This is a good post, and will be helpful to a lot of folks!
Below are some comments for future posts.
You x- and y-axes would benefit from some labels.
A log-log plot would also be helpful here, as it will reign in the crazy differences in scale on the opposite sides of the graph.
You also don't really need to simulate: each card has a well-defined probability mass function, and the sum of PMFs is pretty straightforward.
I thought it would be useful for finding the median and also just modeling for specific levels of CP (ie over 300 has these odds). I appreciate the tips though, and definitely agree I should've included axes.