Magic: the Gathering comes to mind, since the community often focuses explicitly on thinking-about-probabilities due to both the hidden information (what cards does your opponent have?) and the random factor (what cards will I draw later in the game?)

One of my favorite stories is about a high-level competitor who had a tendency to win since he could work out "I will ONLY win if I draw this one card" and would then craft his entire game around the expectation of that card - after all, if he failed to draw it, he was dead anyway :)