Go First Dice Wiki

User Tools

Site Tools

Trace: • significant_solutions
significant_solutions

Differences

This shows you the differences between two versions of the page.

Link to this comparison view

Both sides previous revision Previous revision
Next revision 		Previous revision
significant_solutions [2023/09/24 18:41]
carl Added rendering of Paul Meyer's 5d60 set. 		significant_solutions [2026/09/19 05:15] (current)
bmenrigh added 6d30 place-fair solution
Line 22: Line 22:
  
 Discovered by Eric Harshbarger (who used the fewest-sides-known 4-player set and "induced" a 5-player set from it using Paul Vanetti's method). The d72 in this set is //nearly// suitable for a physical die. Discovered by Eric Harshbarger (who used the fewest-sides-known 4-player set and "induced" a 5-player set from it using Paul Vanetti's method). The d72 in this set is //nearly// suitable for a physical die.
 +
 +===6d30 (place-fair)===
 +**''abcdeffdebcafeacdbcebdafdebafccbfdeafcadbeabdfecaecdbfacfdbefbedcabecdfadefabceabcfdafdcbeebcdfadfcbaecbafedafdcebacdebfebdfcafbdceacefdbaebdacfaedfbccfabedfadbecbdcaefacbedffedcba''**
 +
 +Discovered by Brandon Enright in September 2026. This set uses column-grouping and was found by computer search. For column-grouping this solution is, in some sense, optimal. There are no column-grouped 5d30 or 6d30 sets that are permutation fair, or even place-fair for all subsets. Whether a non-column-grouped 5 or 6 30-sided set exist with permutation fairness or all-subset-place-fair is still an open question.
  
 ===5d60 (place-fair)=== ===5d60 (place-fair)===
Line 27: Line 32:
  
 Discovered by James Grime and Brian Pollock (on 29 November 2015). This set of five 60-sided dice is "place fair" but not "permutation fair" (though it is tantalizingly close to exhibiting that stronger fairness). It was constructed using an original technique that Grime and Pollock call "binary construction". Discovered by James Grime and Brian Pollock (on 29 November 2015). This set of five 60-sided dice is "place fair" but not "permutation fair" (though it is tantalizingly close to exhibiting that stronger fairness). It was constructed using an original technique that Grime and Pollock call "binary construction".
 +
 +===5d30 (place-fair)===
 +**''dbeaceacbdcabdedcbeaacdbeebcadedbacabcedacedbbdecacebdadbaecedacbdcaebbadcedecbabcaedacebdeadbccdebabadceaedbcbcaedcbedaedabcaecdbdcbeabdceacadbeeabdc''**
 +
 +Discovered by Brandon Enright (2012). This set of five 30-sided dice is "place fair". This shows that we cannot prove that a set of 5d30 permutation-fair dice is impossible via Go-First-fairness or place-fairness.
 +
  
 ===d20+d36+2d48+d54=== ===d20+d36+2d48+d54===
significant_solutions.1695580913.txt.gz · Last modified: 2023/09/24 18:41 by carl

Page Tools

Donate Powered by PHP Valid HTML5 Valid CSS Driven by DokuWiki