Random walk probability: return to origin

random.walk <- function(n){
  steps <- rbinom(n, 1,0.5)*2-1
  pos <-0
  k<-n
  pos.hx <- seq(from=0, to=0, length.out=n)
  for (i in 1:n){
    pos <- steps[i]+pos
    pos.hx[i] <- pos
    if (pos==0){k<-i
      return(k)
    }
  }
  return(k)
}

simulations <- function(n, lim=100000){
  termination <- seq(from=0, to=0, length.out=n)
  for (i in 1:n){
    termination[i]<-random.walk(lim)
  }
  no.return <- sum(termination==lim)
  avg.walk<-mean(termination[termination<lim])
  return(c(no.return, avg.walk))
}

# Two input params: number of simulations, and max number of coin flips
# two output values: total number of simulations that did not return to origin,
#   and avg number of flips/steps taken to return
simulations(10000, lim=100000)