I just wanted to create a chart that people could look at in order to decide whether to roll or not. I was about to give up, it was clear that I didn't know enough probability to solve this question. If this game had less amount of possibilities I probably would be able to calculate it with pen and paper but there were just too many possibilities. I had to know the expected value of 6 in order to calculate the expected value of 1 and in order the calculate the expected value of 6 I had to know the expected value of 1! The game had the potential to take an almost infinitely long time. The amount of remaining dice changed so I couldn't just multiply everything with a non-bust probability. I started to see everything difficult about calculating the expected value. But the framework was ready, all I had to do was to just calculate the true expected values, right? Okay maybe this is difficult. Your 1 die throw's expected value has to be higher than 25 since if you roll a 5 or 1, you'll get back your 6 dice (and with those 6 dice the expected value is at least 487.). Here are the results:Ĭan you see where I went wrong? When I looked at this graph, I felt confused. Basically a function took the average of all possible points for an $n$ dice throw. So I wrote a small program which calculated it for me. It was impossible for me to calculate the expected value given a dice throw by hand since there were so many possibilities. If you want more more information on the expected value click here or here. four or more of a kind: Double the points of three of a kind three of a kind: 100 points multiplied by the given number I decided to use the rules from the game Kingdom Come Deliverance. Since farkle is an old game the scoring varies a lot. So it is smart to bank your points when you have too few dice left. Certain dice have scoring value so you can put them aside and throw the rest of the dice again in hopes of scoring more points but if you don't get any scoring dice, you bust, i.e.
You start with 6 dice and you throw them. The aim is to reach 4000 points and the gameplay is kinda similar to dice blackjack.
Farkle is a simple dice game in the video game Kingdom Come Deliverance.