16 Apr

Winner’s Edge: Farkle Dice Odds

Gain a competitive edge knowing the odds in Farkle.

Winner's Edge: Farkle Dice Odds

Knowing how to play a game gives you a chance to win it. But a chance is only a chance. Knowing the odds of a game – the probabilities of achieving the best result, the best score, the best toss of the dice, as the case may be – that’s how you gain an edge over the competition.

Farkle is one of the most strategy-based dice games you’ll come across; far more intricate than Yahtzee or Qwixx. We’ve already discussed a basic strategy guide for Farkle. Today, we’ll delve deeper into the scientific realm of the game, where mathematical probabilities rein supreme over the Farkle universe!

Farkle Math & Probabilities

This introduction to 6-dice odds assumes that you are familiar with official Farkle rules and scoring methods. If not, please press that link for a brief tutorial.

As you know, scoring points requires specific numbers and/or combinations of numbers to be rolled in a single toss of the dice. Any 1 or 5 is worth points. Any 3, 4, 5 or 6 of a Kind scores, as does three Pairs, two 3 of a Kinds, a Pair + 4 of a Kind, or a 1-6 Straight. Below, we’ll discuss the probabilities of each of these combinations resulting from 1 or more rolls of the dice.

One or Five

The most basic form of scoring is to roll a 1 or 5, worth 100 or 50 points respectively. Since there are 6 possible numbers on the dice, and 2 numbers worth rolling, the odds of any single die landing on 1 or 5 is 1 in 3, or 33.33%. We tend to imagine that, with 6 dice to roll, the odds of rolling a 1 or 5 will increase dramatically, and that’s precisely the case. Unlike a coin toss, where every flip has an equal 50/50 chance, the more 6-sided dice you toss, the better your odds of rolling specific numbers – in this case, a 1 or 5.

A big “Thank you!” to D. Anderson for catching and alerting us to an error in our math.

Dice LeftPossibilitiesOdds (appx)Probability
642,560 of 46,65610 in 1191.22%
56,752 of 7,77620 in 2386.83%
41,040 of 1,2964 in 580.25%
3152 of 2167 in 1070.37%
220 of 365 in 955.56%
12 of 62 in 633.33%

Three of a Kind

The score for each set of dice may vary, but the odds of rolling them do not. The chart below depicts the odds of rolling any 3 of a kind.

Dice LeftPossibilitiesOddsProbability
618,000 of 46,6561 in 2.638.46%
51,500 of 7,7761 in 5.219.30%
4126 of 1,2961 in 7.213.88%
36 of 2161 in 362.78%

Four of a Kind

Similarly, the odds of rolling any 4 of a Kind are as follows:

Dice LeftPossibilitiesOddsProbability
62,250 of 46,6561 in 20.874.82%
5375 of 7,7761 in 521.93%
460 of 1,2961 in 21.64.63%

Five of a Kind

And again for a 5 of a Kind…

Dice LeftPossibilitiesOddsProbability
6180 of 46,6561 in 259.20.386%
56 in 7,7761 in 12960.0772%

Six of a Kind

And finally for 6 of a Kind…

Dice LeftPossibilitiesOddsProbability
66 in 77761 in 77760.0129%

6-Dice Single Roll Scorers

This section deals with scoring opportunities that can only be thrown in one roll of the dice (i.e. it takes all 6 dice to score). I’m aware that the 6 of a Kind falls into this description, but it seemed better positioned among its ‘# of a Kind‘ cousins above. I’ll toss it in here again for reference.

6-Dice CombinationsPossibilitiesOddsProbability
Straight 1-6720 of 46,6561 in 64.81.54%
Three Pairs1800 of 46,6561 in 25.93.86%
Two Triplets300 of 46,6561 in 1550.64%
6 of a Kind6 of 46,6561 in 77760.0129%

Odds of Farkling

While the odds of banking score per roll are important, most serious players agree it’s more critical to understand how likely you are to Farkle with each consecutive roll of the dice. Regardless of how many points you’ve achieved thus far in the roll, or how many dice you have left to toss, knowing the probability of Farkling should always be a major part of your decision strategy.

Dice LeftPossibilitiesOddsProbability
61,080 of 46,6561 in 43.22.31%
5600 of 7,7761 in 137.72%
4204 of 1,2961 in 6.415.74%
360 of 2161 in 3.627.78%
216 of 361 in 2.344.44%
14 of 62 in 366.67%

Odds of Hot Dice

Last but not least, here are the odds of making Hot Dice (scoring with all 6 dice, worthy of another 6-dice throw). It’s more likely than you may think, and the less dice you have to throw, the higher your odds of success become. It’s not so advantageous as to impose a positive expectation (1 in 3, or 33.33% at best), but it can be comforting in the final round of play when you’re behind in the count.

Dice LeftPossibilitiesOddsProbability
63,888 of 46,6561 in 128.33%
5243 of 7,7761 in 323.125%
452 of 1,2961 in 254.00%
312 of 2161 in 185.55%
212 of 361 in 911.11%
12 of 61 in 333.33%

Interested in learning more about the dice game Farkle? Check out the links below:

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