Suppose you flip coins for a certain times, say
n. You want to know your chance of getting certain number of heads in a row, say
kheads in a row.
Let's start with the function that'll do a certain number of coin flips:
Let's do 10 flips right away:
Let's suppose you get 1 euro if you get the given number of heads in a row while doing a certain number of flips. Here's the function that'll calculate your payoff:
Let's try our payoff function with doing 10 flips and getting payed for 3 heads in a row. sometimes it is 0, sometimes it is 1:
Now, what is your chance to get your 1 euro for 3 heads in a row from 10 flips? This brings us to the Monte Carlo simulation, which I'wont describe here at all, just give you a function which answers our question regarding the chance:
Running with a million iteration gives us a good approximation for the chance:
monte_carlo_solve(10, 3, 1000000)
This post was inspired by a similar post by Remis.