Farkle
Push your luck with six dice. Rolling one die farkles exactly two thirds of the time; rolling six, just 2.3% — a factor of nearly thirty.
Your odds of farkling, exactly
Computed by enumerating all six to the power n rolls, not sampled.
One die is two-in-three to lose everything
The whole game is a single decision — roll again or bank — and it has an exact answer. Only 1s and 5s score on a single die, so four of the six faces give nothing: rolling one die farkles exactly two thirds of the time, and everything you have accumulated this turn goes with it. Six dice, by contrast, farkle just 2.3 per cent of the time, which is nearly free.
That is a factor of nearly thirty between the safest and the most dangerous roll, and it is why every rule of thumb about Farkle is really a rule about how many dice remain rather than how many points are at stake. The table above is enumerated rather than estimated — all six to the power n possible rolls, counted — so it is the actual probability rather than a simulation of it.
How to use
- Roll six dice; scoring dice are set aside automatically.
- Roll the remainder to add more, or bank what you have.
- A roll that scores nothing is a farkle and loses the turn.
- Score all six and you get all six back — hot dice.
Frequently asked questions
What is a farkle?
A roll that scores nothing at all, which ends your turn and loses every point you had accumulated but not banked. It is the entire tension of the game — each extra roll adds points and risks all of them, and the decision of when to stop is the only real decision Farkle asks of you.
What are the chances of farkling?
It depends only on how many dice you are rolling, and the figures are exact rather than estimated: six dice farkle 2.31 per cent of the time, five 7.72, four 15.74, three 27.78, two 44.44 and one die a full 66.67 per cent. Rolling one die is nearly thirty times more dangerous than rolling six.
Why does one die farkle two thirds of the time?
Because only 1s and 5s score on a single die, so four of the six faces give nothing at all. It falls straight out of the scoring rules rather than needing any calculation, and it is the single most useful number to carry in your head — one die is almost always a bad roll.
How does scoring work?
Each 1 is 100 and each 5 is 50. Three of a kind scores a hundred times the face value, except three ones which score 1,000, and four, five or six of a kind double, treble and quadruple that. A straight of one to six is 1,500, and three pairs is also 1,500.
What are hot dice?
When every one of your six dice has scored, you pick all six up and roll again with your accumulated points intact. It is the main way large turns happen, and it changes the risk calculation completely — a turn that reaches hot dice goes from rolling one or two dice back to rolling six.
When should I stop rolling?
Roughly when the chance of farkling times what you would lose exceeds what you expect to gain. With six or five dice that almost never happens, so rolling is nearly always right. With two dice and several hundred points at risk it flips, and with one die it is essentially always wrong to roll.
Is it better to set aside fewer dice?
Often, yes, and this is the subtlety beginners miss. Setting aside a single 5 for 50 points leaves you rolling more dice, which is far safer than banking every scoring die and rolling two. Fifty points is cheap compared with the difference between a 15 per cent and a 44 per cent chance of losing everything.
What score do you need to start?
Most house rules require 500 points in a single turn before you may bank anything at all, which forces early risk-taking and is where a lot of turns are lost. Some versions use 350 or 1,000, and some drop the rule entirely — worth agreeing before you start.
What is the target score?
Ten thousand in the most common rules, though 5,000 makes for a much shorter game. Many versions also give everyone one final turn once a player crosses the line, which changes the endgame considerably because the trailing players must push far harder than the leader did.
Is Farkle the same as Zilch or Ten Thousand?
Essentially, yes. Zilch, Ten Thousand, Greed and Hot Dice are all names for the same push-your-luck dice game, with local variation in the scoring combinations and the opening threshold. The core mechanic of banking against the risk of losing everything is identical.
Are the odds here simulated or exact?
Exact. The probabilities are computed by enumerating every possible roll — all six to the power n outcomes for n dice — and counting how many score nothing. That is a complete calculation rather than a simulation, so the figures are the true probabilities rather than an approximation of them.
Does the game save my progress?
No. Everything runs in your browser, nothing is stored or uploaded, and closing the tab loses the current score.
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