Reply To: Dice, Probability, and Simulation

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Hans Hellinger

Ok … after thinking that over a bit more, I think I DO get what that guy was trying to say, but I don’t think it’s relevant. I’ll explain why in a minute.

Here are the results of my first test. For this first run I’m only doing 2000 rolls at a time because my program is pretty crude and it runs slow, I’ll fine tune it a bit later. Messing around with this already forced me to address a nagging rounding error on my random number generator for the character lifepath application, so that’s a positive side benefit even though it took me 3 hours to fix it + write this number cruncher thing.

So ok anyway, this is a ‘Monte Carlos’ test of Roll many / Keep one, keeping the highest number of dice rolled out of one, two, three, and four. I’m tracking the number of Critical Failure and Critical Success results which are key for reasons I’ll explain in a followup post.

Anyway, here are preliminary results.

Roll ONE die

Number of Natural 20: 76 (3.8%)
Number of Natural 1: 83 (4.1%)
Iterations: 2000
Cumulative total: 20786
Average: 10.39

Roll TWO dice

Number of Natural 20: 125 (6.2%)
Number of Natural 1: 52 (2.6%)
Iterations: 2000
Cumulative total: 23333
Average: 11.67

Roll THREE dice

Number of Natural 20: 206 (10.3%)
Number of Natural 1: 18 (0.9%)
Iterations: 2000
Cumulative total: 26539
Average: 13.27

Roll FOUR dice

Number of Natural 20: 241 (12.05%)
Number of Natural 1: 5 (0.25%)
Iterations: 2000
Cumulative total: 28063
Average: 14.03