  Solomonoff sequence prediction is a scheme to predict digits of binary
strings without knowing the underlying probability distribution. We call a
prediction scheme informed when it knows the true probability distribution of
the sequence. Several new relations between universal Solomonoff sequence
prediction and informed prediction and general probabilistic prediction schemes
will be proved. Among others, they show that the number of errors in Solomonoff
prediction is finite for computable distributions, if finite in the informed
case. Deterministic variants will also be studied. The most interesting result
is that the deterministic variant of Solomonoff prediction is optimal compared
to any other probabilistic or deterministic prediction scheme apart from
additive square root corrections only. This makes it well suited even for
difficult prediction problems, where it does not suffice when the number of
errors is minimal to within some factor greater than one. Solomonoff's original
bound and the ones presented here complement each other in a useful way.
