Martingale representation theorem

The Martingale Representation Theorem says that any fair game of chance (where there is no house edge) can be represented as the sum of a bunch of random numbers. This means that if you flip a coin, you can predict the outcome by taking the sum of a bunch of random numbers. For example, if you flip a coin three times, the result (either heads or tails) can be predicted by taking the sum of three random numbers. If the sum of the random numbers is an even number, you will get heads and if it is an odd number, you will get tails. The Martingale Representation Theorem is an important concept for understanding probability theory.