Why wouldn't something like an RL environment allow them to specialize in poker playing, gaining those skills as necessary to increase score in that environment?

E.g. given a small code execution environment, it could use some secure random generator to pick between options, it could use a calculator for whatever math it decides it can't do 'mentally', and they are very capable of deception already, even more so when the RL training target encourages it.

I'm not sure why you couldn't train an LLM to play poker quite well with a relatively simple training harness.