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JulianMorrison comments on Bead Jar Guesses - Less Wrong
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Thinking about how an Occamian learner like AIXI would approach the problem, it would probably start from the simplest domain theory "beads have a color, red is a color I've heard mentioned, therefore all beads are red", p=1. If the first bead was grey, it would switch to "all beads are grey", p=0. The second bead is red, "half and half", p = 0.5, and so on, ratcheting up theories from the simplest first.
FYI, AIXI does not work like this; it uses a probability distribution over all Turing machines.
This is not how AIXI [*] works. It considers all possible programs at the start, with some probability. The simplest program that fits the data is not the only one it considers; it just gets most of the probability mass. So, from the start, it will give some tiny probability to a hypothesis that the beads will spell War and Peace is morse code. Only when this hypothesis is falsified by the data, it will drop out of race.
[*] M. Hutter (2003). `A Gentle Introduction to The Universal Algorithmic Agent AIXI'. Tech. rep. [abstract/download]
and thus his bayes-score drops to -Infinity
I don't think AIXI tries to maximize its Bayes score in one round - it tries to minimize the number of rounds until it converges on a good-enough model.