Simulate lots of independent coin flip games, or just one long game.

coin-flip.R

# Inspired by Ole Peters: https://youtu.be/LGqOH3sYmQA

# Play the coin flip game for n rounds.
# Win 50% of your holdings if you get heads
# Lose 40% of your holdings if you get tails
# Keep flipping for n rounds
play <- function(n) 100 * cumprod(ifelse(runif(n) > 0.5, 1.5, 0.6))

n_plays <- 1e4

# Let's simulate lots of idependent games
plays <- lapply(seq(n_plays), function(i) {
  play(100)
})

# Here we plot the results of each game, looks noisy
plot(1, type="n", xlab="", ylab="",
  xlim=c(0, 100), ylim=c(0, log10(max(sapply(plays, max))))
)
for (i in seq(n_plays)) {
  lines(log10(plays[[i]]))
}

# Put each game into a column
mat <- do.call(cbind, plays)
# Average over all the games
avg <- log10(rowMeans(mat))

plot(avg, type="l", xlab="", ylab="")

plot(log10(play(1e4)), type="l", xlab="", ylab="")