Solomonoff sequence prediction is a scheme to predict digits of binary stri
ngs without knowing the underlying probability distribution. We call a pred
iction scheme informed when it knows the true probability distribution of t
he sequence. Several neu relations between universal Solomonoff sequence pr
ediction and informed prediction and general probabilistic prediction schem
es will be proved. Among others. they show that the number of errors in Sol
omonoff prediction is finite for computable distributions, if finite in the
informed case. Deterministic variants will also be studied. The most inter
esting result is that the deterministic variant of Solomonoff prediction is
optimal compared to any other probabilistic or deterministic prediction sc
heme apart from additive square root corrections only. This makes it well s
uited even for difficult prediction problems, where it does not suffice whe
n the number of errors is minimal to within some factor greater than one. S
olomonoff's original bound and the ones presented here complement each othe
r in a useful way. (C) 2001 Academic Press.