1/ Historically, though statistics started in gambling, it has been driven by the risk-management motive, not the luck-creation motive
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3/ Though many applications in science/tech are agnostic to risk-versus-luck angle, most social uses are on that spectrum and focus on risk
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4/ Application of statistics/probability to stock markets is not about luck either, since beating market beyond historical gains is zero-sum
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No, I am not a probability/stats wonk. Only basic engineering understanding. Hoping somebody else will figure this out :)

