(2900 words; 15 minute read.) [5/11 Update: Since the initial post, I've gotten a ton of extremely helpful feedback (thanks everyone!). In light of some of those discussions I've gone back and added a little bit of material. You can find it by skimming for the purple text.] ​ [5/28 Update: If I rewrote this now, I'd now reframe the thesis as: "Either the gambler's fallacy is rational, or it's much less common than it's often taken to be––and in particular,  standard examples used to illustrate i...