To become good at poker it's crucial to be able to distinguish between bad luck and play mistakes. You have to keep your cool when your opponent makes bad moves and wins anyway....In life, we are very often faced with situations where we have to analyze to what extent something is the result of our own actions and to what extent it is the result of factors outside our control.

I think this sounds like a valuable lesson to learn, and as you say, the kind of thing you couldn't get from a deterministic game. And as with go, I suspect that some lessons from poker sink in better when you experience them in play than when you just read them. I would be interested to read more about it, if you (or any other poker players out there) have the time and interest to write a post on rationality in poker or other games with a chance component. I have a feeling that there are lessons related to probability and quantifying your beliefs that could be drawn, or perhaps stories from games that can be used as illustrations of probabilistic or Bayesian reasoning.