### Methods ###
flip <- function(p){
  sample(0:1, 1, prob = c(1 - p, p))
}

flip_n <- function(prob, n){
  res= NULL
  for(i in 1:n){
    res = rbind(res, flip(prob))
  }
  return(res)
}

flip_til_sig <- function(prob, a = 0.05, n_min = 10, n_max = 100){
  res = NULL
  p   = 1
  for(i in 1: n_min){
    res = rbind(res, flip(prob))
  }
  while(p > a & length(res) <= n_max){
    res = rbind(res, flip(prob))
    p   = binom.test(sum(res), length(res), p = 0.5)$p.value
  }
  return(res)
}

### Simulation ###
nsim = 1e3
res1 = replicate(nsim, flip_n(prob = 0.5,  n = 100), simplify = F)
res2 = replicate(nsim, flip_til_sig (prob = 0.5, a = 0.05, n_min = 10, n_max = 100), simplify = F)

par(mfrow = c(2, 1))
hist(sapply(res1, mean), breaks = 20, col = "Grey", xlab = "% Success", main = "Collect N datapoints")
hist(sapply(res2, mean), breaks = 20, col = "Grey", xlab = "% Success", main = "Collect until stopping rule")