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benelliott comments on XKCD - Frequentist vs. Bayesians - Less Wrong Discussion
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Two subtleties here:
1) The neutrino detector is evidence that the Sun has exploded. It's showing an observation which is 36^H^H 35 times more likely to appear if the Sun has exploded than if it hasn't (likelihood ratio of 35:1). The Bayesian just doesn't think that's strong enough evidence to overcome the prior odds, i.e., after multiplying the prior odds by 35 they still aren't very high.
2) If the Sun has exploded, the Bayesian doesn't lose very much from paying off this bet.
Nitpick, the detector lies on double-six regardless of the outcome, so the likelihood ratio is 35:1, not 36:1.