Code to simulate and calculate the number of switches and streaks in a series of coin tosses

switches-and-streaks.R

calc_switches <- function(x) {
  n <- length(x)
  x0 <- x[1:(n - 1)]
  x1 <- x[2:n]
  switches <- sum(x0 != x1)
  return(switches)
} 

calc_streak <- function(x) {
  longest_streak <- 0
  current_streak <- 1
  n <- length(x)
  for (i in 2:n) {
    current_streak <- ifelse(x[i] == x[i - 1], current_streak + 1, 1)
    longest_streak <- ifelse(current_streak > longest_streak, current_streak, longest_streak)
  } 
  return(longest_streak)
} 

x <- rbinom(50, 1, .5)

calc_streak(x)

n_sims <- 1000
switches <- longest_streak <- rep(NA, n_sims)
for (i in 1:n_sims) {
  x <- rbinom(200, 1, .5)
  switches[i] <- calc_switches(x)
  longest_streak[i] <- calc_streak(x)
}

df <- data.frame(switches, longest_streak)

library(ggplot2)
ggplot(df, aes(x = switches, y = longest_streak)) + 
         geom_point(position = "jitter")