Go First Dice
March 18th, 2024 at 10:01:03 AM
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This video on Numberphile got me to thinking about what are called Go First Dice. These are a set of dice, where each player rolls one to determine the order of playing a board game. They don't just determine who goes first, but every position, each order with equal probability.
The two player case is easy. You could have two dice labeled as:
Die 1 = 1,2,3,10,11,12
Die 2 = 4,5,6,7,8,9
Note that die 2 doesn't make any difference. It comes down to whether die 1 is above or below the range of die 2. You could use a coin as well as follows:
Coin 1 = 1,3
Coin 2 = 2,2
It got much more difficult with the three-player. I had to resort to a computer simulation, which came up with the following:
Die 1 = 3,4,9,10,13,18
Die 2 = 2,5,7,12,15,16
Die 3 = 1,6,8,11,14,17
I then used the method explain in the video I linked to above to expand that to four dice, as follows:
Die 1 = 5,6,11,12,15,20,31,32,37,38,41,46
Die 2 = 4,7,9,14,17,18,30,33,35,40,43,44
Die 3 = 3,8,10,13,16,19,29,34,36,39,42,45
Die 4 = 1,2,21,22,23,24,25,26,27,28,47,48
It was fortunate the method worked on a little as 12-sided dice.
To expand the method to five dice, I could do no better than 840-side dice. I will elaborate on the method if there is sufficient interest. As long as I took the trouble, here are those five-player dice:
137,138,143,144,147,152,163,164,169,170,173,178,185,186,191,192,195,200,211,212,217,218,221,226,233,234,239,240,243,248,259,260,265,266,269,274,281,282,287,288,291,296,307,308,313,314,317,322,329,330,335,336,339,344,355,356,361,362,365,370,377,378,383,384,387,392,403,404,409,410,413,418,425,426,431,432,435,440,451,452,457,458,461,466,473,474,479,480,483,488,499,500,505,506,509,514,521,522,527,528,531,536,547,548,553,554,557,562,569,570,575,576,579,584,595,596,601,602,605,610,617,618,623,624,627,632,643,644,649,650,653,658,665,666,671,672,675,680,691,692,697,698,701,706,713,714,719,720,723,728,739,740,745,746,749,754,761,762,767,768,771,776,787,788,793,794,797,802,809,810,815,816,819,824,835,836,841,842,845,850,857,858,863,864,867,872,883,884,889,890,893,898,905,906,911,912,915,920,931,932,937,938,941,946,953,954,959,960,963,968,979,980,985,986,989,994,1001,1002,1007,1008,1011,1016,1027,1028,1033,1034,1037,1042,1049,1050,1055,1056,1059,1064,1075,1076,1081,1082,1085,1090,1097,1098,1103,1104,1107,1112,1123,1124,1129,1130,1133,1138,1145,1146,1151,1152,1155,1160,1171,1172,1177,1178,1181,1186,1193,1194,1199,1200,1203,1208,1219,1220,1225,1226,1229,1234,1241,1242,1247,1248,1251,1256,1267,1268,1273,1274,1277,1282,1289,1290,1295,1296,1299,1304,1315,1316,1321,1322,1325,1330,1337,1338,1343,1344,1347,1352,1363,1364,1369,1370,1373,1378,1385,1386,1391,1392,1395,1400,1411,1412,1417,1418,1421,1426,1433,1434,1439,1440,1443,1448,1459,1460,1465,1466,1469,1474,1481,1482,1487,1488,1491,1496,1507,1508,1513,1514,1517,1522,1529,1530,1535,1536,1539,1544,1555,1556,1561,1562,1565,1570,1577,1578,1583,1584,1587,1592,1603,1604,1609,1610,1613,1618,1625,1626,1631,1632,1635,1640,1651,1652,1657,1658,1661,1666,1673,1674,1679,1680,1683,1688,1699,1700,1705,1706,1709,1714,1721,1722,1727,1728,1731,1736,1747,1748,1753,1754,1757,1762,1769,1770,1775,1776,1779,1784,1795,1796,1801,1802,1805,1810,2392,2393,2398,2399,2402,2407,2418,2419,2424,2425,2428,2433,2440,2441,2446,2447,2450,2455,2466,2467,2472,2473,2476,2481,2488,2489,2494,2495,2498,2503,2514,2515,2520,2521,2524,2529,2536,2537,2542,2543,2546,2551,2562,2563,2568,2569,2572,2577,2584,2585,2590,2591,2594,2599,2610,2611,2616,2617,2620,2625,2632,2633,2638,2639,2642,2647,2658,2659,2664,2665,2668,2673,2680,2681,2686,2687,2690,2695,2706,2707,2712,2713,2716,2721,2728,2729,2734,2735,2738,2743,2754,2755,2760,2761,2764,2769,2776,2777,2782,2783,2786,2791,2802,2803,2808,2809,2812,2817,2824,2825,2830,2831,2834,2839,2850,2851,2856,2857,2860,2865,2872,2873,2878,2879,2882,2887,2898,2899,2904,2905,2908,2913,2920,2921,2926,2927,2930,2935,2946,2947,2952,2953,2956,2961,2968,2969,2974,2975,2978,2983,2994,2995,3000,3001,3004,3009,3016,3017,3022,3023,3026,3031,3042,3043,3048,3049,3052,3057,3064,3065,3070,3071,3074,3079,3090,3091,3096,3097,3100,3105,3112,3113,3118,3119,3122,3127,3138,3139,3144,3145,3148,3153,3160,3161,3166,3167,3170,3175,3186,3187,3192,3193,3196,3201,3208,3209,3214,3215,3218,3223,3234,3235,3240,3241,3244,3249,3256,3257,3262,3263,3266,3271,3282,3283,3288,3289,3292,3297,3304,3305,3310,3311,3314,3319,3330,3331,3336,3337,3340,3345,3352,3353,3358,3359,3362,3367,3378,3379,3384,3385,3388,3393,3400,3401,3406,3407,3410,3415,3426,3427,3432,3433,3436,3441,3448,3449,3454,3455,3458,3463,3474,3475,3480,3481,3484,3489,3496,3497,3502,3503,3506,3511,3522,3523,3528,3529,3532,3537,3544,3545,3550,3551,3554,3559,3570,3571,3576,3577,3580,3585,3592,3593,3598,3599,3602,3607,3618,3619,3624,3625,3628,3633,3640,3641,3646,3647,3650,3655,3666,3667,3672,3673,3676,3681,3688,3689,3694,3695,3698,3703,3714,3715,3720,3721,3724,3729,3736,3737,3742,3743,3746,3751,3762,3763,3768,3769,3772,3777,3784,3785,3790,3791,3794,3799,3810,3811,3816,3817,3820,3825,3832,3833,3838,3839,3842,3847,3858,3859,3864,3865,3868,3873,3880,3881,3886,3887,3890,3895,3906,3907,3912,3913,3916,3921,3928,3929,3934,3935,3938,3943,3954,3955,3960,3961,3964,3969,3976,3977,3982,3983,3986,3991,4002,4003,4008,4009,4012,4017,4024,4025,4030,4031,4034,4039,4050,4051,4056,4057,4060,4065
136,139,141,146,149,150,162,165,167,172,175,176,184,187,189,194,197,198,210,213,215,220,223,224,232,235,237,242,245,246,258,261,263,268,271,272,280,283,285,290,293,294,306,309,311,316,319,320,328,331,333,338,341,342,354,357,359,364,367,368,376,379,381,386,389,390,402,405,407,412,415,416,424,427,429,434,437,438,450,453,455,460,463,464,472,475,477,482,485,486,498,501,503,508,511,512,520,523,525,530,533,534,546,549,551,556,559,560,568,571,573,578,581,582,594,597,599,604,607,608,616,619,621,626,629,630,642,645,647,652,655,656,664,667,669,674,677,678,690,693,695,700,703,704,712,715,717,722,725,726,738,741,743,748,751,752,760,763,765,770,773,774,786,789,791,796,799,800,808,811,813,818,821,822,834,837,839,844,847,848,856,859,861,866,869,870,882,885,887,892,895,896,904,907,909,914,917,918,930,933,935,940,943,944,952,955,957,962,965,966,978,981,983,988,991,992,1000,1003,1005,1010,1013,1014,1026,1029,1031,1036,1039,1040,1048,1051,1053,1058,1061,1062,1074,1077,1079,1084,1087,1088,1096,1099,1101,1106,1109,1110,1122,1125,1127,1132,1135,1136,1144,1147,1149,1154,1157,1158,1170,1173,1175,1180,1183,1184,1192,1195,1197,1202,1205,1206,1218,1221,1223,1228,1231,1232,1240,1243,1245,1250,1253,1254,1266,1269,1271,1276,1279,1280,1288,1291,1293,1298,1301,1302,1314,1317,1319,1324,1327,1328,1336,1339,1341,1346,1349,1350,1362,1365,1367,1372,1375,1376,1384,1387,1389,1394,1397,1398,1410,1413,1415,1420,1423,1424,1432,1435,1437,1442,1445,1446,1458,1461,1463,1468,1471,1472,1480,1483,1485,1490,1493,1494,1506,1509,1511,1516,1519,1520,1528,1531,1533,1538,1541,1542,1554,1557,1559,1564,1567,1568,1576,1579,1581,1586,1589,1590,1602,1605,1607,1612,1615,1616,1624,1627,1629,1634,1637,1638,1650,1653,1655,1660,1663,1664,1672,1675,1677,1682,1685,1686,1698,1701,1703,1708,1711,1712,1720,1723,1725,1730,1733,1734,1746,1749,1751,1756,1759,1760,1768,1771,1773,1778,1781,1782,1794,1797,1799,1804,1807,1808,2391,2394,2396,2401,2404,2405,2417,2420,2422,2427,2430,2431,2439,2442,2444,2449,2452,2453,2465,2468,2470,2475,2478,2479,2487,2490,2492,2497,2500,2501,2513,2516,2518,2523,2526,2527,2535,2538,2540,2545,2548,2549,2561,2564,2566,2571,2574,2575,2583,2586,2588,2593,2596,2597,2609,2612,2614,2619,2622,2623,2631,2634,2636,2641,2644,2645,2657,2660,2662,2667,2670,2671,2679,2682,2684,2689,2692,2693,2705,2708,2710,2715,2718,2719,2727,2730,2732,2737,2740,2741,2753,2756,2758,2763,2766,2767,2775,2778,2780,2785,2788,2789,2801,2804,2806,2811,2814,2815,2823,2826,2828,2833,2836,2837,2849,2852,2854,2859,2862,2863,2871,2874,2876,2881,2884,2885,2897,2900,2902,2907,2910,2911,2919,2922,2924,2929,2932,2933,2945,2948,2950,2955,2958,2959,2967,2970,2972,2977,2980,2981,2993,2996,2998,3003,3006,3007,3015,3018,3020,3025,3028,3029,3041,3044,3046,3051,3054,3055,3063,3066,3068,3073,3076,3077,3089,3092,3094,3099,3102,3103,3111,3114,3116,3121,3124,3125,3137,3140,3142,3147,3150,3151,3159,3162,3164,3169,3172,3173,3185,3188,3190,3195,3198,3199,3207,3210,3212,3217,3220,3221,3233,3236,3238,3243,3246,3247,3255,3258,3260,3265,3268,3269,3281,3284,3286,3291,3294,3295,3303,3306,3308,3313,3316,3317,3329,3332,3334,3339,3342,3343,3351,3354,3356,3361,3364,3365,3377,3380,3382,3387,3390,3391,3399,3402,3404,3409,3412,3413,3425,3428,3430,3435,3438,3439,3447,3450,3452,3457,3460,3461,3473,3476,3478,3483,3486,3487,3495,3498,3500,3505,3508,3509,3521,3524,3526,3531,3534,3535,3543,3546,3548,3553,3556,3557,3569,3572,3574,3579,3582,3583,3591,3594,3596,3601,3604,3605,3617,3620,3622,3627,3630,3631,3639,3642,3644,3649,3652,3653,3665,3668,3670,3675,3678,3679,3687,3690,3692,3697,3700,3701,3713,3716,3718,3723,3726,3727,3735,3738,3740,3745,3748,3749,3761,3764,3766,3771,3774,3775,3783,3786,3788,3793,3796,3797,3809,3812,3814,3819,3822,3823,3831,3834,3836,3841,3844,3845,3857,3860,3862,3867,3870,3871,3879,3882,3884,3889,3892,3893,3905,3908,3910,3915,3918,3919,3927,3930,3932,3937,3940,3941,3953,3956,3958,3963,3966,3967,3975,3978,3980,3985,3988,3989,4001,4004,4006,4011,4014,4015,4023,4026,4028,4033,4036,4037,4049,4052,4054,4059,4062,4063
135,140,142,145,148,151,161,166,168,171,174,177,183,188,190,193,196,199,209,214,216,219,222,225,231,236,238,241,244,247,257,262,264,267,270,273,279,284,286,289,292,295,305,310,312,315,318,321,327,332,334,337,340,343,353,358,360,363,366,369,375,380,382,385,388,391,401,406,408,411,414,417,423,428,430,433,436,439,449,454,456,459,462,465,471,476,478,481,484,487,497,502,504,507,510,513,519,524,526,529,532,535,545,550,552,555,558,561,567,572,574,577,580,583,593,598,600,603,606,609,615,620,622,625,628,631,641,646,648,651,654,657,663,668,670,673,676,679,689,694,696,699,702,705,711,716,718,721,724,727,737,742,744,747,750,753,759,764,766,769,772,775,785,790,792,795,798,801,807,812,814,817,820,823,833,838,840,843,846,849,855,860,862,865,868,871,881,886,888,891,894,897,903,908,910,913,916,919,929,934,936,939,942,945,951,956,958,961,964,967,977,982,984,987,990,993,999,1004,1006,1009,1012,1015,1025,1030,1032,1035,1038,1041,1047,1052,1054,1057,1060,1063,1073,1078,1080,1083,1086,1089,1095,1100,1102,1105,1108,1111,1121,1126,1128,1131,1134,1137,1143,1148,1150,1153,1156,1159,1169,1174,1176,1179,1182,1185,1191,1196,1198,1201,1204,1207,1217,1222,1224,1227,1230,1233,1239,1244,1246,1249,1252,1255,1265,1270,1272,1275,1278,1281,1287,1292,1294,1297,1300,1303,1313,1318,1320,1323,1326,1329,1335,1340,1342,1345,1348,1351,1361,1366,1368,1371,1374,1377,1383,1388,1390,1393,1396,1399,1409,1414,1416,1419,1422,1425,1431,1436,1438,1441,1444,1447,1457,1462,1464,1467,1470,1473,1479,1484,1486,1489,1492,1495,1505,1510,1512,1515,1518,1521,1527,1532,1534,1537,1540,1543,1553,1558,1560,1563,1566,1569,1575,1580,1582,1585,1588,1591,1601,1606,1608,1611,1614,1617,1623,1628,1630,1633,1636,1639,1649,1654,1656,1659,1662,1665,1671,1676,1678,1681,1684,1687,1697,1702,1704,1707,1710,1713,1719,1724,1726,1729,1732,1735,1745,1750,1752,1755,1758,1761,1767,1772,1774,1777,1780,1783,1793,1798,1800,1803,1806,1809,2390,2395,2397,2400,2403,2406,2416,2421,2423,2426,2429,2432,2438,2443,2445,2448,2451,2454,2464,2469,2471,2474,2477,2480,2486,2491,2493,2496,2499,2502,2512,2517,2519,2522,2525,2528,2534,2539,2541,2544,2547,2550,2560,2565,2567,2570,2573,2576,2582,2587,2589,2592,2595,2598,2608,2613,2615,2618,2621,2624,2630,2635,2637,2640,2643,2646,2656,2661,2663,2666,2669,2672,2678,2683,2685,2688,2691,2694,2704,2709,2711,2714,2717,2720,2726,2731,2733,2736,2739,2742,2752,2757,2759,2762,2765,2768,2774,2779,2781,2784,2787,2790,2800,2805,2807,2810,2813,2816,2822,2827,2829,2832,2835,2838,2848,2853,2855,2858,2861,2864,2870,2875,2877,2880,2883,2886,2896,2901,2903,2906,2909,2912,2918,2923,2925,2928,2931,2934,2944,2949,2951,2954,2957,2960,2966,2971,2973,2976,2979,2982,2992,2997,2999,3002,3005,3008,3014,3019,3021,3024,3027,3030,3040,3045,3047,3050,3053,3056,3062,3067,3069,3072,3075,3078,3088,3093,3095,3098,3101,3104,3110,3115,3117,3120,3123,3126,3136,3141,3143,3146,3149,3152,3158,3163,3165,3168,3171,3174,3184,3189,3191,3194,3197,3200,3206,3211,3213,3216,3219,3222,3232,3237,3239,3242,3245,3248,3254,3259,3261,3264,3267,3270,3280,3285,3287,3290,3293,3296,3302,3307,3309,3312,3315,3318,3328,3333,3335,3338,3341,3344,3350,3355,3357,3360,3363,3366,3376,3381,3383,3386,3389,3392,3398,3403,3405,3408,3411,3414,3424,3429,3431,3434,3437,3440,3446,3451,3453,3456,3459,3462,3472,3477,3479,3482,3485,3488,3494,3499,3501,3504,3507,3510,3520,3525,3527,3530,3533,3536,3542,3547,3549,3552,3555,3558,3568,3573,3575,3578,3581,3584,3590,3595,3597,3600,3603,3606,3616,3621,3623,3626,3629,3632,3638,3643,3645,3648,3651,3654,3664,3669,3671,3674,3677,3680,3686,3691,3693,3696,3699,3702,3712,3717,3719,3722,3725,3728,3734,3739,3741,3744,3747,3750,3760,3765,3767,3770,3773,3776,3782,3787,3789,3792,3795,3798,3808,3813,3815,3818,3821,3824,3830,3835,3837,3840,3843,3846,3856,3861,3863,3866,3869,3872,3878,3883,3885,3888,3891,3894,3904,3909,3911,3914,3917,3920,3926,3931,3933,3936,3939,3942,3952,3957,3959,3962,3965,3968,3974,3979,3981,3984,3987,3990,4000,4005,4007,4010,4013,4016,4022,4027,4029,4032,4035,4038,4048,4053,4055,4058,4061,4064
133,134,153,154,155,156,157,158,159,160,179,180,181,182,201,202,203,204,205,206,207,208,227,228,229,230,249,250,251,252,253,254,255,256,275,276,277,278,297,298,299,300,301,302,303,304,323,324,325,326,345,346,347,348,349,350,351,352,371,372,373,374,393,394,395,396,397,398,399,400,419,420,421,422,441,442,443,444,445,446,447,448,467,468,469,470,489,490,491,492,493,494,495,496,515,516,517,518,537,538,539,540,541,542,543,544,563,564,565,566,585,586,587,588,589,590,591,592,611,612,613,614,633,634,635,636,637,638,639,640,659,660,661,662,681,682,683,684,685,686,687,688,707,708,709,710,729,730,731,732,733,734,735,736,755,756,757,758,777,778,779,780,781,782,783,784,803,804,805,806,825,826,827,828,829,830,831,832,851,852,853,854,873,874,875,876,877,878,879,880,899,900,901,902,921,922,923,924,925,926,927,928,947,948,949,950,969,970,971,972,973,974,975,976,995,996,997,998,1017,1018,1019,1020,1021,1022,1023,1024,1043,1044,1045,1046,1065,1066,1067,1068,1069,1070,1071,1072,1091,1092,1093,1094,1113,1114,1115,1116,1117,1118,1119,1120,1139,1140,1141,1142,1161,1162,1163,1164,1165,1166,1167,1168,1187,1188,1189,1190,1209,1210,1211,1212,1213,1214,1215,1216,1235,1236,1237,1238,1257,1258,1259,1260,1261,1262,1263,1264,1283,1284,1285,1286,1305,1306,1307,1308,1309,1310,1311,1312,1331,1332,1333,1334,1353,1354,1355,1356,1357,1358,1359,1360,1379,1380,1381,1382,1401,1402,1403,1404,1405,1406,1407,1408,1427,1428,1429,1430,1449,1450,1451,1452,1453,1454,1455,1456,1475,1476,1477,1478,1497,1498,1499,1500,1501,1502,1503,1504,1523,1524,1525,1526,1545,1546,1547,1548,1549,1550,1551,1552,1571,1572,1573,1574,1593,1594,1595,1596,1597,1598,1599,1600,1619,1620,1621,1622,1641,1642,1643,1644,1645,1646,1647,1648,1667,1668,1669,1670,1689,1690,1691,1692,1693,1694,1695,1696,1715,1716,1717,1718,1737,1738,1739,1740,1741,1742,1743,1744,1763,1764,1765,1766,1785,1786,1787,1788,1789,1790,1791,1792,1811,1812,2388,2389,2408,2409,2410,2411,2412,2413,2414,2415,2434,2435,2436,2437,2456,2457,2458,2459,2460,2461,2462,2463,2482,2483,2484,2485,2504,2505,2506,2507,2508,2509,2510,2511,2530,2531,2532,2533,2552,2553,2554,2555,2556,2557,2558,2559,2578,2579,2580,2581,2600,2601,2602,2603,2604,2605,2606,2607,2626,2627,2628,2629,2648,2649,2650,2651,2652,2653,2654,2655,2674,2675,2676,2677,2696,2697,2698,2699,2700,2701,2702,2703,2722,2723,2724,2725,2744,2745,2746,2747,2748,2749,2750,2751,2770,2771,2772,2773,2792,2793,2794,2795,2796,2797,2798,2799,2818,2819,2820,2821,2840,2841,2842,2843,2844,2845,2846,2847,2866,2867,2868,2869,2888,2889,2890,2891,2892,2893,2894,2895,2914,2915,2916,2917,2936,2937,2938,2939,2940,2941,2942,2943,2962,2963,2964,2965,2984,2985,2986,2987,2988,2989,2990,2991,3010,3011,3012,3013,3032,3033,3034,3035,3036,3037,3038,3039,3058,3059,3060,3061,3080,3081,3082,3083,3084,3085,3086,3087,3106,3107,3108,3109,3128,3129,3130,3131,3132,3133,3134,3135,3154,3155,3156,3157,3176,3177,3178,3179,3180,3181,3182,3183,3202,3203,3204,3205,3224,3225,3226,3227,3228,3229,3230,3231,3250,3251,3252,3253,3272,3273,3274,3275,3276,3277,3278,3279,3298,3299,3300,3301,3320,3321,3322,3323,3324,3325,3326,3327,3346,3347,3348,3349,3368,3369,3370,3371,3372,3373,3374,3375,3394,3395,3396,3397,3416,3417,3418,3419,3420,3421,3422,3423,3442,3443,3444,3445,3464,3465,3466,3467,3468,3469,3470,3471,3490,3491,3492,3493,3512,3513,3514,3515,3516,3517,3518,3519,3538,3539,3540,3541,3560,3561,3562,3563,3564,3565,3566,3567,3586,3587,3588,3589,3608,3609,3610,3611,3612,3613,3614,3615,3634,3635,3636,3637,3656,3657,3658,3659,3660,3661,3662,3663,3682,3683,3684,3685,3704,3705,3706,3707,3708,3709,3710,3711,3730,3731,3732,3733,3752,3753,3754,3755,3756,3757,3758,3759,3778,3779,3780,3781,3800,3801,3802,3803,3804,3805,3806,3807,3826,3827,3828,3829,3848,3849,3850,3851,3852,3853,3854,3855,3874,3875,3876,3877,3896,3897,3898,3899,3900,3901,3902,3903,3922,3923,3924,3925,3944,3945,3946,3947,3948,3949,3950,3951,3970,3971,3972,3973,3992,3993,3994,3995,3996,3997,3998,3999,4018,4019,4020,4021,4040,4041,4042,4043,4044,4045,4046,4047,4066,4067
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,1813,1814,1815,1816,1817,1818,1819,1820,1821,1822,1823,1824,1825,1826,1827,1828,1829,1830,1831,1832,1833,1834,1835,1836,1837,1838,1839,1840,1841,1842,1843,1844,1845,1846,1847,1848,1849,1850,1851,1852,1853,1854,1855,1856,1857,1858,1859,1860,1861,1862,1863,1864,1865,1866,1867,1868,1869,1870,1871,1872,1873,1874,1875,1876,1877,1878,1879,1880,1881,1882,1883,1884,1885,1886,1887,1888,1889,1890,1891,1892,1893,1894,1895,1896,1897,1898,1899,1900,1901,1902,1903,1904,1905,1906,1907,1908,1909,1910,1911,1912,1913,1914,1915,1916,1917,1918,1919,1920,1921,1922,1923,1924,1925,1926,1927,1928,1929,1930,1931,1932,1933,1934,1935,1936,1937,1938,1939,1940,1941,1942,1943,1944,1945,1946,1947,1948,1949,1950,1951,1952,1953,1954,1955,1956,1957,1958,1959,1960,1961,1962,1963,1964,1965,1966,1967,1968,1969,1970,1971,1972,1973,1974,1975,1976,1977,1978,1979,1980,1981,1982,1983,1984,1985,1986,1987,1988,1989,1990,1991,1992,1993,1994,1995,1996,1997,1998,1999,2000,2001,2002,2003,2004,2005,2006,2007,2008,2009,2010,2011,2012,2013,2014,2015,2016,2017,2018,2019,2020,2021,2022,2023,2024,2025,2026,2027,2028,2029,2030,2031,2032,2033,2034,2035,2036,2037,2038,2039,2040,2041,2042,2043,2044,2045,2046,2047,2048,2049,2050,2051,2052,2053,2054,2055,2056,2057,2058,2059,2060,2061,2062,2063,2064,2065,2066,2067,2068,2069,2070,2071,2072,2073,2074,2075,2076,2077,2078,2079,2080,2081,2082,2083,2084,2085,2086,2087,2088,2089,2090,2091,2092,2093,2094,2095,2096,2097,2098,2099,2100,2101,2102,2103,2104,2105,2106,2107,2108,2109,2110,2111,2112,2113,2114,2115,2116,2117,2118,2119,2120,2121,2122,2123,2124,2125,2126,2127,2128,2129,2130,2131,2132,2133,2134,2135,2136,2137,2138,2139,2140,2141,2142,2143,2144,2145,2146,2147,2148,2149,2150,2151,2152,2153,2154,2155,2156,2157,2158,2159,2160,2161,2162,2163,2164,2165,2166,2167,2168,2169,2170,2171,2172,2173,2174,2175,2176,2177,2178,2179,2180,2181,2182,2183,2184,2185,2186,2187,2188,2189,2190,2191,2192,2193,2194,2195,2196,2197,2198,2199,2200,2201,2202,2203,2204,2205,2206,2207,2208,2209,2210,2211,2212,2213,2214,2215,2216,2217,2218,2219,2220,2221,2222,2223,2224,2225,2226,2227,2228,2229,2230,2231,2232,2233,2234,2235,2236,2237,2238,2239,2240,2241,2242,2243,2244,2245,2246,2247,2248,2249,2250,2251,2252,2253,2254,2255,2256,2257,2258,2259,2260,2261,2262,2263,2264,2265,2266,2267,2268,2269,2270,2271,2272,2273,2274,2275,2276,2277,2278,2279,2280,2281,2282,2283,2284,2285,2286,2287,2288,2289,2290,2291,2292,2293,2294,2295,2296,2297,2298,2299,2300,2301,2302,2303,2304,2305,2306,2307,2308,2309,2310,2311,2312,2313,2314,2315,2316,2317,2318,2319,2320,2321,2322,2323,2324,2325,2326,2327,2328,2329,2330,2331,2332,2333,2334,2335,2336,2337,2338,2339,2340,2341,2342,2343,2344,2345,2346,2347,2348,2349,2350,2351,2352,2353,2354,2355,2356,2357,2358,2359,2360,2361,2362,2363,2364,2365,2366,2367,2368,2369,2370,2371,2372,2373,2374,2375,2376,2377,2378,2379,2380,2381,2382,2383,2384,2385,2386,2387,4068,4069,4070,4071,4072,4073,4074,4075,4076,4077,4078,4079,4080,4081,4082,4083,4084,4085,4086,4087,4088,4089,4090,4091,4092,4093,4094,4095,4096,4097,4098,4099,4100,4101,4102,4103,4104,4105,4106,4107,4108,4109,4110,4111,4112,4113,4114,4115,4116,4117,4118,4119,4120,4121,4122,4123,4124,4125,4126,4127,4128,4129,4130,4131,4132,4133,4134,4135,4136,4137,4138,4139,4140,4141,4142,4143,4144,4145,4146,4147,4148,4149,4150,4151,4152,4153,4154,4155,4156,4157,4158,4159,4160,4161,4162,4163,4164,4165,4166,4167,4168,4169,4170,4171,4172,4173,4174,4175,4176,4177,4178,4179,4180,4181,4182,4183,4184,4185,4186,4187,4188,4189,4190,4191,4192,4193,4194,4195,4196,4197,4198,4199,4200
To be honest, I haven't verified my five-dice solution works. I would have to cycle through 840^5 = 418,211,942,400,000 possible dice outcomes, which would take days.
With that, I welcome all questions and comments.
The two player case is easy. You could have two dice labeled as:
Die 1 = 1,2,3,10,11,12
Die 2 = 4,5,6,7,8,9
Note that die 2 doesn't make any difference. It comes down to whether die 1 is above or below the range of die 2. You could use a coin as well as follows:
Coin 1 = 1,3
Coin 2 = 2,2
It got much more difficult with the three-player. I had to resort to a computer simulation, which came up with the following:
Die 1 = 3,4,9,10,13,18
Die 2 = 2,5,7,12,15,16
Die 3 = 1,6,8,11,14,17
I then used the method explain in the video I linked to above to expand that to four dice, as follows:
Die 1 = 5,6,11,12,15,20,31,32,37,38,41,46
Die 2 = 4,7,9,14,17,18,30,33,35,40,43,44
Die 3 = 3,8,10,13,16,19,29,34,36,39,42,45
Die 4 = 1,2,21,22,23,24,25,26,27,28,47,48
It was fortunate the method worked on a little as 12-sided dice.
To expand the method to five dice, I could do no better than 840-side dice. I will elaborate on the method if there is sufficient interest. As long as I took the trouble, here are those five-player dice:
137,138,143,144,147,152,163,164,169,170,173,178,185,186,191,192,195,200,211,212,217,218,221,226,233,234,239,240,243,248,259,260,265,266,269,274,281,282,287,288,291,296,307,308,313,314,317,322,329,330,335,336,339,344,355,356,361,362,365,370,377,378,383,384,387,392,403,404,409,410,413,418,425,426,431,432,435,440,451,452,457,458,461,466,473,474,479,480,483,488,499,500,505,506,509,514,521,522,527,528,531,536,547,548,553,554,557,562,569,570,575,576,579,584,595,596,601,602,605,610,617,618,623,624,627,632,643,644,649,650,653,658,665,666,671,672,675,680,691,692,697,698,701,706,713,714,719,720,723,728,739,740,745,746,749,754,761,762,767,768,771,776,787,788,793,794,797,802,809,810,815,816,819,824,835,836,841,842,845,850,857,858,863,864,867,872,883,884,889,890,893,898,905,906,911,912,915,920,931,932,937,938,941,946,953,954,959,960,963,968,979,980,985,986,989,994,1001,1002,1007,1008,1011,1016,1027,1028,1033,1034,1037,1042,1049,1050,1055,1056,1059,1064,1075,1076,1081,1082,1085,1090,1097,1098,1103,1104,1107,1112,1123,1124,1129,1130,1133,1138,1145,1146,1151,1152,1155,1160,1171,1172,1177,1178,1181,1186,1193,1194,1199,1200,1203,1208,1219,1220,1225,1226,1229,1234,1241,1242,1247,1248,1251,1256,1267,1268,1273,1274,1277,1282,1289,1290,1295,1296,1299,1304,1315,1316,1321,1322,1325,1330,1337,1338,1343,1344,1347,1352,1363,1364,1369,1370,1373,1378,1385,1386,1391,1392,1395,1400,1411,1412,1417,1418,1421,1426,1433,1434,1439,1440,1443,1448,1459,1460,1465,1466,1469,1474,1481,1482,1487,1488,1491,1496,1507,1508,1513,1514,1517,1522,1529,1530,1535,1536,1539,1544,1555,1556,1561,1562,1565,1570,1577,1578,1583,1584,1587,1592,1603,1604,1609,1610,1613,1618,1625,1626,1631,1632,1635,1640,1651,1652,1657,1658,1661,1666,1673,1674,1679,1680,1683,1688,1699,1700,1705,1706,1709,1714,1721,1722,1727,1728,1731,1736,1747,1748,1753,1754,1757,1762,1769,1770,1775,1776,1779,1784,1795,1796,1801,1802,1805,1810,2392,2393,2398,2399,2402,2407,2418,2419,2424,2425,2428,2433,2440,2441,2446,2447,2450,2455,2466,2467,2472,2473,2476,2481,2488,2489,2494,2495,2498,2503,2514,2515,2520,2521,2524,2529,2536,2537,2542,2543,2546,2551,2562,2563,2568,2569,2572,2577,2584,2585,2590,2591,2594,2599,2610,2611,2616,2617,2620,2625,2632,2633,2638,2639,2642,2647,2658,2659,2664,2665,2668,2673,2680,2681,2686,2687,2690,2695,2706,2707,2712,2713,2716,2721,2728,2729,2734,2735,2738,2743,2754,2755,2760,2761,2764,2769,2776,2777,2782,2783,2786,2791,2802,2803,2808,2809,2812,2817,2824,2825,2830,2831,2834,2839,2850,2851,2856,2857,2860,2865,2872,2873,2878,2879,2882,2887,2898,2899,2904,2905,2908,2913,2920,2921,2926,2927,2930,2935,2946,2947,2952,2953,2956,2961,2968,2969,2974,2975,2978,2983,2994,2995,3000,3001,3004,3009,3016,3017,3022,3023,3026,3031,3042,3043,3048,3049,3052,3057,3064,3065,3070,3071,3074,3079,3090,3091,3096,3097,3100,3105,3112,3113,3118,3119,3122,3127,3138,3139,3144,3145,3148,3153,3160,3161,3166,3167,3170,3175,3186,3187,3192,3193,3196,3201,3208,3209,3214,3215,3218,3223,3234,3235,3240,3241,3244,3249,3256,3257,3262,3263,3266,3271,3282,3283,3288,3289,3292,3297,3304,3305,3310,3311,3314,3319,3330,3331,3336,3337,3340,3345,3352,3353,3358,3359,3362,3367,3378,3379,3384,3385,3388,3393,3400,3401,3406,3407,3410,3415,3426,3427,3432,3433,3436,3441,3448,3449,3454,3455,3458,3463,3474,3475,3480,3481,3484,3489,3496,3497,3502,3503,3506,3511,3522,3523,3528,3529,3532,3537,3544,3545,3550,3551,3554,3559,3570,3571,3576,3577,3580,3585,3592,3593,3598,3599,3602,3607,3618,3619,3624,3625,3628,3633,3640,3641,3646,3647,3650,3655,3666,3667,3672,3673,3676,3681,3688,3689,3694,3695,3698,3703,3714,3715,3720,3721,3724,3729,3736,3737,3742,3743,3746,3751,3762,3763,3768,3769,3772,3777,3784,3785,3790,3791,3794,3799,3810,3811,3816,3817,3820,3825,3832,3833,3838,3839,3842,3847,3858,3859,3864,3865,3868,3873,3880,3881,3886,3887,3890,3895,3906,3907,3912,3913,3916,3921,3928,3929,3934,3935,3938,3943,3954,3955,3960,3961,3964,3969,3976,3977,3982,3983,3986,3991,4002,4003,4008,4009,4012,4017,4024,4025,4030,4031,4034,4039,4050,4051,4056,4057,4060,4065
136,139,141,146,149,150,162,165,167,172,175,176,184,187,189,194,197,198,210,213,215,220,223,224,232,235,237,242,245,246,258,261,263,268,271,272,280,283,285,290,293,294,306,309,311,316,319,320,328,331,333,338,341,342,354,357,359,364,367,368,376,379,381,386,389,390,402,405,407,412,415,416,424,427,429,434,437,438,450,453,455,460,463,464,472,475,477,482,485,486,498,501,503,508,511,512,520,523,525,530,533,534,546,549,551,556,559,560,568,571,573,578,581,582,594,597,599,604,607,608,616,619,621,626,629,630,642,645,647,652,655,656,664,667,669,674,677,678,690,693,695,700,703,704,712,715,717,722,725,726,738,741,743,748,751,752,760,763,765,770,773,774,786,789,791,796,799,800,808,811,813,818,821,822,834,837,839,844,847,848,856,859,861,866,869,870,882,885,887,892,895,896,904,907,909,914,917,918,930,933,935,940,943,944,952,955,957,962,965,966,978,981,983,988,991,992,1000,1003,1005,1010,1013,1014,1026,1029,1031,1036,1039,1040,1048,1051,1053,1058,1061,1062,1074,1077,1079,1084,1087,1088,1096,1099,1101,1106,1109,1110,1122,1125,1127,1132,1135,1136,1144,1147,1149,1154,1157,1158,1170,1173,1175,1180,1183,1184,1192,1195,1197,1202,1205,1206,1218,1221,1223,1228,1231,1232,1240,1243,1245,1250,1253,1254,1266,1269,1271,1276,1279,1280,1288,1291,1293,1298,1301,1302,1314,1317,1319,1324,1327,1328,1336,1339,1341,1346,1349,1350,1362,1365,1367,1372,1375,1376,1384,1387,1389,1394,1397,1398,1410,1413,1415,1420,1423,1424,1432,1435,1437,1442,1445,1446,1458,1461,1463,1468,1471,1472,1480,1483,1485,1490,1493,1494,1506,1509,1511,1516,1519,1520,1528,1531,1533,1538,1541,1542,1554,1557,1559,1564,1567,1568,1576,1579,1581,1586,1589,1590,1602,1605,1607,1612,1615,1616,1624,1627,1629,1634,1637,1638,1650,1653,1655,1660,1663,1664,1672,1675,1677,1682,1685,1686,1698,1701,1703,1708,1711,1712,1720,1723,1725,1730,1733,1734,1746,1749,1751,1756,1759,1760,1768,1771,1773,1778,1781,1782,1794,1797,1799,1804,1807,1808,2391,2394,2396,2401,2404,2405,2417,2420,2422,2427,2430,2431,2439,2442,2444,2449,2452,2453,2465,2468,2470,2475,2478,2479,2487,2490,2492,2497,2500,2501,2513,2516,2518,2523,2526,2527,2535,2538,2540,2545,2548,2549,2561,2564,2566,2571,2574,2575,2583,2586,2588,2593,2596,2597,2609,2612,2614,2619,2622,2623,2631,2634,2636,2641,2644,2645,2657,2660,2662,2667,2670,2671,2679,2682,2684,2689,2692,2693,2705,2708,2710,2715,2718,2719,2727,2730,2732,2737,2740,2741,2753,2756,2758,2763,2766,2767,2775,2778,2780,2785,2788,2789,2801,2804,2806,2811,2814,2815,2823,2826,2828,2833,2836,2837,2849,2852,2854,2859,2862,2863,2871,2874,2876,2881,2884,2885,2897,2900,2902,2907,2910,2911,2919,2922,2924,2929,2932,2933,2945,2948,2950,2955,2958,2959,2967,2970,2972,2977,2980,2981,2993,2996,2998,3003,3006,3007,3015,3018,3020,3025,3028,3029,3041,3044,3046,3051,3054,3055,3063,3066,3068,3073,3076,3077,3089,3092,3094,3099,3102,3103,3111,3114,3116,3121,3124,3125,3137,3140,3142,3147,3150,3151,3159,3162,3164,3169,3172,3173,3185,3188,3190,3195,3198,3199,3207,3210,3212,3217,3220,3221,3233,3236,3238,3243,3246,3247,3255,3258,3260,3265,3268,3269,3281,3284,3286,3291,3294,3295,3303,3306,3308,3313,3316,3317,3329,3332,3334,3339,3342,3343,3351,3354,3356,3361,3364,3365,3377,3380,3382,3387,3390,3391,3399,3402,3404,3409,3412,3413,3425,3428,3430,3435,3438,3439,3447,3450,3452,3457,3460,3461,3473,3476,3478,3483,3486,3487,3495,3498,3500,3505,3508,3509,3521,3524,3526,3531,3534,3535,3543,3546,3548,3553,3556,3557,3569,3572,3574,3579,3582,3583,3591,3594,3596,3601,3604,3605,3617,3620,3622,3627,3630,3631,3639,3642,3644,3649,3652,3653,3665,3668,3670,3675,3678,3679,3687,3690,3692,3697,3700,3701,3713,3716,3718,3723,3726,3727,3735,3738,3740,3745,3748,3749,3761,3764,3766,3771,3774,3775,3783,3786,3788,3793,3796,3797,3809,3812,3814,3819,3822,3823,3831,3834,3836,3841,3844,3845,3857,3860,3862,3867,3870,3871,3879,3882,3884,3889,3892,3893,3905,3908,3910,3915,3918,3919,3927,3930,3932,3937,3940,3941,3953,3956,3958,3963,3966,3967,3975,3978,3980,3985,3988,3989,4001,4004,4006,4011,4014,4015,4023,4026,4028,4033,4036,4037,4049,4052,4054,4059,4062,4063
135,140,142,145,148,151,161,166,168,171,174,177,183,188,190,193,196,199,209,214,216,219,222,225,231,236,238,241,244,247,257,262,264,267,270,273,279,284,286,289,292,295,305,310,312,315,318,321,327,332,334,337,340,343,353,358,360,363,366,369,375,380,382,385,388,391,401,406,408,411,414,417,423,428,430,433,436,439,449,454,456,459,462,465,471,476,478,481,484,487,497,502,504,507,510,513,519,524,526,529,532,535,545,550,552,555,558,561,567,572,574,577,580,583,593,598,600,603,606,609,615,620,622,625,628,631,641,646,648,651,654,657,663,668,670,673,676,679,689,694,696,699,702,705,711,716,718,721,724,727,737,742,744,747,750,753,759,764,766,769,772,775,785,790,792,795,798,801,807,812,814,817,820,823,833,838,840,843,846,849,855,860,862,865,868,871,881,886,888,891,894,897,903,908,910,913,916,919,929,934,936,939,942,945,951,956,958,961,964,967,977,982,984,987,990,993,999,1004,1006,1009,1012,1015,1025,1030,1032,1035,1038,1041,1047,1052,1054,1057,1060,1063,1073,1078,1080,1083,1086,1089,1095,1100,1102,1105,1108,1111,1121,1126,1128,1131,1134,1137,1143,1148,1150,1153,1156,1159,1169,1174,1176,1179,1182,1185,1191,1196,1198,1201,1204,1207,1217,1222,1224,1227,1230,1233,1239,1244,1246,1249,1252,1255,1265,1270,1272,1275,1278,1281,1287,1292,1294,1297,1300,1303,1313,1318,1320,1323,1326,1329,1335,1340,1342,1345,1348,1351,1361,1366,1368,1371,1374,1377,1383,1388,1390,1393,1396,1399,1409,1414,1416,1419,1422,1425,1431,1436,1438,1441,1444,1447,1457,1462,1464,1467,1470,1473,1479,1484,1486,1489,1492,1495,1505,1510,1512,1515,1518,1521,1527,1532,1534,1537,1540,1543,1553,1558,1560,1563,1566,1569,1575,1580,1582,1585,1588,1591,1601,1606,1608,1611,1614,1617,1623,1628,1630,1633,1636,1639,1649,1654,1656,1659,1662,1665,1671,1676,1678,1681,1684,1687,1697,1702,1704,1707,1710,1713,1719,1724,1726,1729,1732,1735,1745,1750,1752,1755,1758,1761,1767,1772,1774,1777,1780,1783,1793,1798,1800,1803,1806,1809,2390,2395,2397,2400,2403,2406,2416,2421,2423,2426,2429,2432,2438,2443,2445,2448,2451,2454,2464,2469,2471,2474,2477,2480,2486,2491,2493,2496,2499,2502,2512,2517,2519,2522,2525,2528,2534,2539,2541,2544,2547,2550,2560,2565,2567,2570,2573,2576,2582,2587,2589,2592,2595,2598,2608,2613,2615,2618,2621,2624,2630,2635,2637,2640,2643,2646,2656,2661,2663,2666,2669,2672,2678,2683,2685,2688,2691,2694,2704,2709,2711,2714,2717,2720,2726,2731,2733,2736,2739,2742,2752,2757,2759,2762,2765,2768,2774,2779,2781,2784,2787,2790,2800,2805,2807,2810,2813,2816,2822,2827,2829,2832,2835,2838,2848,2853,2855,2858,2861,2864,2870,2875,2877,2880,2883,2886,2896,2901,2903,2906,2909,2912,2918,2923,2925,2928,2931,2934,2944,2949,2951,2954,2957,2960,2966,2971,2973,2976,2979,2982,2992,2997,2999,3002,3005,3008,3014,3019,3021,3024,3027,3030,3040,3045,3047,3050,3053,3056,3062,3067,3069,3072,3075,3078,3088,3093,3095,3098,3101,3104,3110,3115,3117,3120,3123,3126,3136,3141,3143,3146,3149,3152,3158,3163,3165,3168,3171,3174,3184,3189,3191,3194,3197,3200,3206,3211,3213,3216,3219,3222,3232,3237,3239,3242,3245,3248,3254,3259,3261,3264,3267,3270,3280,3285,3287,3290,3293,3296,3302,3307,3309,3312,3315,3318,3328,3333,3335,3338,3341,3344,3350,3355,3357,3360,3363,3366,3376,3381,3383,3386,3389,3392,3398,3403,3405,3408,3411,3414,3424,3429,3431,3434,3437,3440,3446,3451,3453,3456,3459,3462,3472,3477,3479,3482,3485,3488,3494,3499,3501,3504,3507,3510,3520,3525,3527,3530,3533,3536,3542,3547,3549,3552,3555,3558,3568,3573,3575,3578,3581,3584,3590,3595,3597,3600,3603,3606,3616,3621,3623,3626,3629,3632,3638,3643,3645,3648,3651,3654,3664,3669,3671,3674,3677,3680,3686,3691,3693,3696,3699,3702,3712,3717,3719,3722,3725,3728,3734,3739,3741,3744,3747,3750,3760,3765,3767,3770,3773,3776,3782,3787,3789,3792,3795,3798,3808,3813,3815,3818,3821,3824,3830,3835,3837,3840,3843,3846,3856,3861,3863,3866,3869,3872,3878,3883,3885,3888,3891,3894,3904,3909,3911,3914,3917,3920,3926,3931,3933,3936,3939,3942,3952,3957,3959,3962,3965,3968,3974,3979,3981,3984,3987,3990,4000,4005,4007,4010,4013,4016,4022,4027,4029,4032,4035,4038,4048,4053,4055,4058,4061,4064
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To be honest, I haven't verified my five-dice solution works. I would have to cycle through 840^5 = 418,211,942,400,000 possible dice outcomes, which would take days.
With that, I welcome all questions and comments.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
March 18th, 2024 at 12:39:26 PM
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Quote: Wizard
To be honest, I haven't verified my five-dice solution works. I would have to cycle through 840^5 = 418,211,942,400,000 possible dice outcomes, which would take days.
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What does it mean if a solution works?
(a) must be not result in any ties
(b) must be perfectly fair to all N players
(c) something more ??
Cool problem. Do you think this is a minimal solution or is it just the first solution your algorithm came upon?
Bonus question: Will a 840-side die ever stop rolling?
Note added: I wrote a test program and checking 418,211,942,400,000 possible dice outcomes would take 12 days using one processor.
Last edited by: Mental on Mar 18, 2024
Gambling is a math contest where the score is tracked in dollars. Try not to get a negative score.
March 18th, 2024 at 4:21:57 PM
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Quote: MentalWhat does it mean if a solution works?
(a) must be not result in any ties
(b) must be perfectly fair to all N players
(c) something more ??
Cool problem. Do you think this is a minimal solution or is it just the first solution your algorithm came upon?
Bonus question: Will a 840-side die ever stop rolling?
Note added: I wrote a test program and checking 418,211,942,400,000 possible dice outcomes would take 12 days using one processor.
link to original post
A. The same number can never appear on two different dice.
B. Yes!
C. I don't require this, but the dice should also work for less than the intended number of players. For example, for the 4-player set of dice should work for 2 or 3 players as well. I believe my dice meet this requirement.
Bonus: I never thought of that. It must, otherwise I would make a perpetual motion machine out of it.
Since my post, I wrote a simulator a test the 5-dice case and they seemed to pass.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
March 19th, 2024 at 9:45:10 AM
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Why can't AI create accurate dice?? The design hasn't changed in like 4,000 years....lol
March 19th, 2024 at 2:08:27 PM
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Quote: TigerWuWhy can't AI create accurate dice?? The design hasn't changed in like 4,000 years....lol
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I don't know. My AI porn generator puts body parts in really strange places sometimes.
Last edited by: Wizard on Mar 19, 2024
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
March 23rd, 2024 at 9:41:35 AM
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Quote: WizardQuote: TigerWuWhy can't AI create accurate dice?? The design hasn't changed in like 4,000 years....lol
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I don't know. My AI porn generator puts body parts in really strange places sometimes.
link to original post
Looks like they're in the right spots to me. (Except, doesn't the 2nd girl from the left have two different colors of fingernails?)
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
