Here's a good example of where I was fooled where I shouldn't have been if I'd been thinking like a proper Bayesian. Prior to reading the article I would have given something like 1/1000 that computers could "solve" a main-line chess opening (to the definition given in the article, which is just that the computer evaluates each line as winning, not that every possible position has been examined). I'd also try to plug in reasonable numbers for newspapers reporting a story as true/false when the story is actually true/false as something like p(newspaper reports true given story is actually true)=95% and p(newspaper reports as true given story is actually false) =20%. Doing the math, there is then almost no chance that the article was true (less than 1%)
And I should have been able to do this in my head. Even if the newspaper reported true stories as true 99% of the time, and a false story as true only 1% of the time, there would have still been about 10 to 1 odds that it wasn't true.
So why did I get fooled? I didn't ever stop to think about it probably, which is embarrassing. Why not? I saw the link from MR and I apparently over-trust Tyler Cowen as a gatekeeper. Had a random person told me about the article I probably would have called BS on it (as I've done before with similar situations) but because someone I trust made the assertion I forgot to apply my brain filters, probably assuming he already did it.
Moral of the story, I need to always, at least briefly, think about my priors and how strong of evidence the source is when I learn new information. Especially if it comes from a source I trust because I'm more prone to believe it.
Excellent point.
For me, the problem was one level before yours: I had very bad priors. This is embarrassing for me because (a) I frequently play chess at a USCF affiliated club and have read more than a handful of books specifically on the King's Gambit; and (b) I am a computational science grad student and have studied complexity theory in great detail, even specifically discussing implications of chess on the development of A.I. and complexity theory as a whole.
In retrospect, as @gjm pointed out, there are enough markers in the article (especially the &...
Edit: it was unfortunately a prank. I definitely checked the date of the article (which is dated Apr. 2), before posting on it. Kind of mean to make an April Fool's prank after April Fool's. I didn't realize I'd have a chance to practice what I preach so soon.
I guess I need to just say oops.
Original Post:
Chess analyst Vasik Rajlich had some big news today: solving the King’s Gambit.
I know that this doesn’t add much new to the complexity theory aspects of games like chess, but I would say it’s a beautiful result, very much like the recent improvement on the complexity of matrix multiplication, and it certainly emphasizes the role computation plays as the King’s Gambit is a pretty popular, classical opening. By most any human standard it’s a respectable opening, and yet we can conclusively say it is unequivocally bad for White assuming two rational players.
I wrote up a short blurb about it at my blog.