Would the problem be different if we changed the Alpha-Omega betting odds so that if Alpha wins 1 in 10000 times (which is still plausible given the data) then Alpha would make a profit?

It is a convenient way of representing reputation gain.

Think of Alpha as being the AI society at large, or a reporter detailed to watch and report on Omega, on behalf of the AI society.

So they're not actually doing an explicit bet. Rather it is Omega wanting to improve Omega's reputation at human-prediction within the AI society by doing the experiment. The more Omega does the experiment and makes correct predictions, the higher the others in AI society will rate Omega's expertise. Presumably it is valuable to Omega in some way to have a high reputation for doing this; maybe he wants to sell an algorithm or database, maybe he wants his advice about a human-related problem taken seriously without disclosing his actual source code and evidence - the reason isn't relevant.

From Fred's perspective, when it comes to understanding and planning for Omega's actions, the dynamics of the situation are close enough that, to a first approximation, it is as though Omega had made a bet with some Alpha.

What the odds of that bet are a variable input to the problem, which I shall talk about in part 3, but note for now that this isn't an arbitrage situation where someone else can step in and improve Omega's reputation for him in order to chisel a corner off the odds. The odds for Omega, from the perspective of Omega's knowledge of the situation, will be in Omega's favour of improving Omega's net reputation, else he wouldn't be running the experiment.