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!