Farkle odds and when to bank
How likely you are to farkle with each number of dice, what a scoring throw is worth, and the turn total at which you should bank. Every figure here is exact, worked out by the same engine Grimsby plays with in Farkle & Sons.
| Dice | Farkle chance | 1 throw in | Average score | Bank at |
|---|---|---|---|---|
| 1 | 66.67% | 2 | 75 | 350 |
| 2 | 44.44% | 2 | 90 | 250 |
| 3 | 27.78% | 4 | 120 | 450 |
| 4 | 15.74% | 6 | 170 | 1,050 |
| 5 | 7.72% | 13 | 244 | 3,100 |
| 6 | 2.31% | 43 | 428 | 18,100 |
Average score is what a scoring throw is worth when you take every scoring die, counted over the throws that score. Bank at is the turn total, counting the points set aside so far this turn, from which banking beats throwing those dice again.
When to bank
- Six dice: throw. You farkle about one throw in 43, and best play does not bank six dice until the turn reaches 18,100.
- Five dice: throw until the turn reaches 3,100. A farkle comes about one throw in 13.
- Three dice: bank from 450. More than a quarter of three-dice throws farkle.
- Two dice: bank from 250. Nearly half of two-dice throws farkle.
- One die: throw below 350. You farkle two times in three, but a 1 or a 5 is hot dice and hands you all six back, so one die is worth throwing at totals where two dice should bank.
Played this way, an average turn from six dice is worth about 590 points.
Keep fewer dice early
Taking every scoring die is often a mistake. Say your first throw of six shows a 1, a 5 and nothing else that scores. Keep both and throw four dice, and the rest of your turn is worth about 310 points on average. Keep the 1 alone and throw five, and it is worth about 403. The extra die is worth far more than the 50 points you leave behind.
These figures use the scores on our scoring chart, hot dice that hand all six back, and a player after the most points from one turn. They do not know the score of the game: when a rival is close to winning, throwing on is right more often. Grimsby weighs his chance of winning the round rather than points alone, so he plays close to these figures but not exactly to them.
Do straights and three pairs change the odds?
Three pairs does, on a throw of six dice only. Counting it, six dice farkle 2.31% of the time, about one throw in 43. Without it they farkle 3.09%, about one in 32. A straight never changes the odds, because every straight holds a 1 and a 5, which score anyway.