        if (pos == N) 
            status <- "win"
        if (pos == 0) 
            status <- "ruin"
    }
    l <- list(rw = rw, result = status)
    return(l)
}


simRW = function(num, k, N, p) {


      q = 1 - p
      
	count = 0
      	count1 = 0
	exp.length = rep(0, num)
	for(i in 1:num) {
          a  = RW(k, N, p)
          exp.length[i] = (length(a$rw) - 1)
          if(a$result == "ruin") {
            count = count + 1
            if(a$rw[2] == (k-1)) count1 = count1 + 1
          }
          if(i == 1) {
            plot(1:length(a$rw) - 1, a$rw, xlim = c(0, 2 *length(a$rw)), ylim = c(0, N), typ = "l", lwd = 3, xlab = "Number of Games", ylab = "Money (£)", main =  paste("Gambler's Ruin Simulation : p = ", round(p, 2), ", k = ",round(k, 0), ", N = ", round(N, 0), sep = "")) } else {
              lines(  1:length(a$rw) - 1, a$rw, col = i, lwd = 3)
        }
        }
	cat(paste("Proportion absorbed at 0 = ", round(count/num,3), "\n", sep = ""))
	cat(paste("Proportion of walks absorbed at 0 for which 1st move was down = ", round(count1/count,3), "\n", sep = ""))
	cat(paste("Average game length (until absorption at 0 or N) = ", mean(exp.length), "\n", sep = ""))
}