PlayGame <- function(winnings=0, turn=1) {
  if(sample(0:1, 1)) {
    winnings <- winnings + (2^turn)
    turn <- turn + 1
    PlayGame(winnings, turn)
  }
  else {
    winnings
  }
}

RunSimulation <- function(timesToPlay=20000) {
  results <- rep(NA, timesToPlay)
  results1 <- rep(NA, timesToPlay)
  rollingAvg <- rep(NA, timesToPlay)
  rollingAvg1 <- rep(NA, timesToPlay)

  for(i in 1:timesToPlay) {
    results[i] <- PlayGame()
    results[i] = results[i]
    rollingAvg[i] <- mean(results[1:i])
  }
  plot1 = plot(rollingAvg, type="l")

}
RunSimulation()