Farkle on Facebook →
I’ve been spending some time on the facebook application “Farkle”. It’s a ridiculously simple dice game, but I’ve found it to be excellent to play while you’re doing something else that demands less than your full attention - watching videos, listening to podcasts, etcetera. It’s also nice to post the highest score among your friends each week, although I don’t have as much raw time as some of my friends and, consequently, less chance for luck to feed me great scores. Despite that, I’ve done some looking at the odds and kept track round-by-round of some of these games. I have found a handful of rules that I now play by, and wanted to share some tips and tricks and odds here.
Rule 1 - Be willing to leave points on the table. Just because there are two fives or you rolled three twos, don’t cash them if you don’t have to. The more dice you leave on the table, the better chance of surviving subsequent rounds and rolling the high-scoring threes of a kind. I see this one violated all the time.
Rule 2 - When you have 4-6 die to roll, it’s about points. When you have 1-3 die to roll, it’s about damage control. All of the higher scoring combinations require three or more die, and your best chance of a farkle is under three die.
Rule 3 - Related to Rule 1, only take three twos if you can’t avoid it, it clears all 6 die, or you are ready to cash out. The points are not worth taking the dice and the potential for higher scores off the table. Also, if you roll six dice and have three threes, don’t take it if you can cash out something else instead. Odds are you’ll make up the 300 points by continuing to roll.
In my sample of 100 rounds of farkle, the highest single round I scored was a 3550. The lowest, naturally, was a farkle, and I scored 39 of those. Following my own rules (which I developed after examining this set) would undoubtedly have reduced those a bunch.
I found some great odds posted at farklefun.com, which is intended more for a non-facebook version of the game. Still, its odds are useful:
Odds of getting AT LEAST one 1 or 5 with one roll of…
- 6 dice: 91% chance you will get a 1 or 5 (so, one in eleven 6 dice rolls will Farkle)
- 5 dice: 87% chance you will get a 1 or 5
- 4 dice: 80% chance you will get a 1 or 5
- 3 dice: 70% chance you will get a 1 or 5
- 2 dice: 55% chance you will get a 1 or 5
- 1 dice: 33% chance you will get a 1 or 5 (so, 2 of 3 one dice rolls will Farkle)
With 6 dice:
- Odds of getting a straight, is 1 in 65 or 1.5 %
- Odds of getting 3 pairs: 9.7 % (or 1 in 10.3 rolls)
- Odds of getting six of one specific value: 1 in 46656. (I.e., odds of getting 111111)
- Odds of getting ANY six of a kind: 1 in 7776 (I.e., 222222 OR 333333 OR 555555,etc)
- Odds of ANY triple: 55%, or more than 1 in 2.
- Odds of SPECIFIC triple (555, for example) is 9.3% or 1 in 11
- Odds of getting 2 triples (333666 or 222555, etc): 1 in 62 or 1.6 %
- Odds of any 4 of kind: 6% or about 6 in 100, or 1 in 17
- Odds of any 5 of a kind: 1 in 216 rolls or 0.5 %
With these stats in mind, I’ve developed a few other rules:
- Always roll six dice. My current tolerance for pain starts making exceptions around 1400. Much beyond that, and I’d prefer to bank than take the chance of farkling with six die. Still, you have less than a 9% chance of farkling. You also have a 1 in 11 chance of a straight, a 1 in 10 chance of three pair, and a 1 of 2 chance of getting three of a kind. It seems that high scores are directly proportional to the number of times you get to roll six dice.
- Always roll five dice unless your score is over 1250. (when you have less than a 13% chance of farkle)
- Always roll four dice unless your score is over 1100. (You have less than a 20% chance of farkling, and a score higher than 80% of my set of rounds.)
After three, it’s damage control:
- Roll three dice with 450 points, but bank points at 500.
- Roll two dice with 400 points, but bank points at 450.
- Roll one dice with less than 400 points. Bank points at 400. The rationale is that you have little to lose and a 1/3 shot to roll six dice again.
Naturally, these strategies should lead you to an average round of around 600, which should score you 6000 in a ten-round game. Luck should make that vary anywhere between 3500 and 8500 without much trouble. If you’re after a much higher score, however, you’re going to have to push these chances harder and be willing to accept more Farkles.
If you have corrections or other thoughts on these strategies, please comment!
Links:
Play Farkle (Not on Facebook)
