[Strilanc]

If you feed biased random bits into Solomonoff induction, the shortest surviving programs at any given point would tend to be things like arithmetic encoders that match the bias and specify just a bit more output. (Assuming you're not using pseudo-random numbers, of course.) So it will at least start to predict probabilities with the correct bias.

If you're feeding in unbiased independent random bits, any and every process is already an optimal predictor.