coins.R

fairness_ratio <- function(coins, flips, trials = 10^6) {
  all_heads <- rbinom(trials, flips, 1/2) == flips
  is_unfair <- rbinom(trials, 1, 1 / coins)
  ratio <- sum(all_heads & !is_unfair) / sum(is_unfair)
  return(ratio)
}

# the problem as Daniel stated it
fairness_ratio(coins = 10000, flips = 10)

# a common variant with roughly equal probability
fairness_ratio(coins = 1000, flips = 10)