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1. Andy says:

   November 1, 2012 at 5:11 pm

   Thanks Matt for your interest in Farkle. I love it. But how to use your strategy and a table in real game with other players ? Do you have any idea ?
   Best regards,
   Andy.

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   • matt says:

     November 1, 2012 at 7:09 pm

     Hey Andy,

     What? You can’t memorize a few tables with a few hundred random numbers each? Me neither. Here’s a secret I’ll share just with you — just don’t tell anyone: I never use the strategy tables that sequence the desirability of states. I mainly present the strategies that way because I think it is easier for the average Joe to conceptualize. But if you’re not the average Joe, but instead a vastly superior Andy, you should really use the E(S,N) tables instead. With those tables all you need do is memorize the scoring breakpoints for each column.

     To understand what I mean by that, bring up a separate browser window and run the Farkle Strategy Generator for Facebook Super Farkle Scoring rules and display the E(S,N) table. Place that window next to this comment so you can follow along. What we’re going to do is come up with a simple set of rules that will guide your decisions of whether to roll N dice or just bank all the points you can.

     First, if you have 6 dice to roll, then you always roll unless you have 16,400 or more points. Easy peasy. Now when you have 5 or fewer dice to roll, things are a little more complicated because you may have multiple scoring choices to consider.

     The numbers in the E(S,N) table tell you how many more points you can expect to gain if you (forcibly) roll N dice, but then follow the optimal strategy. Consider the case where you’ve already accumulated 550 points and have just thrown 5 dice. Suppose you threw a 1, a 5 and three other non-scoring dice. One way to play it is to just take the 1 (for a total of 650 turn points) and roll the remaining four dice. Is that the best way to play it? If you look at table position (4, 650) you will see that rolling 4 dice when you have 650 points is worth 55.824 points to your expected score. So the 4 die roll is worth MORE than the 50 points you could get by also taking the 5. You are indeed better off putting that 5 back in the dice pool and re-rolling it.

     That is the key: instead of memorizing a strange sequence of game state desirability, memorize the expected value of rolling N dice for different turn scores. This is far easier because you really only need to memorize the points where the expected values drop BELOW multiples of 50. So for the 4 dice column, you need only memorize these summary rules:

     TURN         4 DICE IS WORTH
     SCORE            LESS THAN
      200                150
      400                100
      700                 50
     1000                  0
     

     So, if you have 1000 or more points with 4 dice to roll, then always bank. If you have between 700 and 950 points, then the value of a 4 dice roll is worth less than 50 points, so you should keep rolling unless you have at least 50 additional optional points you can bank. If you have between 400 and 650 points then keep rolling unless you have at least 100 additional optional points you can bank. If you have between 200 and 350 points then keep rolling unless you have at least 150 additional optional points you can bank.

     Make sense?

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2. Bo says:

   July 14, 2018 at 4:06 am

   Matt,
   This is really great…however, my family and I usually only play with five dice. I’m wondering if there is a way to generate a table for such a game. I will check this out further and see if I can gather the data myself to plug it into a spreadsheet…otherwise, any assistance would be appreciated!

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   • matt says:

     July 31, 2018 at 12:30 am

     You left this comment on my about page, so I’m not sure whether your commenting on my optimal farkle strategy, or max expected score farkle strategy. Todd Neller and I found many different Farkle game variants during our research, but never stumbled upon a version played with 5 dice. Surely it wouldn’t be too hard to modify my software to handle a 5 dice game, but how would you score a 5-die straight? Or is that even worth anything?

     If you sent me the specific rules of the game, and told me exactly what you’re looking for, maybe I could email you some results, but I’m not sure I’d want to permanently modify my software to handle this rarely played version of the game.

     Reply