Confusingly, while this betting strategy is the original "Martingale", it's not really what's meant by the term in probability theory. An intuitive explanation

Confusingly, while this betting strategy is the original "Martingale", it's not really what's meant by the term in probability theory. An intuitive explanation of martingale in the more technical sense is simply that "your best guess for the future value of a series is its current value". I.e. on average it won't deviate up or down from where it is now, regardless of past values. But, crucially, that applies at any given time. It means that every time the value moves up and down, you should reset your expectation and believe that whatever value it is now is the new normal. Some things that are not martingales are - processes that are biased to move more up than down, or vice versa, - processes that are mean-reverting, i.e. when they have gone up for a while they are likely to go down again, and - more generally, processes whose future value can be predicted better by using more information about their recent past.