-------------------------------- 1000000 dice total 2584963 bits of entropy (theoretical) 323120 bytes of entropy (theoretical) 344896 bytes compressed bzip2 -9 369446 bytes compressed gzip -9 1000000 bytes raw (ascii encoded as digits) -------------------------------- Statistics: 1 2 3 4 5 6 166698 166886 166141 166183 167445 166647 0.16670 0.16689 0.16614 0.16618 0.16745 0.16665 --------------- average: 3.5007320 (vs 3.5000000 theoretical) variance: 2.9187315 (vs 2.9166666 theoretical) Pair statistics: 1 2 3 4 5 6 1 13868 13923 13667 13998 14097 13769 2 13872 13823 14078 13754 13952 13793 3 13981 14216 13853 13763 13726 13687 4 13849 13910 13470 13891 13918 13801 5 13987 13809 13856 14045 14025 14032 6 13820 13933 13991 13893 13972 13978 1 2 3 4 5 6 1 0.0277 0.0278 0.0273 0.0280 0.0282 0.0275 2 0.0277 0.0276 0.0282 0.0275 0.0279 0.0276 3 0.0280 0.0284 0.0277 0.0275 0.0275 0.0274 4 0.0277 0.0278 0.0269 0.0278 0.0278 0.0276 5 0.0280 0.0276 0.0277 0.0281 0.0280 0.0281 6 0.0276 0.0279 0.0280 0.0278 0.0279 0.0280 average sum: 7.0014560 (vs 7.0000000 theoretical) variance sum: 5.8471419 (vs 5.8333333 theoretical) ---------------------------- Runs by length: 1 2 3 4 5 6 ---- ----- ---- 115788 116297 115747 115264 116019 115533 19335 19216 19049 19434 19554 19291 3147 3188 3148 3103 3137 3242 577 533 557 550 577 568 81 72 102 86 99 86 13 12 15 14 15 16 0 3 1 4 2 0 1 1 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 ---------------------------- Random walks: estimates for pi below are deduced from average distance 10000 walks (per dimension) of length 100: average square of distance 1D walk: 102.079200 (vs 100.000000 theoretical) average square of distance 3D walk: 100.948400 (vs 100.000000 theoretical) estimate for pi from 1D walks: 3.090599 estimate for pi from 3D walks: 3.113787 2000 walks (per dimension) of length 500: average square of distance 1D walk: 507.560000 (vs 500.000000 theoretical) average square of distance 3D walk: 498.587000 (vs 500.000000 theoretical) estimate for pi from 1D walks: 3.125190 estimate for pi from 3D walks: 3.165278 1000 walks (per dimension) of length 1000: average square of distance 1D walk: 1009.584000 (vs 1000.000000 theoretical) average square of distance 3D walk: 999.588000 (vs 1000.000000 theoretical) estimate for pi from 1D walks: 3.106852 estimate for pi from 3D walks: 3.180356 500 walks (per dimension) of length 2000: average square of distance 1D walk: 1932.112000 (vs 2000.000000 theoretical) average square of distance 3D walk: 1980.384000 (vs 2000.000000 theoretical) estimate for pi from 1D walks: 3.178986 estimate for pi from 3D walks: 3.165788 total average estimate for pi: 3.140855 -------------------------------- coprimality of n digit (base 6) random numbers: n = 5 digits: 60789 of 100000 are coprime pairs estimate for pi: 3.14169 n = 50 digits: 6063 of 10000 are coprime pairs estimate for pi: 3.14581 n = 500 digits: 616 of 1000 are coprime pairs estimate for pi: 3.12094 n = 5000 digits: 61 of 100 are coprime pairs estimate for pi: 3.13625