Decided to provide my solution since others have done so as well.
Solution
The public dataset is approximately symmetrical, so it is very likely that the distribution of the Bernoulli rate is also symmetrical (probability at p is equal to probability at 1-p). Let the probabilities of getting k Rs over all 5 trials for k=0...5 be . Then, from the public dataset, we have . These have standard deviation which is negligible, so we can treat these as linear equations. Solving, we get , and we can then solve for the marginal frequencies etc.
Not sure if this (experiment set?) is a good test of priors, since I got an exact answer without having to consider priors, other than the data being symmetrical. (This also means that any symmetric distribution for the Bernoulli rate will result in the same answer.) Though @DaemonicSigil has a similar solution without using symmetry, instead using
maximum entropy as a prior (if i understand it correctly).
Still, almost all reasonable priors will result in very similar outcomes, differing by a factor probably on the order of the standard deviation (around .) This is likely less than, or at least comparable to, the noise in the actual marginal frequencies.
Answer:
[0.111020, 0.324512, 0.5, 0.675488, 0.888980]
I will provide my solution when the market is resolved.
No; your distribution gives probabilities [0.253247, 0.168831, 0.155844, 0.168831, 0.253247] for the number of Rs in the first four trials. This predicts that the number of experiments with two Rs is binomially (i.e. approximately normally) distributed with mean ~155844 and standard deviation ~363, but the actual number is 161832, around 16 standard deviations away from the mean.
Was this written by AI? The self-altering of consistency makes no sense and I can't think of a reason that just discovering an inconsistency in the universe would cause a vacuum decay. Even if the universe was a simulation, discovering a bug doesn't mean exploiting it, though maybe the simulators would end the simulation (which wouldn't create any propagation, it'd just end it at once.)
I had an interesting solution due to binary-operation tunnel vision:
Solution
Represent numbers not as numbers themselves but as their "prime factorization" (generalized to non-rationals as in sqrt(2)=2^(1/2))
[x] = 2^x
and
concat(a, 2^a 3^b ...) = a*(3^a 5^b ...), right-associative (e.g. [][[]] = concat(1, 2^1) = 1*(3^1) = 3).
so i should write a rationalist hololive fic
redacted for privacy concerns
not sure if this has already been said but 10^30 FLOP is a LOT, and i think an ai that passes the strong turing test is incredibly unlikely (<1%). The detector space is enormous and it seems unlikely that it'd be possible to copy any human that perfectly, let alone one human, at least barring a preexisting superintelligence.
I think it's well known that it's optimizing for watch time.