Gambler's Fallacy again, looking for a succinct explanation of a variant of Martingale

[Big Bad Barney]

Surely a martingale would work if you roll it enough times?

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?

[Tuco]

if you did implement this strategy, how are you going to decide which horse to bet on?

Out of a hat? Pin the donkey tail? Back the rank outsider? or are you going to 'place it on Lucky Dan' for the win?