The Limits of Bayesian Reasoning

by Gene Callahan

In a seminar I’ve been attending at NYU this semester, David Chalmers contended that “resetting priors” is irrational in a Bayesian framework. (If you’re not familiar with Bayesian inference, the Wikipedia article just linked to does a good job of introducing the topic, so I will refer you to that, rather than lengthening an already long post with my own introduction to the subject.) This seemed wrong to me and seemed wrong to me long before Chalmers raised the issue for me again. But his remarks renewed my interest in the subject, and resulted in this post.
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Strange Gambling

by Gene Callahan

The ‘Sports Guy‘ over at talks about the big betting mistake he made during the playoffs:

‘Anyway, I’m talking about intentionally going for 4-0 with my wild-card picks. I thought two home teams would cover, only one of the rookie QBs would cover and two super-obvious road teams would not cover. After studying it from every angle, I locked in on Arizona and Baltimore (my favorite of the four) and already liked Indy; because the Philly-Minny game was a crapshoot, that meant Minnesota had to be the fourth pick. What I should have done: Take Arizona, Indy, Baltimore and Philly and aim for 3-1. But I was trying to be a hero — in this case, finish 4-0 — and inadvertently broke Rule 14 of the Playoff Manifesto, which specifically says, “Don’t try to be a hero, just try to make money.” Call it a lesson learned. By my wallet.’

What in the world can this fellow be talking about? (And note, he makes his living giving gamblers advice.) He seems to be saying that, by intentionally picking one of the games with the aim of getting a bet wrong, he would have been ‘safer’ than by trying to pick all four games correctly! There certainly are situations in which you can reduce your gambling risk by not ‘going for broke’, but I can’t for the life of me see how this is one of them. He calls the Philly-Minnesota game a ‘crapshoot’, presumably meaning he thought it was 50-50 that either side would cover — so how does swapping one even bet for another reduce his risk? Any ideas what he might be thinking of here?