Bi Statistics of the Number of Rounds, and Final Destination, for Reaching a\ n integer with property, "isprime", rolling a fair die with n faces for n from 2 to, 20, starting at , 0 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, "isprime" You are allowed up to, 200, die-rolls The table below tells you the probability of not finishing in <=, 200, rounds\ followed by, conditioned on finishing by that number of rolls, the exp\ ected duration of such a game, followed by the standard-deviation and th\ e scaled moments followed by the analogous displacement of final destination, followed by the\ condional correlation between duration and destination up to the, 4, moment with Fair Dice with number of faces from 2 to, 20 Number of faces=, 2, prob. of not finishing=, 0. [AveDuration,SD,ThirdScaledMoment,Etc]= , [1.500000000, 0.5000000000, 0., 1.000000000] [AveDisplacement,SD,ThirdScaledMoment,Etc]= , [2.250000000, 0.4330127019] conditioned correlation=, 0.5773502692 --------------------- -25 Number of faces=, 3, prob. of not finishing=, 0.1427204082 10 [AveDuration,SD,ThirdScaledMoment,Etc]= , [1.544351140, 1.093203268, 4.239610075, 35.12950774] [AveDisplacement,SD,ThirdScaledMoment,Etc]= , [3.088702281, 2.149114771] conditioned correlation=, 0.8905924612 --------------------- -21 Number of faces=, 4, prob. of not finishing=, 0.1826793606 10 [AveDuration,SD,ThirdScaledMoment,Etc]= , [2.043595185, 1.805274648, 3.716041239, 25.12096317] [AveDisplacement,SD,ThirdScaledMoment,Etc]= , [5.108987968, 5.212677966] conditioned correlation=, 0.9561076179 --------------------- -21 Number of faces=, 5, prob. of not finishing=, 0.3695070799 10 [AveDuration,SD,ThirdScaledMoment,Etc]= , [1.929375346, 1.772482368, 3.712393908, 25.22161529] [AveDisplacement,SD,ThirdScaledMoment,Etc]= , [5.788126038, 5.760117015] conditioned correlation=, 0.9402073206 --------------------- -18 Number of faces=, 6, prob. of not finishing=, 0.2902015204 10 [AveDuration,SD,ThirdScaledMoment,Etc]= , [2.428497913, 2.498555316, 3.390424740, 20.62144846] [AveDisplacement,SD,ThirdScaledMoment,Etc]= , [8.499742696, 9.829707025] conditioned correlation=, 0.9656445377 --------------------- -18 Number of faces=, 7, prob. of not finishing=, 0.2174052499 10 [AveDuration,SD,ThirdScaledMoment,Etc]= , [2.136485647, 2.203692711, 3.784173598, 25.05163660] [AveDisplacement,SD,ThirdScaledMoment,Etc]= , [8.545942591, 9.422182383] conditioned correlation=, 0.9507732524 --------------------- -17 Number of faces=, 8, prob. of not finishing=, 0.1737157760 10 [AveDuration,SD,ThirdScaledMoment,Etc]= , [2.568470349, 2.685612893, 3.211403394, 18.95514035] [AveDisplacement,SD,ThirdScaledMoment,Etc]= , [11.55811658, 13.29876675] conditioned correlation=, 0.9626308541 --------------------- -17 Number of faces=, 9, prob. of not finishing=, 0.2242492602 10 [AveDuration,SD,ThirdScaledMoment,Etc]= , [2.728801365, 2.751672786, 3.061630144, 17.71623451] [AveDisplacement,SD,ThirdScaledMoment,Etc]= , [13.64400686, 15.17298984] conditioned correlation=, 0.9612205640 --------------------- -16 Number of faces=, 10, prob. of not finishing=, 0.1289587401 10 [AveDuration,SD,ThirdScaledMoment,Etc]= , [2.971357553, 3.027345349, 2.985737396, 16.99707995] [AveDisplacement,SD,ThirdScaledMoment,Etc]= , [16.34246655, 18.41139892] conditioned correlation=, 0.9650757134 --------------------- -16 Number of faces=, 11, prob. of not finishing=, 0.1440029947 10 [AveDuration,SD,ThirdScaledMoment,Etc]= , [2.782372226, 2.909435892, 3.113325226, 18.20074545] [AveDisplacement,SD,ThirdScaledMoment,Etc]= , [16.69423339, 18.83434087] conditioned correlation=, 0.9605734979 --------------------- -15 Number of faces=, 12, prob. of not finishing=, 0.1000912942 10 [AveDuration,SD,ThirdScaledMoment,Etc]= , [3.081421878, 3.263023678, 2.989141403, 16.98468858] [AveDisplacement,SD,ThirdScaledMoment,Etc]= , [20.02924218, 23.10414101] conditioned correlation=, 0.9661947857 --------------------- -15 Number of faces=, 13, prob. of not finishing=, 0.1040242759 10 [AveDuration,SD,ThirdScaledMoment,Etc]= , [2.887203293, 3.127753293, 3.127783136, 18.26333085] [AveDisplacement,SD,ThirdScaledMoment,Etc]= , [20.21042308, 23.41064239] conditioned correlation=, 0.9628126016 --------------------- -15 Number of faces=, 14, prob. of not finishing=, 0.2287773839 10 [AveDuration,SD,ThirdScaledMoment,Etc]= , [3.133255552, 3.363733797, 2.976708849, 16.89438002] [AveDisplacement,SD,ThirdScaledMoment,Etc]= , [23.49941662, 27.22898568] conditioned correlation=, 0.9658544044 --------------------- -15 Number of faces=, 15, prob. of not finishing=, 0.1995479173 10 [AveDuration,SD,ThirdScaledMoment,Etc]= , [3.236593616, 3.398415438, 2.919336729, 16.47352591] [AveDisplacement,SD,ThirdScaledMoment,Etc]= , [25.89274892, 29.39178887] conditioned correlation=, 0.9652372364 --------------------- -15 Number of faces=, 16, prob. of not finishing=, 0.4118415444 10 [AveDuration,SD,ThirdScaledMoment,Etc]= , [3.390024914, 3.538938889, 2.873529147, 16.07120028] [AveDisplacement,SD,ThirdScaledMoment,Etc]= , [28.81521174, 32.57195065] conditioned correlation=, 0.9664047038 --------------------- -15 Number of faces=, 17, prob. of not finishing=, 0.4348778897 10 [AveDuration,SD,ThirdScaledMoment,Etc]= , [3.234868318, 3.454579575, 2.963631434, 16.84842592] [AveDisplacement,SD,ThirdScaledMoment,Etc]= , [29.11381484, 33.17634348] conditioned correlation=, 0.9644742656 --------------------- -14 Number of faces=, 18, prob. of not finishing=, 0.1460501302 10 [AveDuration,SD,ThirdScaledMoment,Etc]= , [3.453380765, 3.692810474, 2.893136224, 16.16957111] [AveDisplacement,SD,ThirdScaledMoment,Etc]= , [32.80711734, 37.69413835] conditioned correlation=, 0.9674340887 --------------------- -14 Number of faces=, 19, prob. of not finishing=, 0.1308710622 10 [AveDuration,SD,ThirdScaledMoment,Etc]= , [3.297052898, 3.600050891, 2.983732928, 16.94075770] [AveDisplacement,SD,ThirdScaledMoment,Etc]= , [32.97052898, 38.20066162] conditioned correlation=, 0.9657984481 --------------------- -14 Number of faces=, 20, prob. of not finishing=, 0.2488218393 10 [AveDuration,SD,ThirdScaledMoment,Etc]= , [3.472341126, 3.765131246, 2.905077416, 16.23442790] [AveDisplacement,SD,ThirdScaledMoment,Etc]= , [36.45958189, 42.17940822] conditioned correlation=, 0.9674796082 --------------------- This ends this paper that took, 193.705, seconds to produce.