Comparing a simple strategy vs random play
I randomly felt like analyzing two simple strategies for Yatzee: playing randomly and simple greedy. To use the latter strat, just find the category you haven't played that would give you the most points based on what you rolled. If you have nothing, roll everything again and repeat.
The results for random aren't surprising: the mean score is 39, most games get 30-50 points, a small few get a decent amount. What I like is that with even a simple strat like greedy, the results are immediately better by a good amount. The mean score is 114 and even poor games get more points than a majority of random games.
It's not surprising that almost anything does better than random, but it's a satisfying example of the Pareto principle: "80% of the work is just showing up." Also, I think it's a pretty graph.