## Farkle Odds Probabilities

Wondering what your chances are when rolling dice in Farkle.  Here's a quick look (without all the complicated math) to tell you what the probabilities are for scoring different Farkle combinations when you throw six dice.

Farkle combinations and the chance of getting them
Three of a kind is 1 in 3.240
Four of a kind         is 1 in 20.736
Three pair               is 1 in 25.92
Straight                   is 1 in 64.8
Two triplets            is 1 in 155.52
Five of a kind         is 1 in 259.2
Six of a kind           is 1 in 7776

From the above you can see that, for the most part, less likely Farkle combinations are scored higher than more easy to get combinations.

And now the probabilities of scoring different Farkle combinations after your first throw of the dice.

Dice combination   Five dice left   Four dice left   Three dice left
Three of a kind       1 in 5.184        1 in 10.8          1 in 36
Four of a kind         1 in 51.84        1 in 216
Five of a kind         1 in 1296

When you have a roll with no scoring possibilities, that's a Farkle -- and you lose any points you've accumulated for that turn.  What are your chances of Farkling?

Dice thrown Probability of a Farkle
6                       1 in 42
5                       1 in 13
4                       1 in 6.35
3                       1 in 3.6
2                       1 in 2.25
1                       1 in 1.5

Three-pair is the only scoring possibility that changes the chances of farkling, and only on the first throw of six dice for a turn. If you don't score three pairs, the probability of Farkling on the initial throw increases to 1 in 32.