### Optimal Strategy for Farkle Dice

In this post, I will discuss my findings in terms of an optimal strategy for Farkle, which is a dice game of chance. If you are unfamiliar with the game, I encourage you to skim the linked article so that you can better understand this blog post. All of my findings are based on sound mathematical methods and a computer program was used to determine the optimal strategy. Before I begin, let me first state the value of different dice rolls I assumed while developing the strategy.

Each 1: 100 points

Each 5: 50 points

3 1's: 1000 points

3 2's: 200 points

...

3 6's: 600 points

4 1's: 2000 points

...

4 6's 1200 points

5 1's 3000 points

...

5 6's 1800 points

Straight 1-6 1500 points

3 Pairs (e.g., 22 33 44): 750 points

Everything else is considered to be a Farkle (0 points).

There are many variants to Farkle, but I like to play by this set of rules.

The "game state" of Farkle roll can roughly be characterized by 2 values: the current score accumulate…

Each 1: 100 points

Each 5: 50 points

3 1's: 1000 points

3 2's: 200 points

...

3 6's: 600 points

4 1's: 2000 points

...

4 6's 1200 points

5 1's 3000 points

...

5 6's 1800 points

Straight 1-6 1500 points

3 Pairs (e.g., 22 33 44): 750 points

Everything else is considered to be a Farkle (0 points).

There are many variants to Farkle, but I like to play by this set of rules.

The "game state" of Farkle roll can roughly be characterized by 2 values: the current score accumulate…