In the following, I’m going to use the notation (n m) to stand for “the number of combinations of n objects taken m at a time”. The difficulty in probability is not really in the math, it is in paying attention to how you count things (and making sure you don’t count them twice!) The following table shows the number of possibilities for rolling up to 6 dice. Calculating probability is all about counting some things that can happen and dividing by everything that can happen. But if mathematics makes you run screaming for the door, you’d best turn back now!īut seriously, this stuff isn’t too bad.
#Rules for farkle with 6 dice how to#
In the following section, I will show how to calculate the above Farkle probabilities. Number of DiceĬalculation Details: Probability for Everyone! Number of DiceĪnd the following table shows the simulation results corresponding to the the above table, out of 10 million throws. Comboįinally, below is a table which shows the probabilities and odds for getting “N of a Kind” for various numbers of dice being rolled. I’m also considering the case of double trips – while it does not lead to a special score in the Facebook variation (it is scored just like two “3 of a Kind” throws), it has special value because it clears all the dice. Probabilities, odds and simulation results for these cases appear in the next table. There are also some special die combinations that you can only get with six dice: the 1 through 6 straight and the triple pairs. But of course we knew that already! More interesting to me is that it is almost 1 in 2 to Farkle on two dice, and almost 1 in 3 to Farkle on three dice! So the probability of Farkling is pretty low when you’re rolling 6 dice, and it is pretty high (2 in 3) with only one die. Counting die combinations can be tricky, and so I wrote a small Farkle simulation that would run through 10 million rolls of 6 dice and count the Farkles. For each number, a calculated probability is shown with odds. The most important question you should be asking yourself on every throw is, “what are the chances that I’m going to Farkle on this throw?” So we’ll start with a table that shows the odds of Farkling versus various numbers of remaining dice. So I got to wondering, what are the probabilities of rolling various die combinations in Farkle? How often do you score, and how often do you Farkle? So I made the following tables.
If you happen to score all of your remaining dice during a roll, you can continue the round with all 6 dice again. On every successful roll, you should be taking at least one die away.
In the flash version on Facebook, the following die combinations can score:
If you stand pat, then you can “bank” your points from the current round towards your total points for the game. If at any time you roll and you don’t score, you “Farkle” and lose all of your points scored so far for the round. Then you have the option of rolling again or standing pat. If you score some points during a roll, then you must take at least some scoring dice away and add those points to your point total for the round. Certain die combinations are worth points. During each round, you roll up to 6 dice. I was introduced to the game on Facebook, where there is an online flash version. It’s a folk game, so the exact rules and scoring vary from place to place. Farkle is an old dice game popular at parties and in bars.
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