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, but that’s actually not the case. Every individual die still has a 1 in 3 chance, so even with 6 dice, the probability of a 1 or 5 remains 33.33%.

Dice Left Odds Probability
6 12 in 36 33.33%
5 10 in 30 33.33%
4 8 in 24 33.33%
3 6 in 18 33.33%
2 4 in 12 33.33%
1 2 in 6 33.33%

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 Left Odds Probability
6 1 in 3.24 30.86%
5 1 in 5.2 19.30%
4 1 in 10.8 9.26%
3 1 in 36 2.78%
2 N/A 0.00%
1 N/A 0.00%

Four of a Kind

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

Dice Left Odds Probability
6 1 in 20.87 20.70%
5 1 in 51.8 1.93%
4 1 in 216 0.46%
3 N/A 0.00%
2 N/A 0.00%
1 N/A 0.00%

Five of a Kind

And again for a 5 of a Kind…

Dice Left Odds Probability
6 1 in 259.2 0.386%
5 1 in 1296 0.0772%
4 N/A 0.00%
3 N/A 0.00%
2 N/A 0.00%
1 N/A 0.00%

Six of a Kind

And finally for 6 of a Kind…

Dice Left Odds Probability
6 1 in 7776 0.0129%
5 N/A 0.00%
4 N/A 0.00%
3 N/A 0.00%
2 N/A 0.00%
1 N/A 0.00%

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 Combinations Odds Probability
Straight 1-6 1 in 64.8 1.54%
Three Pairs 1 in 25.9 3.86%
Two Triplets 1 in 155 0.64%
6 of a Kind 1 in 7776 0.0129%

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 Left Odds Probability
6 1 in 43.2 2.31%
5 1 in 13 7.72%
4 1 in 6.4 15.74%
3 1 in 3.6 27.78%
2 1 in 2.3 44.44%
1 2 in 3 66.67%

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 Left Odds Probability
6 1 in 12 8.33%
5 1 in 32 3.125%
4 1 in 25 4.00%
3 1 in 18 5.55%
2 1 in 9 11.11%
1 1 in 3 33.33%

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

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