Boxes (any arrangement of the digits) data for Massachusetts Lottery The Numbers Game game. Frequency and last draw of non-repeating, doubles, and triples are listed.

# Massachusetts Lottery The Numbers Game Boxes(numbers in any order) Data

 Data updated on Sunday, March 09, 2014 When playing Massachusetts The Numbers Game boxes and combos the order in which the number is drawn doesn't matter. In this case, we have only 705 possible boxes, plus 10 quadrupets; thus a total of 715 box combinations, instead of the 10,000 permutations of straights, will cover all the numbers as box (or combo). It follows that the chance of winning with a The Numbers Game box or a combo play is obviously higher than the chance of winning with a straight play. On this page...

## The Chance of Winning with a MassachusettsThe Numbers Game box (any order).

Since there are 715 possible outcomes, one may be tempted to conclude that the chance is 1 in 715. This is not exactly true since not all boxes have equal chances of winning; The Numbers Game numbers with non-repeating digits have a better chance of winning than numbers with one digit repeated, two digits repeated, or one digit tripled. For example, the number 1234 has more chance of winning than the numbers 1223, 1122, and 1222. The reason is that 1234 covers 24 possible permutations (1234, 1243, 1423, 4123, etc.), while 1223 covers only twelve (1223, 1232, 1322, 3122, etc.), 1122 six (1122, 2211, 1221, 2112, 1212, 2121), and 1222 four (1222, 2122, 2212, 2221).

Consequently, we shall classify all the The Numbers Game numbers into five categories, namely, Non-Repeating numbers, One-Repeated numbers, Dual-Doubles numbers (like 1122), One-Tripled numbers (like 1222), and quadruples. Very often, the first four categories are referred to as 24-way, 12-way, 6-way, 4-way boxes (or combos), respectively. Of the 10000 The Numbers Game numbers, 5040 are non-repeating, 4320 one-repeated, 270 dual-doubles, 360 one-tripled, and 10 quadruples. This means that out of 1000 draws, we should theoretically expect about 504 non-repeating numbers (50.4%), 432 one-repeated (43.2%), 27 dual doubles (2.7%), 36 one-tripled (3.6%), and 1 quadruple (0.1%). Note that one thousand draws is about 2 years and 9 months, if drawings are held once a day; 1 year and 4½ months for bi-daily draws; and about 8 months if drawings are held 4 times a day. The chance of winning with a non-repeat box (or combo), such as the number 1234, is about 1 in 417, while for a one-repeat box it is about 1 in 833; for a dual double number it is 1 in 1667, and for a one-tripled number 1 in 2500. The chance of winning with a quadrupled number is the same as the chance of winning with any other straight number - that is, 1 in 1000.

## MassachusettsThe Numbers Game Box Analysis Results and Summary by Category

There are 210 distinct non-repeating boxes, 360 one-repeated, 45 dual-doubles, and 90 one-tripled boxes. All the possible MassachusettsThe Numbers Game boxes are listed below by category together with the number of times drawn and the number of draws since last appearance (NDSLA). But, prior that we shall list some analysis results to show how the actual data of MassachusettsThe Numbers Game results are close to the theoretical expectations cited above.

Although we cannot comment on how close the actual data are to the theoretical data right at this moment (since all figures are updated after every draw), we were amazed to see a perfect harmony between the two at the time of writing of these pages.

See MassachusettsThe Numbers Game Boxes (Combos) Analysis for a more elaborate analysis of boxes.

MassachusettsThe Numbers Gamewinnig numbers by category
From Saturday, April 10, 1976 to Sunday, March 09, 2014)

• Total number of draws             = 15226
• Number of non-repeats drawn   = 7805 (51.26%)
• Number of one-repeating drawn = 6457 (42.41%)
• Number of dual-doubles drawn   = 404 (2.65%)
• Number of one-tripled drawn     = 550 (3.61%)
• Number of quadruples drawn      = 10 (0.07%)

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Non-repeating Numbers (Total 210)ND = Number of times Drawn, NDSLA = Number of Draws Since Last Appearance

 Number ND NDSLA 0123 43 40 0124 41 269 0125 34 22 0126 38 117 0127 37 437 0128 47 262 0129 39 349 0134 40 18 0135 36 346 0136 29 95 0137 52 230 0138 43 53 0139 37 32 0145 35 490 0146 43 208 0147 44 608 0148 40 436 0149 38 190 0156 33 102 0157 43 6 0158 33 1694 0159 35 2407 0167 33 866 0168 37 202 0169 31 1187 0178 36 384 0179 44 128 0189 47 371 0234 45 228 0235 38 1008 0236 30 212 0237 31 77 0238 39 342 0239 33 298 0245 21 1014 0246 33 313 0247 44 27 0248 37 686 0249 39 101 0256 40 10 0257 44 36 0258 38 411

 Number ND NDSLA 0259 43 451 0267 44 96 0268 40 51 0269 51 125 0278 46 113 0279 38 677 0289 34 457 0345 27 196 0346 32 62 0347 43 1093 0348 28 835 0349 41 28 0356 37 155 0357 46 179 0358 34 929 0359 45 642 0367 39 244 0368 35 233 0369 41 191 0378 38 513 0379 41 521 0389 34 214 0456 39 659 0457 47 142 0458 41 382 0459 35 57 0467 33 395 0468 47 9 0469 37 523 0478 50 310 0479 47 58 0489 42 435 0567 29 272 0568 52 35 0569 25 1154 0578 42 463 0579 41 920 0589 41 75 0678 43 545 0679 32 1761 0689 29 246 0789 37 47

 Number ND NDSLA 1234 37 687 1235 45 1180 1236 38 56 1237 44 151 1238 35 284 1239 38 49 1245 37 972 1246 26 67 1247 33 20 1248 30 629 1249 26 912 1256 28 554 1257 34 98 1258 43 360 1259 38 152 1267 47 676 1268 37 491 1269 47 175 1278 32 2 1279 40 1103 1289 32 11 1345 44 222 1346 41 249 1347 37 87 1348 31 165 1349 38 724 1356 27 1492 1357 37 572 1358 42 63 1359 29 528 1367 36 88 1368 31 24 1369 41 118 1378 39 604 1379 30 217 1389 29 299 1456 32 5 1457 33 844 1458 36 441 1459 32 446 1467 34 199 1468 33 33

 Number ND NDSLA 1469 36 319 1478 39 73 1479 37 505 1489 32 14 1567 32 273 1568 36 1249 1569 34 465 1578 28 278 1579 38 828 1589 34 7 1678 44 103 1679 34 599 1689 35 509 1789 26 667 2345 39 469 2346 46 174 2347 46 25 2348 42 400 2349 25 1355 2356 29 184 2357 37 430 2358 33 425 2359 44 17 2367 38 23 2368 46 171 2369 34 1591 2378 46 227 2379 23 198 2389 26 345 2456 37 768 2457 40 372 2458 51 91 2459 36 205 2467 34 874 2468 41 137 2469 44 41 2478 37 471 2479 26 649 2489 29 163 2567 33 548 2568 34 283 2569 30 200

 Number ND NDSLA 2578 30 81 2579 42 206 2589 30 534 2678 40 126 2679 36 953 2689 41 533 2789 30 38 3456 33 1203 3457 46 331 3458 33 12 3459 32 891 3467 34 330 3468 32 279 3469 40 362 3478 37 176 3479 31 352 3489 31 183 3567 28 150 3568 44 665 3569 47 34 3578 33 192 3579 38 189 3589 42 119 3678 43 122 3679 32 134 3689 40 682 3789 41 26 4567 44 239 4568 34 369 4569 43 376 4578 37 197 4579 50 141 4589 43 147 4678 40 31 4679 42 8 4689 40 131 4789 36 974 5678 31 3 5679 32 575 5689 31 110 5789 32 97 6789 28 417

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One-Repeated (Total 360)ND = Number of times Drawn, NDSLA = Number of Draws Since Last Appearance

 Number ND NDSLA 0012 17 267 0013 15 3466 0014 14 1528 0015 15 216 0016 27 162 0017 15 72 0018 14 187 0019 17 1004 0023 18 2517 0024 25 1028 0025 17 2117 0026 16 875 0027 19 1224 0028 17 738 0029 15 3035 0034 24 83 0035 14 527 0036 22 1490 0037 16 1404 0038 17 488 0039 16 229 0045 14 252 0046 19 439 0047 13 240 0048 17 747 0049 18 3310 0056 21 494 0057 10 811 0058 11 3307 0059 24 563 0067 8 701 0068 22 538 0069 14 1894 0078 23 1374 0079 13 2276 0089 22 276 0112 10 1344 0113 19 486 0114 12 2311 0115 16 37 0116 9 646 0117 20 501 0118 18 3724 0119 26 794 0122 18 156 0133 15 1972 0144 9 802 0155 16 315 0166 18 617 0177 17 476 0188 14 396 0199 13 410 0223 19 2393 0224 19 84 0225 23 16 0226 9 136 0227 18 48 0228 18 596 0229 23 1723 0233 20 1094 0244 13 1535 0255 20 880 0266 15 280 0277 17 1177 0288 18 799 0299 15 1750 0334 13 1621 0335 18 2394 0336 8 4 0337 20 508 0338 25 1024 0339 17 547

 Number ND NDSLA 0344 14 1246 0355 14 745 0366 21 108 0377 17 356 0388 17 1027 0399 19 998 0445 16 1564 0446 24 1295 0447 16 583 0448 15 749 0449 16 170 0455 18 1913 0466 14 816 0477 18 741 0488 22 1089 0499 13 1033 0556 14 1174 0557 19 2675 0558 15 104 0559 18 997 0566 13 3131 0577 20 50 0588 13 727 0599 16 552 0667 24 335 0668 13 867 0669 19 999 0677 19 61 0688 13 836 0699 12 135 0778 23 908 0779 15 225 0788 19 648 0799 16 795 0889 19 379 0899 12 4168 1123 15 414 1124 22 650 1125 14 1774 1126 25 64 1127 21 366 1128 13 1953 1129 20 293 1134 19 1181 1135 22 291 1136 22 683 1137 21 1548 1138 18 585 1139 21 416 1145 12 3658 1146 15 144 1147 8 1105 1148 13 2580 1149 12 1055 1156 18 1273 1157 21 85 1158 11 6038 1159 17 124 1167 24 215 1168 25 780 1169 12 1495 1178 17 2168 1179 17 92 1189 16 1049 1223 20 1499 1224 22 455 1225 26 207 1226 14 1 1227 9 1982 1228 16 1937 1229 18 46 1233 27 481

 Number ND NDSLA 1244 18 830 1255 17 2874 1266 20 994 1277 18 186 1288 14 1754 1299 11 1189 1334 13 777 1335 17 107 1336 27 242 1337 18 959 1338 23 368 1339 20 65 1344 18 277 1355 25 29 1366 13 80 1377 20 985 1388 19 412 1399 19 1647 1445 15 1522 1446 16 2166 1447 17 426 1448 22 3588 1449 15 1285 1455 15 393 1466 18 1572 1477 16 90 1488 27 145 1499 15 1199 1556 21 487 1557 23 855 1558 21 66 1559 22 320 1566 14 1157 1577 12 2751 1588 19 1190 1599 21 1133 1667 15 1001 1668 17 45 1669 24 1030 1677 15 848 1688 21 1717 1699 14 3482 1778 23 955 1779 21 565 1788 13 1092 1799 15 68 1889 17 1898 1899 22 1012 2234 21 275 2235 17 822 2236 18 130 2237 18 2340 2238 15 945 2239 20 1410 2245 18 720 2246 21 601 2247 25 161 2248 20 378 2249 17 351 2256 19 1231 2257 19 281 2258 19 459 2259 17 39 2267 16 489 2268 16 1229 2269 16 195 2278 24 381 2279 13 3468 2289 17 543 2334 18 13 2335 7 1126 2336 19 445

 Number ND NDSLA 2337 11 1102 2338 13 431 2339 26 718 2344 15 204 2355 18 518 2366 13 1185 2377 18 1316 2388 20 612 2399 16 292 2445 21 295 2446 19 495 2447 16 178 2448 18 771 2449 19 94 2455 20 2436 2466 25 168 2477 22 43 2488 24 21 2499 16 154 2556 14 1366 2557 12 433 2558 10 296 2559 14 792 2566 17 203 2577 24 149 2588 23 164 2599 15 515 2667 12 566 2668 25 398 2669 24 19 2677 21 339 2688 19 690 2699 17 3541 2778 17 858 2779 19 1485 2788 17 1579 2799 30 182 2889 15 1542 2899 21 1128 3345 21 394 3346 17 60 3347 20 1338 3348 20 15 3349 14 468 3356 22 115 3357 16 42 3358 17 1173 3359 12 3052 3367 14 264 3368 19 1970 3369 17 1057 3378 10 1570 3379 19 2290 3389 19 86 3445 11 895 3446 21 211 3447 21 1653 3448 16 2476 3449 22 407 3455 20 201 3466 16 429 3477 17 380 3488 18 702 3499 14 909 3556 24 1196 3557 17 1066 3558 19 1111 3559 14 243 3566 15 79 3577 14 231 3588 19 238 3599 19 535

 Number ND NDSLA 3667 20 306 3668 20 255 3669 26 235 3677 21 482 3688 23 1586 3699 21 502 3778 9 1770 3779 15 160 3788 22 1461 3799 21 862 3889 19 473 3899 20 1137 4456 19 662 4457 21 180 4458 12 1067 4459 33 748 4467 23 453 4468 22 1869 4469 15 1274 4478 19 1202 4479 15 263 4489 21 1284 4556 16 388 4557 24 892 4558 15 1544 4559 19 52 4566 15 303 4577 19 308 4588 20 3150 4599 23 274 4667 18 1447 4668 24 694 4669 22 348 4677 25 742 4688 25 361 4699 17 427 4778 15 1303 4779 17 854 4788 23 584 4799 17 146 4889 17 287 4899 11 2392 5567 19 1426 5568 19 209 5569 14 1062 5578 22 462 5579 21 579 5589 20 0 5667 24 2655 5668 16 223 5669 23 112 5677 17 312 5688 19 59 5699 17 1651 5778 27 254 5779 11 5279 5788 19 132 5799 16 580 5889 21 948 5899 25 219 6678 15 923 6679 22 413 6689 17 261 6778 20 1064 6779 23 597 6788 17 337 6799 20 1440 6889 16 1804 6899 12 286 7789 28 1005 7889 11 1536 7899 25 120

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Dual-Doubles (Total 45)ND = Number of times Drawn, NDSLA = Number of Draws Since Last Appearance

 Number ND NDSLA 0011 11 428 0022 8 193 0033 14 399 0044 8 30 0055 7 562 0066 9 2370 0077 12 3154 0088 7 705 0099 8 2692

 Number ND NDSLA 1122 5 7371 1133 13 680 1144 9 1277 1155 10 173 1166 5 3606 1177 6 224 1188 5 3254 1199 7 6741 2233 10 1241

 Number ND NDSLA 2244 7 340 2255 7 1312 2266 7 699 2277 13 2438 2288 9 767 2299 11 236 3344 12 166 3355 7 1988 3366 11 2788

 Number ND NDSLA 3377 6 1826 3388 8 1959 3399 10 1334 4455 10 357 4466 11 641 4477 8 89 4488 7 2854 4499 13 188 5566 6 1209

 Number ND NDSLA 5577 8 1080 5588 8 1612 5599 12 882 6677 8 619 6688 14 390 6699 11 44 7788 9 127 7799 8 7854 8899 9 2376

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One-Tripled (Total 90)ND = Number of times Drawn, NDSLA = Number of Draws Since Last Appearance

 Number ND NDSLA 0001 5 271 0002 6 1692 0003 6 1289 0004 3 4853 0005 3 6839 0006 6 121 0007 5 5481 0008 6 963 0009 10 139 0111 4 1679 0222 7 3144 0333 5 2474 0444 4 7273 0555 1 153 0666 4 7882 0777 15 2578 0888 9 1152 0999 2 2849

 Number ND NDSLA 1112 7 4814 1113 6 843 1114 7 2072 1115 2 9403 1116 5 421 1117 5 2361 1118 4 4637 1119 7 1051 1222 8 818 1333 9 2466 1444 7 1878 1555 10 1074 1666 4 1778 1777 9 169 1888 5 3410 1999 8 9372 2223 5 3581 2224 9 2247

 Number ND NDSLA 2225 9 1892 2226 4 4944 2227 4 250 2228 4 365 2229 5 2682 2333 6 8309 2444 9 55 2555 4 9178 2666 4 1244 2777 5 10293 2888 7 282 2999 7 2801 3334 4 2173 3335 10 2144 3336 5 2198 3337 6 1719 3338 11 245 3339 6 4225

 Number ND NDSLA 3444 6 1557 3555 3 10298 3666 4 5461 3777 4 7592 3888 3 70 3999 5 5275 4445 8 1889 4446 7 647 4447 8 1501 4448 8 419 4449 8 4338 4555 3 363 4666 8 2953 4777 3 8827 4888 14 2001 4999 8 466 5556 6 3002 5557 6 1470

 Number ND NDSLA 5558 3 3007 5559 7 2162 5666 7 1547 5777 6 651 5888 6 756 5999 6 2425 6667 5 3267 6668 3 385 6669 10 105 6777 3 2694 6888 8 1208 6999 8 1543 7778 6 2822 7779 3 8584 7888 7 3019 7999 9 4795 8889 8 1593 8999 5 1453

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Quadruples (Total 10)ND = Number of times Drawn, NDSLA = Number of Draws Since Last Appearance

 Number ND NDSLA 0000 0 - 1111 2 4177 2222 1 499 3333 1 7737 4444 2 1123 5555 4 461 6666 0 - 7777 0 - 8888 0 - 9999 0 -

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