So I've seen the posts from Sisyphus and mccombju about probabilities and statistics, but they didn't convey the information as well as I hope these graphs do.
A brief explanation of the graphs: they start out with attack dice only then defense dice only (future posts will show complete probabilites of attack vs. defense combinations).
The "PDF" (probability density function) graphs show the probability of getting any given number of skulls (0A, 1A, 2A...) (or shields (0D, 1D, 2D...)) when rolling "N" dice. E[X] is the expected value (the mean, or average) of a dice roll. SD is the standard deviation of a dice roll (a measure of how spread out the probability is, a smaller number means your actual roll will be pretty close to the calculated average, a larger number means your actual roll has a better chance of being way off the calculated average). The numbers under the bars indicate the percent each bar is (to one decimal place), the second number is the "1 in <number>" description of the bar. Like if a certain outcome has a 25% chance, the number below the percent will be "4", because 25% is "1 in 4", a 2% chance is "1 in 50", etc. when the numbers get too large scientific notation is used so X.Xe+NN = X.X*(10^NN), so 3.5e+09 = 3.5*(10^9) = 3,500,000,000.
The "Modified CDF" (cumulative distribution function) shows the probability of rolling "N-or-more" skulls (or shields) when rolling "N" dice. I only listed the percent under the bar, because over 50% the "1 in <number>" description of the probability loses relevance.
What ultimately motivated me to make these graphs was my appearance on The Dork Forest podcast discussing Heroscape, and how the Samurai's counterstrike ability made me want to figure this out. The episode:
or
http://tdf.libsyn.com/heroscape-with...errmann-ep-528
The graphs:
https://sites.google.com/site/beagle...ice_graphs.pdf