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Optimal Play of the Farkle Dice Game

  • Matthew Busche
  • Todd W. NellerEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10664)

Abstract

We present and solve optimality equations for the 2-player, jeopardy dice game Farkle (a.k.a. Dix Mille, Ten Thousand). For fairest play, we recommend 200 compensation points at the beginning of the game for the second player. We then compute the strategy that maximizes expected score, demonstrate a means for replicating such play with mental mathematics, and augment this method so as to enable human Farkle play against which complex optimal play maintains only a small win advantage of \({\sim }1.7754\%\).

References

  1. 1.
    Knizia, R.: Dice Games Properly Explained. Elliot Right-Way Books, Tadworth (1999)Google Scholar
  2. 2.
    Jacobs, G.: The World’s Best Dice Games. John N. Hanson Co., Inc., Millbrae (1993)Google Scholar
  3. 3.
    Vanhegan, G.: Zilch (2008). http://zilch.playr.co.uk/. Accessed 11 Mar 2017
  4. 4.
    Neller, T.W., Presser, C.G.: Optimal play of the dice game pig. UMAP J. 25, 25–47 (2004)Google Scholar
  5. 5.
    Neller, T.W., Presser, C.G.: Pigtail: a pig addendum. UMAP J. 26, 443–458 (2005)Google Scholar
  6. 6.
    Mohr, M.S.: The New Games Treasury. Houghton Mifflin, New York (1997)Google Scholar
  7. 7.
  8. 8.
    Patch Products: Farkle Rules (2007). http://www.boardgamecapital.com/game_rules/farkle.pdf. Accessed 11 Mar 2017
  9. 9.
    Arnold, P. (ed.): The Book of Games. Exeter Books, New York (1985)Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.LakewoodUSA
  2. 2.Department of Computer ScienceGettysburg CollegeGettysburgUSA

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