The universal prior implies you should say "substantially less than 1 million".
Why do you say this? Are you merely suggesting that my prior experience with quantum coins is << a million tosses?
No, I'm not suggesting that. I think the statement stays true even if you've already seen 100 million quantum coinflips and they looked "fair". The universal prior still thinks that switching to a more ordered generator for the next million coinflips is more likely than continuing with the random generator, because at that point the algorithmic complexity of preceding coinflips is already "sunk" anyway, and the algorithmic complexity of switching universes is just a small constant.
ETA: after doing some formal calculations I'm no longer so sure of this. Halp.
You're about to flip a quantum coin a million times (these days you can even do it on the internet). What's your estimate of the K-complexity of the resulting string, conditional on everything else you've observed in your life so far? The Born rule, combined with the usual counting argument, implies you should say "about 1 million". The universal prior implies you should say "substantially less than 1 million". Which will it be?
EDIT: Wei Dai's comment explains why this post is wrong.