Math: Luck as Critical Failure Insurance

Ah, pithy quotes on a kitschy poster.

Yesterday, I graphed the value of luck, and someone asked me what might be the value of luck if it were solely used for "Critical Failure Insurance" as in, only saved for critical failures to make sure we don't have them. So today, a slight variant on yesterday's post, what is the value of Luck if used in this limited context?

Math: What's Luck Got To Do With It?

It's physical, only logical

For some reason, figuring out an easy way to graph this has eluded me for a while, but then I decided to just write a little loop to go through the numbers. Originally, I was going to run through all 216 * 216 * 216 = 10,077,696 combinations together, but that was a little slow, so I used a fun little memoization technique to reduce it to 16 * 16 * 16 = 4,096 combinations, which is a lot more manageable, friends! Let's investigate these numbers further then.