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HandWiki. Nontransitive Dice. Encyclopedia. Available online: https://encyclopedia.pub/entry/36846 (accessed on 02 October 2026).
HandWiki. Nontransitive Dice. Encyclopedia. Available at: https://encyclopedia.pub/entry/36846. Accessed October 02, 2026.
HandWiki. "Nontransitive Dice" Encyclopedia, https://encyclopedia.pub/entry/36846 (accessed October 02, 2026).
HandWiki. (2022, November 28). Nontransitive Dice. In Encyclopedia. https://encyclopedia.pub/entry/36846
HandWiki. "Nontransitive Dice." Encyclopedia. Web. 28 November, 2022.
Nontransitive Dice
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The content is sourced from: https://handwiki.org/wiki/Nontransitive_dice

A set of dice is nontransitive if it contains three dice, A, B, and C, with the property that A rolls higher than B more than half the time, and B rolls higher than C more than half the time, but it is not true that A rolls higher than C more than half the time. In other words, a set of dice is nontransitive if the binary relation – X rolls a higher number than Y more than half the time – on its elements is not transitive. It is possible to find sets of dice with the even stronger property that, for each die in the set, there is another die that rolls a higher number than it more than half the time. Using such a set of dice, one can invent games which are biased in ways that people unused to nontransitive dice might not expect (see Example).

binary relation dice nontransitive

References

  1. Bill Gates; Janet Lowe (1998-10-14). Bill Gates speaks: insight from the world's greatest entrepreneur. New York: Wiley. ISBN 9780471293538. https://books.google.com/books?id=Qoho6AIXTksC&pg=PA148&dq=Buffet+suggested+that+each+of+them+choose+one+of+the+dice,+then+discard+the+other+two.+They+would+bet+on+who+would+roll+the+highest+number+most+often.+Buffet+offered+to+let+Gates+pick+his+dice+first.+This+suggestion+instantly+aroused+Gates%27s+curiosity.+He+asked+to+examine+the+dice,+after+which+he+demanded+that+Buffet+choose+first. Retrieved 2011-11-29. 
  2. "like-a-marriage-only-more-enduring: Personal Finance News from Yahoo! Finance". Finance.yahoo.com. 2010-12-06. https://finance.yahoo.com/career-work/article/111491/like-a-marriage-only-more-enduring?mod=career-leadership. Retrieved 2011-11-29. 
  3. "Math Games - Tournament Dice by Ed Pegg Jr.". The Mathematical Association of America. 2005-07-11. http://www.mathpuzzle.com/MAA/39-Tournament%20Dice/mathgames_07_11_05.html. Retrieved 2012-07-06. 
  4. Nontransitive Dice ("Grime Dice") http://grime.s3-website-eu-west-1.amazonaws.com/
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