  Can a probabilistic gambler get arbitrarily rich when all deterministic
gamblers fail? We study this problem in the context of algorithmic randomness,
introducing a new notion -- almost everywhere computable randomness. A binary
sequence $X$ is a.e.\ computably random if there is no probabilistic computable
strategy which is total and succeeds on $X$ for positive measure of oracles.
Using the fireworks technique we construct a sequence which is partial
computably random but not a.e.\ computably random. We also prove the separation
between a.e.\ computable randomness and partial computable randomness, which
happens exactly in the uniformly almost everywhere dominating Turing degrees.
