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# Pick 3 Root Sums Chart

## Introduction

Pick 3 games are known by a variety of names, including Cash 3, Play 3, Daily 3, Pick 3, Numbers, Daily Number, Daily Game, DC-3, Pega 3, and La Quotidienne 3, but they are all basically played in the same manner.

The "root sum" of a Pick 3 combination is an extension of the sums principle: an addition of a combination's three digits.  However, unlike a regular sum, if the sum is more than one digit in length, the sum's digits are added — and added again if necessary — until the resulting sum is one digit in length.

For example, the root sum of 123 is 6.  That is calculated by adding the three digits of the combination (1 + 2 + 3).  Since the sum is one digit in length, we can stop right there.

In another example, the root sum of 757 is 1.  That is calculated by adding the three digits of the combination (7 + 5 + 7) to get 19, which is more than one digit in length, so we need to keep going.  We add the 1 + 9, and we get 10, which is still more than one digit in length.  So we add the 1 + 0, and we get 1, which is one digit in length, so we have arrived at the root sum of 1.

Choosing numbers based on root sums is distinctly different from using regular sums because of the even distribution of numbers, unlike regular sums, which form a "bell curve" distribution of numbers.  Root sums analysis tends to make biases more clearly apparent.

Below you can find a listing of all the possible root sums from 0 to 9, first presented with all the straight combinations for each root sum, and then with just the unique box combinations for each root sum.

## Root Sums with Straight Combinations

"Quant" is the number of straight combinations for each root sum.

Root SumQuantStraight Combinations
01000
1111001, 010, 019, 028, 037, 046, 055, 064, 073, 082, 091, 100, 109, 118, 127, 136, 145, 154, 163, 172, 181, 190, 199, 208, 217, 226, 235, 244, 253, 262, 271, 280, 289, 298, 307, 316, 325, 334, 343, 352, 361, 370, 379, 388, 397, 406, 415, 424, 433, 442, 451, 460, 469, 478, 487, 496, 505, 514, 523, 532, 541, 550, 559, 568, 577, 586, 595, 604, 613, 622, 631, 640, 649, 658, 667, 676, 685, 694, 703, 712, 721, 730, 739, 748, 757, 766, 775, 784, 793, 802, 811, 820, 829, 838, 847, 856, 865, 874, 883, 892, 901, 910, 919, 928, 937, 946, 955, 964, 973, 982, 991
2111002, 011, 020, 029, 038, 047, 056, 065, 074, 083, 092, 101, 110, 119, 128, 137, 146, 155, 164, 173, 182, 191, 200, 209, 218, 227, 236, 245, 254, 263, 272, 281, 290, 299, 308, 317, 326, 335, 344, 353, 362, 371, 380, 389, 398, 407, 416, 425, 434, 443, 452, 461, 470, 479, 488, 497, 506, 515, 524, 533, 542, 551, 560, 569, 578, 587, 596, 605, 614, 623, 632, 641, 650, 659, 668, 677, 686, 695, 704, 713, 722, 731, 740, 749, 758, 767, 776, 785, 794, 803, 812, 821, 830, 839, 848, 857, 866, 875, 884, 893, 902, 911, 920, 929, 938, 947, 956, 965, 974, 983, 992
3111003, 012, 021, 030, 039, 048, 057, 066, 075, 084, 093, 102, 111, 120, 129, 138, 147, 156, 165, 174, 183, 192, 201, 210, 219, 228, 237, 246, 255, 264, 273, 282, 291, 300, 309, 318, 327, 336, 345, 354, 363, 372, 381, 390, 399, 408, 417, 426, 435, 444, 453, 462, 471, 480, 489, 498, 507, 516, 525, 534, 543, 552, 561, 570, 579, 588, 597, 606, 615, 624, 633, 642, 651, 660, 669, 678, 687, 696, 705, 714, 723, 732, 741, 750, 759, 768, 777, 786, 795, 804, 813, 822, 831, 840, 849, 858, 867, 876, 885, 894, 903, 912, 921, 930, 939, 948, 957, 966, 975, 984, 993
4111004, 013, 022, 031, 040, 049, 058, 067, 076, 085, 094, 103, 112, 121, 130, 139, 148, 157, 166, 175, 184, 193, 202, 211, 220, 229, 238, 247, 256, 265, 274, 283, 292, 301, 310, 319, 328, 337, 346, 355, 364, 373, 382, 391, 400, 409, 418, 427, 436, 445, 454, 463, 472, 481, 490, 499, 508, 517, 526, 535, 544, 553, 562, 571, 580, 589, 598, 607, 616, 625, 634, 643, 652, 661, 670, 679, 688, 697, 706, 715, 724, 733, 742, 751, 760, 769, 778, 787, 796, 805, 814, 823, 832, 841, 850, 859, 868, 877, 886, 895, 904, 913, 922, 931, 940, 949, 958, 967, 976, 985, 994
5111005, 014, 023, 032, 041, 050, 059, 068, 077, 086, 095, 104, 113, 122, 131, 140, 149, 158, 167, 176, 185, 194, 203, 212, 221, 230, 239, 248, 257, 266, 275, 284, 293, 302, 311, 320, 329, 338, 347, 356, 365, 374, 383, 392, 401, 410, 419, 428, 437, 446, 455, 464, 473, 482, 491, 500, 509, 518, 527, 536, 545, 554, 563, 572, 581, 590, 599, 608, 617, 626, 635, 644, 653, 662, 671, 680, 689, 698, 707, 716, 725, 734, 743, 752, 761, 770, 779, 788, 797, 806, 815, 824, 833, 842, 851, 860, 869, 878, 887, 896, 905, 914, 923, 932, 941, 950, 959, 968, 977, 986, 995
6111006, 015, 024, 033, 042, 051, 060, 069, 078, 087, 096, 105, 114, 123, 132, 141, 150, 159, 168, 177, 186, 195, 204, 213, 222, 231, 240, 249, 258, 267, 276, 285, 294, 303, 312, 321, 330, 339, 348, 357, 366, 375, 384, 393, 402, 411, 420, 429, 438, 447, 456, 465, 474, 483, 492, 501, 510, 519, 528, 537, 546, 555, 564, 573, 582, 591, 600, 609, 618, 627, 636, 645, 654, 663, 672, 681, 690, 699, 708, 717, 726, 735, 744, 753, 762, 771, 780, 789, 798, 807, 816, 825, 834, 843, 852, 861, 870, 879, 888, 897, 906, 915, 924, 933, 942, 951, 960, 969, 978, 987, 996
7111007, 016, 025, 034, 043, 052, 061, 070, 079, 088, 097, 106, 115, 124, 133, 142, 151, 160, 169, 178, 187, 196, 205, 214, 223, 232, 241, 250, 259, 268, 277, 286, 295, 304, 313, 322, 331, 340, 349, 358, 367, 376, 385, 394, 403, 412, 421, 430, 439, 448, 457, 466, 475, 484, 493, 502, 511, 520, 529, 538, 547, 556, 565, 574, 583, 592, 601, 610, 619, 628, 637, 646, 655, 664, 673, 682, 691, 700, 709, 718, 727, 736, 745, 754, 763, 772, 781, 790, 799, 808, 817, 826, 835, 844, 853, 862, 871, 880, 889, 898, 907, 916, 925, 934, 943, 952, 961, 970, 979, 988, 997
8111008, 017, 026, 035, 044, 053, 062, 071, 080, 089, 098, 107, 116, 125, 134, 143, 152, 161, 170, 179, 188, 197, 206, 215, 224, 233, 242, 251, 260, 269, 278, 287, 296, 305, 314, 323, 332, 341, 350, 359, 368, 377, 386, 395, 404, 413, 422, 431, 440, 449, 458, 467, 476, 485, 494, 503, 512, 521, 530, 539, 548, 557, 566, 575, 584, 593, 602, 611, 620, 629, 638, 647, 656, 665, 674, 683, 692, 701, 710, 719, 728, 737, 746, 755, 764, 773, 782, 791, 800, 809, 818, 827, 836, 845, 854, 863, 872, 881, 890, 899, 908, 917, 926, 935, 944, 953, 962, 971, 980, 989, 998
9111009, 018, 027, 036, 045, 054, 063, 072, 081, 090, 099, 108, 117, 126, 135, 144, 153, 162, 171, 180, 189, 198, 207, 216, 225, 234, 243, 252, 261, 270, 279, 288, 297, 306, 315, 324, 333, 342, 351, 360, 369, 378, 387, 396, 405, 414, 423, 432, 441, 450, 459, 468, 477, 486, 495, 504, 513, 522, 531, 540, 549, 558, 567, 576, 585, 594, 603, 612, 621, 630, 639, 648, 657, 666, 675, 684, 693, 702, 711, 720, 729, 738, 747, 756, 765, 774, 783, 792, 801, 810, 819, 828, 837, 846, 855, 864, 873, 882, 891, 900, 909, 918, 927, 936, 945, 954, 963, 972, 981, 990, 999

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## Root Sums with Box Combinations

"Quant" is the number of box combinations for each root sum.

Root SumQuantBox Combinations
01000
124001, 019, 028, 037, 046, 055, 118, 127, 136, 145, 199, 226, 235, 244, 289, 334, 379, 388, 469, 478, 559, 568, 577, 667
224002, 011, 029, 038, 047, 056, 119, 128, 137, 146, 155, 227, 236, 245, 299, 335, 344, 389, 479, 488, 569, 578, 668, 677
325003, 012, 039, 048, 057, 066, 111, 129, 138, 147, 156, 228, 237, 246, 255, 336, 345, 399, 444, 489, 579, 588, 669, 678, 777
424004, 013, 022, 049, 058, 067, 112, 139, 148, 157, 166, 229, 238, 247, 256, 337, 346, 355, 445, 499, 589, 679, 688, 778
524005, 014, 023, 059, 068, 077, 113, 122, 149, 158, 167, 239, 248, 257, 266, 338, 347, 356, 446, 455, 599, 689, 779, 788
625006, 015, 024, 033, 069, 078, 114, 123, 159, 168, 177, 222, 249, 258, 267, 339, 348, 357, 366, 447, 456, 555, 699, 789, 888
724007, 016, 025, 034, 079, 088, 115, 124, 133, 169, 178, 223, 259, 268, 277, 349, 358, 367, 448, 457, 466, 556, 799, 889
824008, 017, 026, 035, 044, 089, 116, 125, 134, 179, 188, 224, 233, 269, 278, 359, 368, 377, 449, 458, 467, 557, 566, 899
925009, 018, 027, 036, 045, 099, 117, 126, 135, 144, 189, 225, 234, 279, 288, 333, 369, 378, 459, 468, 477, 558, 567, 666, 999

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## Odds of Root Sum Being Drawn

The odds below reflect the approximate odds of that a particular root sum will be drawn during any given Pick 3 drawing.

Root SumOdds of Root Sum Being Drawn
01 in 1,000
11 in 9.01
21 in 9.01
31 in 9.01
41 in 9.01
51 in 9.01
61 in 9.01
71 in 9.01
81 in 9.01
91 in 9.01

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