As an amateur, I've always wondered if reinforcement learning could work with games where there are some probabilities in place (e.g. poker).
What happens when the action taken is a good one but the outcome is negative due to bad luck?
Absolutely. Q-learning has this capabilities and a shallow neural network was used back in 1992 to play backgammon, which has a lot of stochasticity.
See https://en.wikipedia.org/wiki/TD-Gammon