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June 30, 2014 01:42
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| #Iterations Mean Other Winners | |
| 10000 0 | |
| 20000 0 | |
| 24652 4.056301464324829 0 | |
| 30000 3.3332222259258026 | |
| 40000 2.499937501562461 | |
| 50000 1.999960000799984 | |
| 60000 1.6666388893518442 | |
| 63998 3.125048828887951 0 | |
| 70000 2.8571020413994086 | |
| 80000 2.4999687503906203 | |
| 90000 2.222197531138543 | |
| 100000 1.999980000199998 | |
| 110000 1.81816528940646 | |
| 118018 2.54196358213508 0 | |
| 120000 2.4999791668402764 | |
| 123003 3.2519267666092158 0 | |
| 123587 4.045700229795773 0 | |
| 126098 4.758166202745462 0 | |
| 130000 4.615349112699133 | |
| 135185 5.178050981610522 0 | |
| 140000 4.999964285969386 | |
| 150000 4.666635555762961 | |
| 160000 4.374972656420898 | |
| 170000 4.11762283751272 | |
| 174264 4.590709551545061 0 | |
| 177898 4.684305888921991 2 | |
| 180000 4.62960390960791 | |
| 190000 4.3859418283763425 | |
| 200000 4.166645833437499 | |
| 210000 3.9682350718964834 | |
| 220000 3.7878615703261955 | |
| 230000 3.623172652872524 | |
| 240000 3.472207754689911 | |
| 250000 3.3333200000533334 | |
| 260000 3.205115877759445 | |
| 270000 3.0864083219444867 | |
| 280000 2.9761798469767373 | |
| 281267 3.3183061469251154 0 | |
| 290000 3.2183797067366435 | |
| 300000 3.1111007407753086 | |
| 306848 3.367562981575085 0 | |
| 310000 3.333322580679847 | |
| 320000 3.229156575552368 | |
| 321273 3.527622320303957 0 | |
| 330000 3.4343330272736554 | |
| 338105 3.647771211789597 0 | |
| 340000 3.627440311450065 | |
| 350000 3.523799455811079 | |
| 351845 3.789536710189496 0 | |
| 360000 3.7036934156664385 | |
| 370000 3.603593864160728 | |
| 380000 3.508762696238519 | |
| 390000 3.418794652663284 | |
| 400000 3.333325000020834 | |
| 408144 3.389318338662322 1 | |
| 410000 3.3739755106288363 | |
| 420000 3.293642951643766 | |
| 429235 3.4557523910700256 0 | |
| 430000 3.4496043807650065 | |
| 440000 3.371204459383805 | |
| 441793 3.583872423195728 0 | |
| 450000 3.5185106996058533 | |
| 460000 3.4420215028518055 | |
| 470000 3.3687871586088827 | |
| 480000 3.298604239018947 | |
| 490000 3.2312859225457364 | |
| 500000 3.1666603333460004 | |
| 510000 3.104569076008348 | |
| 520000 3.044865939360373 | |
| 530000 2.987415747014314 | |
| 539360 3.120977106860402 0 | |
| 540000 3.1172781778799177 | |
| 550000 3.0606004958778867 | |
| 560000 3.0059470131898576 | |
| 570000 2.9532111931967373 | |
| 580000 2.902293846619805 | |
| 588402 3.0308025848497264 0 | |
| 590000 3.022593747016248 | |
| 593307 3.1742928349749766 0 | |
| 597848 3.317448608818169 0 | |
| 600000 3.3055500463054788 | |
| 610000 3.2513607901189236 | |
| 620000 3.1989195716350998 | |
| 630000 3.148143151095528 | |
| 640000 3.0989534912185035 | |
| 650000 3.0512773570091944 | |
| 660000 3.005045951950578 | |
| 670000 2.9601945867742487 | |
| 680000 2.916662377457288 | |
| 683928 2.973018154418563 1 | |
| 685083 3.113973371635206 0 | |
| 690000 3.091782958768659 | |
| 700000 3.0476146938837707 | |
| 705758 3.164441875106564 0 | |
| 710000 3.1455354757716307 | |
| 717586 3.2516382450258066 0 | |
| 720000 3.240736239718186 | |
| 730000 3.1963426534118904 | |
| 733732 3.316374394137014 0 | |
| 737306 3.4359274133208197 0 | |
| 740000 3.4234187971818058 | |
| 750000 3.377773274080079 | |
| 758808 3.4044579509907416 1 | |
| 760000 3.3991183344934197 | |
| 770000 3.354973997869267 | |
| 780000 3.3119615658612407 | |
| 790000 3.27003805480415 | |
| 800000 3.229162630213379 | |
| 810000 3.1892964741195793 | |
| 820000 3.150402662110575 | |
| 824645 3.253921480651496 0 | |
| 830000 3.2329278318138575 | |
| 840000 3.194440641538919 | |
| 850000 3.156859031146238 | |
| 860000 3.1201514106766544 | |
| 870000 3.0842876425812538 | |
| 880000 3.049238959198153 | |
| 890000 3.014977885792638 | |
| 900000 2.981478168727961 | |
| 906442 3.0706104336768374 0 | |
| 910000 3.0586046975039958 | |
| 920000 3.025359030406851 | |
| 930000 2.992828323123667 | |
| 940000 2.9609897578123148 | |
| 950000 2.929821477380901 | |
| 960000 2.899302535448748 | |
| 970000 2.869412849402561 | |
| 974844 2.9577351613162435 0 | |
| 978334 3.049398552983726 0 | |
| 979528 3.14777136086153 0 | |
| 980000 3.146255292936776 | |
| 987978 3.222065786148626 0 | |
| 990000 3.215484967523602 | |
| 1000000 3.1833301500031834 | |
| 1010000 3.151812060912151 | |
| 1020000 3.120911972962118 | |
| 1030000 3.0906118861373275 | |
| 1040000 3.0608944927296546 | |
| 1050000 3.0317431443716085 | |
| 1058561 3.10169204386076 0 | |
| 1060000 3.0974813545773388 | |
| 1070000 3.0685329577573603 | |
| 1074244 3.149498795277924 0 | |
| 1080000 3.1327131487223934 | |
| 1090000 3.103972687486831 | |
| 1100000 3.075754779616867 | |
| 1108977 3.1410301496813586 0 | |
| 1110000 3.1381353109892096 | |
| 1114065 3.2164461830208744 0 | |
| 1120000 3.199401905295918 | |
| 1130000 3.171088639154597 | |
| 1140000 3.1432720965449445 | |
| 1150000 3.1159393194730556 | |
| 1153364 3.150202523341122 1 | |
| 1160000 3.1321812078897633 | |
| 1170000 3.1054104512161387 | |
| 1180000 3.0790934357965236 | |
| 1190000 3.0532187227853873 | |
| 1199234 3.113095709625998 0 | |
| 1200000 3.111108518520679 | |
| 1209596 3.1690995706283442 0 | |
| 1210000 3.1680414589189048 | |
| 1220000 3.1420739272618086 | |
| 1230000 3.116528631548538 | |
| 1239151 3.174213763390878 0 | |
| 1240000 3.172040452655549 | |
| 1250000 3.146664149335347 | |
| 1256335 3.210393822459385 0 | |
| 1260000 3.2010556605378357 | |
| 1270000 3.1758505177030045 | |
| 1273369 3.2459798278060057 0 | |
| 1280000 3.2291641438821794 | |
| 1284378 3.257086368846994 1 | |
| 1288862 3.284548732746098 1 | |
| 1290000 3.2816512028543654 | |
| 1300000 3.256407751481217 | |
| 1310000 3.2315496960180443 | |
| 1313448 3.2992018215654615 0 | |
| 1320000 3.282825795839044 | |
| 1330000 3.2581429136770077 | |
| 1340000 3.2338284324663444 | |
| 1350000 3.20987416552531 | |
| 1360000 3.1862721669567406 | |
| 1370000 3.1630147228603 | |
| 1374817 3.224669253190847 0 | |
| 1380000 3.2125580585328084 | |
| 1390000 3.18944614668143 | |
| 1396707 3.2457273340836696 0 | |
| 1400000 3.2380929251717205 | |
| 1410000 3.21512774340822 | |
| 1420000 3.1924860146812106 | |
| 1430000 3.170160953267399 | |
| 1440000 3.148145961935675 | |
| 1450000 3.126434625447385 | |
| 1460000 3.105020704323719 | |
| 1466831 3.1246477669789954 1 | |
| 1470000 3.117911711171172 | |
| 1480000 3.0968447543841755 | |
| 1490000 3.0760605753508448 | |
| 1496019 3.1305285579961057 0 | |
| 1500000 3.1222201407421286 | |
| 1502078 3.1844752062530226 0 | |
| 1510000 3.1677683215662333 | |
| 1514742 3.223869219618994 0 | |
| 1520000 3.2127171846158875 | |
| 1530000 3.191719046806724 | |
| 1540000 3.1709936119089104 | |
| 1550000 3.1505356018049886 | |
| 1556412 3.2018065470625947 0 | |
| 1560000 3.1944423967249596 | |
| 1570000 3.174095642826555 | |
| 1580000 3.1540064426119567 | |
| 1580281 3.185085531147817 1 | |
| 1590000 3.16561645768357 | |
| 1600000 3.145831367188729 | |
| 1610000 3.126292054062907 | |
| 1620000 3.1069939668761526 | |
| 1630000 3.0879326658899804 | |
| 1636565 3.1366491380936266 0 | |
| 1640000 3.1300793922280135 | |
| 1650000 3.1111092255903685 | |
| 1660000 3.09236761503959 | |
| 1667004 3.139362709369998 0 | |
| 1670000 3.133730658444716 | |
| 1673335 3.157365486270142 1 | |
| 1680000 3.1448393979130573 | |
| 1687726 3.1896943838270846 0 | |
| 1690000 3.18540245439697 | |
| 1700000 3.166664803922665 | |
| 1710000 3.1481463071269165 | |
| 1720000 3.1298431415640655 | |
| 1730000 3.111751573168648 | |
| 1740000 3.0938679537157356 | |
| 1744819 3.1426355345154997 0 | |
| 1750000 3.1333315428581665 | |
| 1760000 3.115528532843637 | |
| 1770000 3.097926686670422 | |
| 1772679 3.1496566404163944 0 | |
| 1780000 3.136702357657852 | |
| 1780876 3.1913115466892625 0 | |
| 1790000 3.1750447811667892 | |
| 1800000 3.157405653293156 | |
| 1810000 3.1399614328021554 | |
| 1815438 3.185639029090668 0 | |
| 1820000 3.1776539316919794 | |
| 1820134 3.232360969561782 0 | |
| 1820697 3.286285442908892 0 | |
| 1830000 3.269579269810964 | |
| 1830786 3.322796880977052 0 | |
| 1840000 3.3061576234650603 | |
| 1850000 3.288286510836121 | |
| 1853933 3.3352499783343603 0 | |
| 1860000 3.324370972560409 | |
| 1870000 3.306593597187025 | |
| 1880000 3.289005342727655 | |
| 1890000 3.2716032072646173 | |
| 1897689 3.311043075177365 0 | |
| 1900000 3.307015803325016 | |
| 1910000 3.2897015935244713 | |
| 1920000 3.27256773998208 | |
| 1930000 3.2556114392341424 | |
| 1940000 3.2388299456203034 | |
| 1940151 3.264349047566033 1 | |
| 1950000 3.247861582293206 | |
| 1960000 3.231290868389013 | |
| 1964810 3.2742759142397584 0 | |
| 1970000 3.265649780550027 | |
| 1980000 3.2491566081700634 | |
| 1990000 3.232829196233235 | |
| 2000000 3.216665058334138 | |
| 2010000 3.200661757548048 | |
| 2020000 3.184816905206153 | |
| 2030000 3.1691281597069825 | |
| 2037847 3.205996390964063 0 | |
| 2040000 3.2026128091767276 | |
| 2044507 3.244464356868906 0 | |
| 2050000 3.2357707792988073 | |
| 2060000 3.220063161781637 | |
| 2070000 3.2045073086116065 | |
| 2072622 3.248701444176454 0 | |
| 2080000 3.2371779308439437 | |
| 2083303 3.2800461830502576 0 | |
| 2090000 3.2695359156925448 | |
| 2098117 3.3045488067560234 0 | |
| 2100000 3.3015857294036213 | |
| 2110000 3.285938411087641 | |
| 2115041 3.325387076631733 0 | |
| 2120000 3.317608497983413 | |
| 2130000 3.3020328785448148 | |
| 2140000 3.2866028255750037 | |
| 2150000 3.271316307914896 | |
| 2160000 3.2561713320194454 | |
| 2170000 3.2411659410909643 | |
| 2177813 3.2754557245629488 0 | |
| 2180000 3.2721697528273306 | |
| 2190000 3.2572283452534196 | |
| 2200000 3.2424227685957114 | |
| 2203469 3.2827010730045494 0 | |
| 2210000 3.2730000273001387 | |
| 2212402 3.31464626170428 0 | |
| 2220000 3.303301815329513 | |
| 2230000 3.2884888093473204 | |
| 2240000 3.273808062288068 | |
| 2250000 3.2592578107002326 | |
| 2260000 3.2448363223438106 | |
| 2270000 3.2305418955028364 | |
| 2280000 3.216372858315998 | |
| 2290000 3.2023275681247885 | |
| 2300000 3.1884044108386624 | |
| 2310000 3.1746018003166814 | |
| 2320000 3.1609181777651534 | |
| 2324616 3.1976593706977683 0 | |
| 2330000 3.190270447666475 | |
| 2340000 3.1766368191010748 | |
| 2340958 3.2180543671774404 0 | |
| 2350000 3.2056723947493357 | |
| 2360000 3.192089042900123 | |
| 2370000 3.1786203184443105 | |
| 2380000 3.1652647764993938 | |
| 2388546 3.174872980658674 1 | |
| 2390000 3.1729414897037005 | |
| 2400000 3.159720905671845 | |
| 2410000 3.146610035984771 | |
| 2414780 3.181793021120066 0 | |
| 2420000 3.174929817522114 | |
| 2420874 3.215090962289806 0 | |
| 2430000 3.2030165145336706 | |
| 2440000 3.1898894030507914 | |
| 2450000 3.176869451617911 | |
| 2460000 3.163955353405683 | |
| 2470000 3.15114582274798 | |
| 2480000 3.1384395947152175 | |
| 2481330 3.177058334149428 0 | |
| 2490000 3.165996051139471 | |
| 2500000 3.153332072000505 | |
| 2509090 3.1817631697428808 0 | |
| 2510000 3.1806096225990883 | |
| 2520000 3.1679881608512592 | |
| 2530000 3.1554664734651623 | |
| 2540000 3.1430433820039183 | |
| 2546275 3.1745707587603755 0 | |
| 2550000 3.16993339741174 | |
| 2550174 3.20893010610383 0 | |
| 2560000 3.1966133346562495 | |
| 2570000 3.1841751553144664 | |
| 2580000 3.1718333959302085 | |
| 2590000 3.1595869396704224 | |
| 2600000 3.147434686884095 | |
| 2604348 3.1805773086991542 0 | |
| 2610000 3.1736897163385507 | |
| 2620000 3.1615764014339436 | |
| 2630000 3.149555202957464 | |
| 2640000 3.1376250741319165 | |
| 2650000 3.1257849839805094 | |
| 2660000 3.114033917029856 | |
| 2670000 3.102370873019648 | |
| 2680000 3.090794866618831 | |
| 2690000 3.0793049271481068 | |
| 2700000 3.067900098308606 | |
| 2704155 3.1001663119040965 0 | |
| 2710000 3.0934797933038896 | |
| 2720000 3.0821067100097883 | |
| 2730000 3.070816945976699 | |
| 2740000 3.0596095889502717 | |
| 2750000 3.048483739945307 | |
| 2760000 3.03743851300537 | |
| 2770000 3.026473034967617 | |
| 2773110 3.0591394766864126 0 | |
| 2780000 3.0515576553149923 | |
| 2789555 3.076953226009205 0 | |
| 2790000 3.076462457659812 | |
| 2794077 3.1077633957725355 0 | |
| 2800000 3.101189368622845 | |
| 2810000 3.0901531114520364 | |
| 2820000 3.079195125580925 | |
| 2830000 3.0683145812787114 | |
| 2840000 3.0575106605009412 | |
| 2850000 3.0467825566844833 | |
| 2850667 3.0636094183304876 1 | |
| 2860000 3.053611985916555 | |
| 2868156 3.0797942139615557 0 | |
| 2870000 3.0778154200410848 | |
| 2880000 3.0671285646544337 | |
| 2890000 3.056515666718916 | |
| 2900000 3.0459759611577146 | |
| 2910000 3.0355086934105295 | |
| 2910525 3.0693191998055793 0 | |
| 2920000 3.059359682867689 | |
| 2930000 3.0489181858072176 | |
| 2940000 3.0385477193148347 | |
| 2950000 3.0282475610460247 | |
| 2960000 3.018016998417681 | |
| 2970000 3.007855328443773 | |
| 2975336 3.036070647907559 0 | |
| 2980000 3.0313188932934363 | |
| 2990000 3.021180706405561 | |
| 3000000 3.011110107407742 | |
| 3010000 3.001106422666748 | |
| 3020000 2.991168987471638 | |
| 3030000 2.9812971458865305 | |
| 3038226 3.0061392165013787 0 | |
| 3040000 3.0043849766277493 | |
| 3050000 2.9945345373110808 | |
| 3060000 2.984748479929691 | |
| 3066922 3.010617916828474 0 | |
| 3070000 3.0075994546364426 | |
| 3080000 2.9978345245126006 | |
| 3082860 3.027490805888859 0 | |
| 3090000 3.020495246873167 | |
| 3100000 3.010751716961812 | |
| 3110000 3.001070846386652 | |
| 3111866 3.0314063336682877 0 | |
| 3120000 3.023503304432702 | |
| 3130000 3.013843552552646 | |
| 3140000 3.004245327735034 | |
| 3150000 2.9947080440080285 | |
| 3154850 3.02180145221861 0 | |
| 3157570 3.0350333637258937 1 | |
| 3160000 3.0326994622259087 | |
| 3170000 3.023132589968689 | |
| 3180000 3.013625886700455 | |
| 3190000 3.0041787865688234 | |
| 3200000 2.9947907307945636 | |
| 3200906 3.02518421601544 0 | |
| 3210000 3.0166138058316285 | |
| 3220000 3.007245442884438 | |
| 3230000 2.99793508835859 | |
| 3233115 3.025976591416248 0 | |
| 3240000 3.0195463931441173 | |
| 3250000 3.0102554840239537 | |
| 3260000 3.0010215743287607 | |
| 3270000 2.9918441411281935 | |
| 3280000 2.9827226678691057 | |
| 3290000 2.973656644278629 | |
| 3295006 2.999487810900958 0 | |
| 3300000 2.994948587389317 | |
| 3310000 2.985900407079434 | |
| 3320000 2.9769067338634336 | |
| 3325409 3.002136077456113 0 | |
| 3330000 2.9979970976985695 | |
| 3340000 2.9890210611713393 | |
| 3350000 2.980098612905887 | |
| 3360000 2.971229274435732 | |
| 3370000 2.96241257297352 | |
| 3380000 2.9536480413270096 | |
| 3388103 2.9613416038390006 1 | |
| 3390000 2.959684476002613 | |
| 3400000 2.950979524221709 | |
| 3404701 2.961590568964137 1 | |
| 3408009 2.988058524867396 0 | |
| 3410000 2.9863138847564366 | |
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| 3430000 2.968900980884068 | |
| 3440000 2.96027045728572 | |
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| 3460000 2.9431590723047 | |
| 3470000 2.934677348315846 | |
| 3480000 2.9262443698531504 | |
| 3490000 2.9178597179007495 | |
| 3500000 2.9095229782315304 | |
| 3510000 2.901233741338915 | |
| 3511660 2.9283388497162264 0 | |
| 3520000 2.921400685208139 | |
| 3530000 2.913124764931606 | |
| 3533742 2.9194728271599457 2 | |
| 3536930 2.9451144697667746 0 | |
| 3540000 2.9425603740413258 | |
| 3545143 2.966499151139324 0 | |
| 3550000 2.962440480063715 | |
| 3560000 2.9541190203785526 | |
| 3570000 2.9458441795020978 | |
| 3580000 2.9376155667740504 | |
| 3590000 2.929432795886872 | |
| 3600000 2.9212954848253285 | |
| 3610000 2.9132032558070393 | |
| 3620000 2.9051557352240147 | |
| 3630000 2.8971525535851557 | |
| 3640000 2.889193345459704 | |
| 3650000 2.8812777494216215 | |
| 3660000 2.8734054079948796 | |
| 3670000 2.865575967599646 | |
| 3670185 2.892678100419616 0 | |
| 3680000 2.8849629841586095 | |
| 3690000 2.877144658407049 | |
| 3700000 2.8693685938643445 | |
| 3710000 2.8616344487957464 | |
| 3720000 2.8539418851410705 | |
| 3722998 2.87850377254108 0 | |
| 3730000 2.873100212752401 | |
| 3733521 2.8971750177624958 0 | |
| 3740000 2.892156089441331 | |
| 3750000 2.884443675259465 | |
| 3760000 2.8767722845463783 | |
| 3770000 2.8691415908554583 | |
| 3780000 2.8615512711945494 | |
| 3783181 2.885577978185207 0 | |
| 3790000 2.880386223292993 | |
| 3800000 2.872806261542212 | |
| 3810000 2.865266089606451 | |
| 3817749 2.8856438128915376 0 | |
| 3820000 2.8839433986186567 | |
| 3830000 2.876413522259307 | |
| 3840000 2.8689228639957824 | |
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| # Output from an example run: http://i.imgur.com/iwpuFXZ.png | |
| def run | |
| j = 100_000 | |
| t = 6_000 | |
| prob = 34_220 | |
| iterations = 10_000_000 | |
| won = 0 | |
| sum = 0 | |
| # So we can watch output with tail | |
| $stdout.sync = true | |
| guess = Random.rand(prob) | |
| puts "#Iterations\tMean\tOther Winners" | |
| (0..iterations).each do |i| | |
| winner = Random.rand(prob) | |
| # See how many of the remaining t-1 tickets won | |
| winners = 0 | |
| (t-1).times do | |
| if winner == Random.rand(prob) | |
| winners += 1 | |
| end | |
| end | |
| if winner == guess | |
| won += 1 | |
| sum += j/(winners+1.0) | |
| puts "#{i}\t#{sum/(i+1)}\t#{winners}" | |
| end | |
| if !i.zero? && (i % 10_000).zero? | |
| # Update our progress progress | |
| # print "." | |
| puts "#{i}\t#{sum/(i+1)}" | |
| end | |
| end | |
| puts "#{iterations}\t#{sum/(iterations+1)}" | |
| end | |
| run |
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