![]() ![]() I believe it is better to roll 1 die because of the reward of the expected value of re-rolling 6 dice.Īlright, anybody who has read this far deserves some results. I believe that it is more risk averse to roll with 2 dice remaining than it is with 1 die. I stopped after the third iteration of a re-roll because this they begin to become insignificant near this point.Īlso, I included scoring values identical to that of the Farkle game included on Facebook.īefore the results, I will present my hypothesis. Thus, I added the Expected value of a 6 die roll dependent upon the condition that the player gets one.Īs for the above assumption, it is completely possible (not likely) to continue re-rolling forever. In my calculations I assumed that the player would (or perhaps is forced to) always re-roll 6 dice. I sought to find the expected value of any given roll, compare this to the risk associated with any given roll to come up with a risk:reward ratio.Īfter finding the raw expected value of a given roll, I also factored in the chance that it may clear the board and give the player another roll of 6 dice. However, I do feel very confident that my results are at the very least close. ![]() I’m not guaranteeing that I haven’t made a mistake along the way, I’m almost sure that I’ve missed something. It got a little tricky when it came to scoring three pairs, but I managed to do this as well. I enumerated every single roll combination and wrote a function to calculate the scores. Rules for farkle simulator#I've done a bit of work in excel to come up with some expected values of farkle, but haven't written a simulator (yet). Rules for farkle free#Since it is a folk game, players are free to agree upon whatever scores they choose for whatever combinations they choose to recognize. These are the variations listed in the above-cited descriptions of farkle scoring, but further variations presumably exist. Like the standard combinations, any of these variant combinations must be achieved in a single throw. In addition, some players score one or more combinations of dice beyond the standard ones. ![]() For example, the commercially marketed game of Pocket Farkel differs in that three 1's are scored as 300 rather than 1000. ![]() While the standard rules described above are widely used, even they are not universal. Since farkle is a folk game, variant rules are used in different playing communities. Rules for farkle series#I've tried a few times to make a massive series of if/then statements or lookups, but it is making my head hurt. Based upon a certain strategy (no 5's, only 1's, straights etc.), is it possible to use Excel to analyze my strategy to see if it makes sense or not. I wonder a lot of things, but this pretty simple dice game has got me thinking. ![]()
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