Find the best strategy for playing Farkle

On Linux, this should be as simple as

make
./playfarkle

The rules as programmed here are how I play with my family. Your rules, and the official rules, may differ.

Well, for the rules as programmed, the following strategy will get you 515 points per round on average:

• Keep 222 if you roll it (it's only worth 200 points, but keep it anyway).
• Always keep a leftover 1, but only one of them, and if no 1, keep one 5; do this even if you already have other points.
• Re-roll when you have 3 or more dice left over, BUT increase that number by 1 for every 500 points you've racked up this round; so if you have 1000 points this round, only re-roll if you have 5 or 6 dice left, not 1-4.

This problem has been addressed before, most notably here: AI-GameTheory, FarkleSolver.

Farkle is probably a trademark, and I am using it, and the rules here, without permission.