At least intuitively, I find it easier to think of martingales as betting strategies, basically a process where given a past sequence of events it spits out som

At least intuitively, I find it easier to think of martingales as betting strategies, basically a process where given a past sequence of events it spits out some wager on a prediction of the next outcome. Then there's a correspondence between the fairness criterion and betting functions. https://math.berkeley.edu/~slaman/papers/mlreals.pdf https://math.berkeley.edu/~slaman/papers/mlreals.pdf