Blogging by Heath™

TL;DR: I saw a random dice game on social media with no satisfying solutions in the comments, so I played around with it using simulation to test my intuition and then worked out the optimal strategy using dynamic programming. The game The game has $n$ rounds. You start with $0$ dollars and a 20 sided die (d20) showing the number $1$. Each round, you can take money equal to the number shown, or reroll.