Statistics of the Number of Rounds for Reaching an integer with property,

    "n -> IsDP(n,4)", rolling a fair die with n faces for n from 2 to, 20



                              By Shalsoh B. Ekhad



Suppose you start at, 0, and roll a fair die with n faces, with 1 through n d\
    ots, and walk forward according to the number of dots, and stop as soon \

    as you hit an integer with property, "n -> IsDP(n,4)"



You are allowed up to, 1000, die-rolls, but you are interested in the smalles\
    t number of rolls that would guarantee that you would reach your goal wi\

    th prob at least, 0.99999990000000000000



The table below tells you that number of rolls, followed by, conditioned on \
    finishing by that number of rolls, the expected duration of such a game,\
     followed by the standard-deviation and the scaled moments

                                  up to the, 4



               with Fair Dice with number of faces from 2 to, 20



                  Number of faces=, 2, Number of rounds=, 624



[Ave,SD,ThirdScaledMoment,Etc]= , [173.44611263631596757, 51.350517728707594998,

    1.3398955243423236840, 4.2186538557773026407]



                             ---------------------

                  Number of faces=, 3, Number of rounds=, 638



[Ave,SD,ThirdScaledMoment,Etc]= , [149.85491400795571503, 53.049403997986095819,

    1.0934397875123806153, 4.1741193137814633112]



                             ---------------------

                  Number of faces=, 4, Number of rounds=, 609



[Ave,SD,ThirdScaledMoment,Etc]= , [133.66670961677702722, 52.059022147223615201,

    1.0878317693847600104, 4.5056264190850631955]



                             ---------------------

                  Number of faces=, 5, Number of rounds=, 608



[Ave,SD,ThirdScaledMoment,Etc]= , [121.88771125821333200, 50.777206589939717144,

    1.1187245320955820505, 4.7115888817076741319]



                             ---------------------

                  Number of faces=, 6, Number of rounds=, 579



[Ave,SD,ThirdScaledMoment,Etc]= , [112.90787228949423796, 49.543395447373381849,

    1.1461536135579212927, 4.8032835408615819425]



                             ---------------------

                  Number of faces=, 7, Number of rounds=, 556



[Ave,SD,ThirdScaledMoment,Etc]= , [105.80409106684191268, 48.386766558010214618,

    1.1611254404163724123, 4.8078560985938874042]



                             ---------------------

                  Number of faces=, 8, Number of rounds=, 550



[Ave,SD,ThirdScaledMoment,Etc]= , [100.00691026251526135, 47.280040926707922193,

    1.1644236678221864855, 4.7642274567583318397]



                             ---------------------

                  Number of faces=, 9, Number of rounds=, 538



[Ave,SD,ThirdScaledMoment,Etc]= , [95.172779881945286518, 46.240774447221896059,

    1.1613522248344973974, 4.7101779665650859800]



                             ---------------------

                  Number of faces=, 10, Number of rounds=, 534



[Ave,SD,ThirdScaledMoment,Etc]= , [91.055950628791650834, 45.263187853859704274,

    1.1568823873732586877, 4.6691199956136295050]



                             ---------------------

                  Number of faces=, 11, Number of rounds=, 513



[Ave,SD,ThirdScaledMoment,Etc]= , [87.489495972603128865, 44.336696841556624069,

    1.1522358432689959448, 4.6431907807151285250]



                             ---------------------

                  Number of faces=, 12, Number of rounds=, 497



[Ave,SD,ThirdScaledMoment,Etc]= , [84.496288333938407750, 43.733408493694546769,

    1.1637396804650964120, 4.6810194756474047209]



                             ---------------------

                  Number of faces=, 13, Number of rounds=, 483



[Ave,SD,ThirdScaledMoment,Etc]= , [81.746303452458838842, 42.908311199870101755,

    1.1561942056493176387, 4.6596123854455734020]



                             ---------------------

                  Number of faces=, 14, Number of rounds=, 485



[Ave,SD,ThirdScaledMoment,Etc]= , [79.279865802328234522, 42.134294385362043804,

    1.1518000819891542215, 4.6550602987940943511]



                             ---------------------

                  Number of faces=, 15, Number of rounds=, 483



[Ave,SD,ThirdScaledMoment,Etc]= , [77.052197278694186685, 41.415249842109592926,

    1.1515302762913821673, 4.6741927272677880921]



                             ---------------------

                  Number of faces=, 16, Number of rounds=, 478



[Ave,SD,ThirdScaledMoment,Etc]= , [75.023392804928886068, 40.728904218033113397,

    1.1512917175964668879, 4.6906016380475029153]



                             ---------------------

                  Number of faces=, 17, Number of rounds=, 469



[Ave,SD,ThirdScaledMoment,Etc]= , [73.172859468429953940, 40.084803417524054334,

    1.1513065938193952805, 4.7036004634825970561]



                             ---------------------

                  Number of faces=, 18, Number of rounds=, 462



[Ave,SD,ThirdScaledMoment,Etc]= , [71.489239841015476383, 39.500892269420727704,

    1.1531686765604198228, 4.7226281202732090173]



                             ---------------------

                  Number of faces=, 19, Number of rounds=, 454



[Ave,SD,ThirdScaledMoment,Etc]= , [69.941219412797303956, 38.956044608309514053,

    1.1556092468438260942, 4.7422244732747223316]



                             ---------------------

                  Number of faces=, 20, Number of rounds=, 448



[Ave,SD,ThirdScaledMoment,Etc]= , [68.568910465785013343, 38.548680555926583920,

    1.1634553172754001657, 4.7788281168101022482]



                             ---------------------

         This ends this paper that took, 2068.352, seconds to produce.