Pick 3 Combinations Chart

Show 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 123 box, you would win if any of the following combinations were drawn: 123, 132, 213, 312, 231, or 321. 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, 123. 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, 112. 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.

Singles (6-way combinations)

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

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

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

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

Doubles (3-way combinations)

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

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

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

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

Triples

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

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Pick 3 Combinations Chart

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Singles (6-way combinations)

Doubles (3-way combinations)

Triples