I sent a link to my previous blog post on the optimal play of Farkle to Professor Todd Neller, at Gettysburg College. (I thought he might be interested in it since it was largely based on his previous analysis of the simpler dice game Pig.) We ended up talking and decided to write a paper together on optimal Farkle play. Todd presented our paper at The 15th Advances in Computer Games Conference (ACG 2017), Leiden, Netherlands, July 4, 2017. Our paper was voted second place in the best paper competition.
The paper focuses on a more minimalist rule set (whereas my previous blog post solved for facebook farkle rules). The optimization equations are much simplified by using a pair of self-referential equations describing pre-roll and post-roll game states. The paper also includes a comparison of optimal play vs max-expected-score play, a mechanism allowing a human to perfectly replicate max-expected-score play, and some simple techniques you can use to win over 49% of your games against an optimal player.
As of the time of this post, the proceedings from the conference have not yet been published, but a link to our paper is provided here for your convenience:
Optimal Play of the Farkle Dice Game
There are some POV-Ray images included in the paper that graphically show the game states from which you should roll. For your viewing pleasure, I've included below links to the images in their original 16 mega-pixel detail.