Extension of Arbitrage agent - use conditional probabilities between markets as part of arbitrage strategy

[gabrielfior]

On #137 a simple Arbitrage agent was developed, allowing markets (on the same platform, Omen) to be arbitraged when correlation between them was close to 1 or -1.

We can expand that approach for the case where correlation (which can also be seen as P(A|B), i.e. likelihood that event A occurs if B also occurs) lies somewhere -1 < c < 1.
Some math calculations are available here (notion link).

[kongzii]

Some math calculations are available here (notion link).

To anyone who picks this up: When implementing this task and using math equations -- don't forget that everything is estimated by LLMs (probability of first market, probability of second market, and also their correlation). So don't forget that even if math promises 100% confident profits, reality can be way different. (in the same way as Kelly, theoretically perfect, practically losing all the money if higher bets are allowed).