I've studied rigorous probability theory at university but I find myself struggling to solve questions in probability as quickly as some of my peers. I think that what I try to do is 'translate' the problem into a rigorous framework and solve it there, while others are simply thinking about most problems in probability on a heuristic/intuitive level, and only resort to the framework when there is some confusion to be cleared up. Are there any good books or places on the internet where I can encounter a list of useful heuristics for probability?
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Are your colleagues actually using heuristics, or merely applying the formulas at a more-appropriate level of specificity than you do? Might they simply be faster calculators than you? – David G. Stork May 11 '22 at 17:53
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Some of them are certainly faster, but it feels like too many to be a coincidence, since I'm not THAT slow ;) – May 11 '22 at 17:56
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Like anna says, I don't think you will find a single source containing what you want. I also second the suggestion to talk to those you consider to be faster than you and ask them how they approach specific problems. You can learn something from their answer and possibly generalize it to broader contexts. Ultimately, what has helped me the most in a field like probability is practice, practice, practice. Seeing more problems and how they are solved will help you ignore the inessential details with time. Algebraic Topology was a similar field for me; there too it takes a while to build geometric intuition about CW complexes and the geometric interpretations of various algebraic/analytic constructions, but once you get that intuition you rarely, if ever follow arguments back to their logical foundations.
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Are you familiar with Terence Tao's blog? (https://terrytao.wordpress.com). There are several articles there on heuristics in probabilistic contexts. I suspect this is not what you want, not entirely at least. I don't believe there is a single source containing what you're looking for, as the subject is pretty far-flung with many loosely connected parts. I think that your own intuition and 'heuristic ability' will get better with practice and experience. You should, of course, also talk to others (especially those who you mention 'are much faster than you') and ask them how they approach a specific problem to gain insight.