Probability

As one can easily guess, this blog is about a mental model of thought. I chose to write about it since I feel that introspection about ways of thinking (and consequently what “thinking before doing something” means) is greatly lacking among people, and that it is critical to make better decisions (and realizing when there is no “better” decision). I won’t bore you with the philosophical details, so I’ll approach it from a probabilistic perspective, which is closer to what I personally choose to think in terms of....

This post was originally written on Codeforces; relevant discussion can be found here. Recently someone asked me to explain how to solve a couple of problems which went like this: “Find the expected time before XYZ happens”. Note that here the time to completion is a random variable, and in probability theory, such random variables are called “stopping times” for obvious reasons. It turned out that these problems were solvable using something called martingales which are random processes with nice invariants and a ton of properties....