Martingales are a representation of a class of "do a random thing 'forever'" problems, with a self-similarity constraint and also the restriction that your rewa

Martingales are a representation of a class of "do a random thing 'forever'" problems, with a self-similarity constraint and also the restriction that your reward is finite, both of which prevent them from being applied to most problems but make them vastly more computationally tractable. That they're well studied means we know some of those features. The author then mentions a few of those computational properties (like "Azuma's inequality") and gives a smattering of problems where directly applying them and ignoring most of the rest of the article would help build an intuition. The rest of the article is useful mostly because it puts all of the above in a more rigorous context and because if you're closer to uni maths it'll help provide some sort of intuition for why the restrictions were necessary and what sort of things might or might not be achievable with them. There's probably a less dense version somewhere, but I'm not quite sure what it would be. Hopefully this short summary helps you know what to look for when you find it.