https://en.wikipedia.org/wiki/Law_of_large_numbers
Could you argue that the closer you get to whatever that large number is...something different happens?
What about instances where the coin flip DOES have a memory? I.e. Non-determinism, freewill or quantum something or other
What if there is a bias towards brown horses amongst foolish punters with lots of money? A martingales would work in ones favour instead of the house in that instance?