royf comments on How Much Evidence Does It Take? - Less Wrong
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The number of false bleeps is distributed almost exactly Poisson with
. The important figure is not the expected number of bleeps (
, which is indeed 2). It's the expected probability that a random bleep is the true one,
. At the moment I can't find an analytic solution (and a short search suggests none is known), but a computation shows the result is around 63.2%, much better than 50%.
Similarly, with 14 boxes (arguably "28 bits of evidence"), the chance of winning is about 79.1% on average, much better than
.