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Introduction

In any Pick 3 game, there are 3 digit positions, with each position containing a digit from 0 to 9.  If one were to list all of the possible combinations of digits in each of the three positions, there would be a total of 1,000 different number combinations.  Each of these 1,000 possibilities is called a straight combination.  Thus, if you were to place one straight Pick 3 wager, your odds of winning would be 1 in 1,000.

However, another way to wager in Pick 3 is called a box wager, in which you can win if your combination matches the 3 digits drawn in any order.  If you wager on 823 boxed, you would win if any of the following combinations were drawn: 823, 832, 283, 382, 238, or 328.  If one were to list all of the unique box combinations in the Pick 3 game, there would be a total of 220 different number combinations.

The odds of winning a box wager are not a simple calculation like it is for a straight wager.  The odds depend on the number of unique digits in the combination, because that affects how many possible combinations can be matched.  In the Pick 3 game, there are three different types of box combinations:

  • Single (6-way): Each of the three positions has a different digit.  For example, 937.  Each combination of this type has 6 different box combinations, so your odds of winning by playing one “single” box combination would be approximately 1 in 167.
  • Double (3-way): Two of the three positions have the same digit, and the third digit is different.  For example, 662.  Each combination of this type has 3 different box combinations, so your odds of winning by playing one “double” box combination would be approximately 1 in 333.
  • Triple: Each of the three positions has the same digit.  For example, 111.  Because each triple is unique, your odds of winning by playing one “triple” combination would be 1 in 1,000 — the same odds as playing a straight.  (A triple is also known as a straight, in fact.)

Below you can find a listing of all the single, double, and triple combinations presented in two ways:  first, as a listing of all straight combinations, and second, as a listing of the unique box combinations.  The triples are only presented once since they are all unique to start with. 

All Triples:  10 straight/box combinations
000, 111, 222, 333, 444, 555, 666, 777, 888, 999

Singles (6-way combinations)

Unique Singles:  120 box combinations
012, 013, 014, 015, 016, 017, 018, 019, 023, 024, 025, 026, 027, 028, 029, 034, 035, 036, 037, 038, 039, 045, 046, 047, 048, 049, 056, 057, 058, 059, 067, 068, 069, 078, 079, 089, 123, 124, 125, 126, 127, 128, 129, 134, 135, 136, 137, 138, 139, 145, 146, 147, 148, 149, 156, 157, 158, 159, 167, 168, 169, 178, 179, 189, 234, 235, 236, 237, 238, 239, 245, 246, 247, 248, 249, 256, 257, 258, 259, 267, 268, 269, 278, 279, 289, 345, 346, 347, 348, 349, 356, 357, 358, 359, 367, 368, 369, 378, 379, 389, 456, 457, 458, 459, 467, 468, 469, 478, 479, 489, 567, 568, 569, 578, 579, 589, 678, 679, 689, 789
All Singles:  720 straight combinations
012, 021, 102, 120, 201, 210, 013, 031, 103, 130, 301, 310, 014, 041, 104, 140, 401, 410, 015, 051, 105, 150, 501, 510, 016, 061, 106, 160, 601, 610, 017, 071, 107, 170, 701, 710, 018, 081, 108, 180, 801, 810, 019, 091, 109, 190, 901, 910, 023, 032, 203, 230, 302, 320, 024, 042, 204, 240, 402, 420, 025, 052, 205, 250, 502, 520, 026, 062, 206, 260, 602, 620, 027, 072, 207, 270, 702, 720, 028, 082, 208, 280, 802, 820, 029, 092, 209, 290, 902, 920, 034, 043, 304, 340, 403, 430, 035, 053, 305, 350, 503, 530, 036, 063, 306, 360, 603, 630, 037, 073, 307, 370, 703, 730, 038, 083, 308, 380, 803, 830, 039, 093, 309, 390, 903, 930, 045, 054, 405, 450, 504, 540, 046, 064, 406, 460, 604, 640, 047, 074, 407, 470, 704, 740, 048, 084, 408, 480, 804, 840, 049, 094, 409, 490, 904, 940, 056, 065, 506, 560, 605, 650, 057, 075, 507, 570, 705, 750, 058, 085, 508, 580, 805, 850, 059, 095, 509, 590, 905, 950, 067, 076, 607, 670, 706, 760, 068, 086, 608, 680, 806, 860, 069, 096, 609, 690, 906, 960, 078, 087, 708, 780, 807, 870, 079, 097, 709, 790, 907, 970, 089, 098, 809, 890, 908, 980, 123, 132, 213, 231, 312, 321, 124, 142, 214, 241, 412, 421, 125, 152, 215, 251, 512, 521, 126, 162, 216, 261, 612, 621, 127, 172, 217, 271, 712, 721, 128, 182, 218, 281, 812, 821, 129, 192, 219, 291, 912, 921, 134, 143, 314, 341, 413, 431, 135, 153, 315, 351, 513, 531, 136, 163, 316, 361, 613, 631, 137, 173, 317, 371, 713, 731, 138, 183, 318, 381, 813, 831, 139, 193, 319, 391, 913, 931, 145, 154, 415, 451, 514, 541, 146, 164, 416, 461, 614, 641, 147, 174, 417, 471, 714, 741, 148, 184, 418, 481, 814, 841, 149, 194, 419, 491, 914, 941, 156, 165, 516, 561, 615, 651, 157, 175, 517, 571, 715, 751, 158, 185, 518, 581, 815, 851, 159, 195, 519, 591, 915, 951, 167, 176, 617, 671, 716, 761, 168, 186, 618, 681, 816, 861, 169, 196, 619, 691, 916, 961, 178, 187, 718, 781, 817, 871, 179, 197, 719, 791, 917, 971, 189, 198, 819, 891, 918, 981, 234, 243, 324, 342, 423, 432, 235, 253, 325, 352, 523, 532, 236, 263, 326, 362, 623, 632, 237, 273, 327, 372, 723, 732, 238, 283, 328, 382, 823, 832, 239, 293, 329, 392, 923, 932, 245, 254, 425, 452, 524, 542, 246, 264, 426, 462, 624, 642, 247, 274, 427, 472, 724, 742, 248, 284, 428, 482, 824, 842, 249, 294, 429, 492, 924, 942, 256, 265, 526, 562, 625, 652, 257, 275, 527, 572, 725, 752, 258, 285, 528, 582, 825, 852, 259, 295, 529, 592, 925, 952, 267, 276, 627, 672, 726, 762, 268, 286, 628, 682, 826, 862, 269, 296, 629, 692, 926, 962, 278, 287, 728, 782, 827, 872, 279, 297, 729, 792, 927, 972, 289, 298, 829, 892, 928, 982, 345, 354, 435, 453, 534, 543, 346, 364, 436, 463, 634, 643, 347, 374, 437, 473, 734, 743, 348, 384, 438, 483, 834, 843, 349, 394, 439, 493, 934, 943, 356, 365, 536, 563, 635, 653, 357, 375, 537, 573, 735, 753, 358, 385, 538, 583, 835, 853, 359, 395, 539, 593, 935, 953, 367, 376, 637, 673, 736, 763, 368, 386, 638, 683, 836, 863, 369, 396, 639, 693, 936, 963, 378, 387, 738, 783, 837, 873, 379, 397, 739, 793, 937, 973, 389, 398, 839, 893, 938, 983, 456, 465, 546, 564, 645, 654, 457, 475, 547, 574, 745, 754, 458, 485, 548, 584, 845, 854, 459, 495, 549, 594, 945, 954, 467, 476, 647, 674, 746, 764, 468, 486, 648, 684, 846, 864, 469, 496, 649, 694, 946, 964, 478, 487, 748, 784, 847, 874, 479, 497, 749, 794, 947, 974, 489, 498, 849, 894, 948, 984, 567, 576, 657, 675, 756, 765, 568, 586, 658, 685, 856, 865, 569, 596, 659, 695, 956, 965, 578, 587, 758, 785, 857, 875, 579, 597, 759, 795, 957, 975, 589, 598, 859, 895, 958, 985, 678, 687, 768, 786, 867, 876, 679, 697, 769, 796, 967, 976, 689, 698, 869, 896, 968, 986, 789, 798, 879, 897, 978, 987 

Doubles (3-way combinations)

Unique Doubles:  90 box combinations
001, 002, 003, 004, 005, 006, 007, 008, 009, 011, 022, 033, 044, 055, 066, 077, 088, 099, 112, 113, 114, 115, 116, 117, 118, 119, 122, 133, 144, 155, 166, 177, 188, 199, 223, 224, 225, 226, 227, 228, 229, 233, 244, 255, 266, 277, 288, 299, 334, 335, 336, 337, 338, 339, 344, 355, 366, 377, 388, 399, 445, 446, 447, 448, 449, 455, 466, 477, 488, 499, 556, 557, 558, 559, 566, 577, 588, 599, 667, 668, 669, 677, 688, 699, 778, 779, 788, 799, 889, 899
All Doubles:  270 straight combinations
001, 010, 100, 002, 020, 200, 003, 030, 300, 004, 040, 400, 005, 050, 500, 006, 060, 600, 007, 070, 700, 008, 080, 800, 009, 090, 900, 011, 101, 110, 022, 202, 220, 033, 303, 330, 044, 404, 440, 055, 505, 550, 066, 606, 660, 077, 707, 770, 088, 808, 880, 099, 909, 990, 112, 121, 211, 113, 131, 311, 114, 141, 411, 115, 151, 511, 116, 161, 611, 117, 171, 711, 118, 181, 811, 119, 191, 911, 122, 212, 221, 133, 313, 331, 144, 414, 441, 155, 515, 551, 166, 616, 661, 177, 717, 771, 188, 818, 881, 199, 919, 991, 223, 232, 322, 224, 242, 422, 225, 252, 522, 226, 262, 622, 227, 272, 722, 228, 282, 822, 229, 292, 922, 233, 323, 332, 244, 424, 442, 255, 525, 552, 266, 626, 662, 277, 727, 772, 288, 828, 882, 299, 929, 992, 334, 343, 433, 335, 353, 533, 336, 363, 633, 337, 373, 733, 338, 383, 833, 339, 393, 933, 344, 434, 443, 355, 535, 553, 366, 636, 663, 377, 737, 773, 388, 838, 883, 399, 939, 993, 445, 454, 544, 446, 464, 644, 447, 474, 744, 448, 484, 844, 449, 494, 944, 455, 545, 554, 466, 646, 664, 477, 747, 774, 488, 848, 884, 499, 949, 994, 556, 565, 655, 557, 575, 755, 558, 585, 855, 559, 595, 955, 566, 656, 665, 577, 757, 775, 588, 858, 885, 599, 959, 995, 667, 676, 766, 668, 686, 866, 669, 696, 966, 677, 767, 776, 688, 868, 886, 699, 969, 996, 778, 787, 877, 779, 797, 977, 788, 878, 887, 799, 979, 997, 889, 898, 988, 899, 989, 998