The First to Reach 10 – Simulation

We have seen how Amy can win the coin-tossing game after leading 8-7. Let’s simulate the game and see what comes out.

AM <- 8
BE <- 7

itr <- 1000000
game <- replicate(itr,{
  
for (i in 1:5) {
card <- sample(c(1,0), 1, replace = TRUE, prob = c(1/2,1/2))

if(card ==1 ){
  AM <- AM + 1
} else{
  BE <- BE + 1
}

if(AM == 10| BE == 10 ) break
}  

if(AM == 10){
  counter <- 1
}else{
  counter <- 0
}
  
})

mean(game)

0.6873

Not very far from the analytical solution.