What is a 'Martingale'?

What is a 'Martingale'?

Approach: Define a sequence of random variables where the future expectation is the current value.

A model of a fair game where the conditional expectation of the next value, given all prior values, is equal to the current value: E[X_{n+1} | X_1, ..., X_n] = X_n.

Follow-up: What is a sub-martingale?

Key concepts: fair game, conditional expectation.