Farkle is an old dice game popular at parties and in bars. It’s a folk game, so the exact rules and scoring vary from place to place. I was introduced to the game on Facebook, where there is an online flash version. Basically, the game is played in rounds. During each round, you roll up to 6 dice. Certain die combinations are worth points. If you score some points during a roll, then you must take at least some scoring dice away and add those points to your point total for the round. Then you have the option of rolling again or standing pat. If at any time you roll and you don’t score, you “Farkle” and lose all of your points scored so far for the round. If you stand pat, then you can “bank” your points from the current round towards your total points for the game. In the flash version on Facebook, the following die combinations can score:

- Any single 1 or 5
- Three of a kind
- Four of a kind
- Five of a kind
- Six of a kind
- Three pairs
- 1 through 6 straight run

On every successful roll, you should be taking at least one die away. If you happen to score all of your remaining dice during a roll, you can continue the round with all 6 dice again.

So I got to wondering, what are the probabilities of rolling various die combinations in Farkle? How often do you score, and how often do you Farkle? So I made the following tables.

(more…)