You appear to be unclear on the meaning of "arbitrage". Simply taking a position that has positive expected return is not arbitrage; it's just plain investing. Arbitrage has positive (or at least nonnegative) 'guaranteed' return.

Casino owners are often said to be practicing "statistical arbitrage". What would you call it?

Is there a fundamental difference between 1) a casino's "really high" probability of earning a profit (on bets before expenses), 2) real-world true arbitrage, and 3) positive expected return in the large?

It seems related to the P=BPP problem, in which you can have confidence in a probabilistic solution that's higher than your confidence that your computer works, but which some people deem inferior to a deterministic solution coming from the same hardware.