Computable Prediction.

We try to predict the next bit from a given finite binary string when the sequence is sampled from a computable probability measure on the Cantor space. There exists the best betting strategy among a class of effective ones up to a multiplicative constant, the induced prediction from which is called algorithmic probability or universal induction by Solomonoff. The prediction converges to the true induced measure for sufficiently random sequences. However, the prediction is not computable.