clock stepping simulation

clock.R

ids <- 1:12
take_step <- function(i){
  x <- NA_integer_
  if (i == 1) {
    x <- sample(c(2, 12), size = 1)
  } else if  (i == 12) {
    x <- sample(c(11, 1), size = 1)
  } else {
    x <- i + sample(c(-1, 1), size = 1)
  }
  return(x)
}

take_step(12)

library(tidyverse)

around_clock <- function(){
  outs <- c(12,rep(NA_integer_, 300))
  i <- 2
  while(length(table(outs))<12) {
    outs[i] <- take_step(outs[i-1])
    i <- i + 1
  }
  
  cum_out <- cumsum(is.finite(outs))
  # get the last one
  last <- outs[which.max(cum_out)]
  # get the length
  len <- max(cum_out)
  tibble::tibble(last, len, outs = list(outs))
}

dd <- around_clock()
dd$outs

sim_df <- purrr::map_df(1:1000, ~around_clock(), .id = "sim")
sim_df |> 
  count(last) |> 
  mutate(freq = n/1000) |> 
  ggplot(aes(x= last, y = freq)) + geom_point() + 
  scale_x_continuous(breaks = 1:11) + 
  ylim(c(0, 1)) + 
  geom_hline(yintercept = 1/11)

1/11

sim_df |> 
  ggplot(aes(x = len)) + 
  geom_histogram() + 
  geom_vline(xintercept = 66, col = "red", lwd = 2)

mean(sim_df$len-1)

sim_df |> 
  ggplot(aes(y = len, x = last)) +
  geom_count(alpha = .5) + 
  theme_bw()