I paused and wrote out all the probabilities and saw no way to improve beyond 80% - I scrolled down hoping to be proven wrong!

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eieio 5 hours ago | parent [-]

(I'm the author)

I think there's an annoying thing where by saying "hey, here's this neat problem, what's the answer" I've made you much more likely to actually get the answer!

What I really wanted to do was transfer the experience of writing a simulation for a related problem, observing this result, assuming I had a bug in my code, and then being delighted when I did the math. But unfortunately I don't know how to transfer that experience over the internet :(

(to be clear, I'm totally happy you wrote out the probabilities and got it right! Just expressing something I was thinking about back when I wrote this blog)

	▲	Aerroon 3 hours ago \| parent [-]
		I, erroneously, thought that "when Alice and Bob agree there's a 96% chance of them being correct, then surely you can leverage this to get above the 80% chance. What if we trust them both when they agree and trust Alice when they disagree?" Did some (erroneous) napkin math and went to write a simulation. As I was writing the simulation I realized my error. I finished the simulation anyway, just because, and it has the expected 80% result on both of them. My error: when we trust "both" we're also trusting Alice, which means that my case was exactly the same as just trusting Alice. PS as I was writing the simulation I did a small sanity test of 9 rolls: I rolled heads 9 times in a row (so I tried it again with 100 million and it was a ~50-50 split). There goes my chance of winning the lottery!