Information of 4D lottery

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Analysis of 4-digit Lottery Games

The analysis of 4-digit games involves the analysis of individual digits, pairs, sums, the numbers themselves in exact order (straight), numbers in any order (boxes), and so on.
The purpose of 4-digit game analysis is to determine the most and least frequently drawn numbers, digits, pairs, etc., and to identify late entities in order to predict the winning numbers.

Such analysis calls for the actual statistics of the drawn number which are available at different web sites.

Groupping and probabilities of 4-Digit Games

Each one of the 10000 numbers in 4-digit lottery games have equal chance of being drawn at any given time, therefore, the chance of winning with one selected number in exact order (straight) is 1 in 10,000.
In mathamatical terms, we say the probability of winning is 0.0001 or 0.01%.
On the other hand, when playing boxes and combos (any order) of a 4-digit game, the order in which the number is drawn doesn't matter, therefore instead of 10,000 possibilities we have only 715.
In this later case, the numbers 1122,2211, 1221, 2112, 1212, 2121, for example, can be represented by only one number - 1122.
For this reason, the chance of winning with a box or a combo play is obviously higher than the chance of winning with a straight play.
Since there are 715 possible outcomes, one may be tempted to conclude that the chance winning in a box is 1 in 715.


This is not exactly true since not all boxes have equal chances of winning; numbers with non-repeating digits have a better chance of winning than numbers with one digit repeated, two digits repeated, and one digit tripled. For example, the number 1234 has a better chance of winning than the number 1122, since 1234 covers 24 possible permutations (thus the name 24-way box), while 1122 covers only the six shown above.


Consequently, we shall classify all the 4-digit numbers into five groups, namely, non-repeating numbers, doubles (one-repeating) numbers, dual-doubles (two-repeating), triples (one-tripled) and quadruplets (all four identical).



Very often, the first four groups are referred to as 24-way, 12-way, 6-way, and 4-way boxes (or combos), respectively.


Of the 10,000 4-digit numbers 5040 are non-repeating, 4320 one-repeating (doubles), 270 two-repeating (dual-doubles), 360 one-tripled, and 10 quadruples.
Since a non-repeating number has 23 more siblings, we can divide 5040 by 24 to obtain 210 distinct non-reapeating numbers.
Similarly, there are 4320/12=360 distinct one-repeating numbers, 270/6=45 distinct dual-doubles, 360/4=90 distinct triples.
The following table and figures summarize the foregoing facts and the probability of winning.
Group name and aliases How many 4-dig Numbers fall into this group How many distinct members of the group odds of winning with a number in the group Probability of a number drawn to be in the goup
Non-repeating (24-way) 5040 210 1:417 50.40%
One-repeating (12-way) (Doubles) 4320 360 1:833 43.20%
Two-repeating (6-way) (Dual-Doubles) 270 45 1:1667 2.70%
One-tripled (4-way) (triples) 360 90 1:2500 3.60%
Quadruples 10 10 1:10,000 0.1%

For instance, if you play 1234, 1122, and 0000, the chance of winning with these numbers in any arrangement are 1 in 417, 1 in 1,667, and 1 in 10,000, respectively.

Sum of Digits of 4-Digit Games

The sum
of the 4 digits of the lottery games ranges from 0 to 36. The digits of the
number 0000 sum up to 0, and that of 9999 sum up to 36, the rest lie in between.


Well over 50% of 4-digit numbers have a sum between 14 and 22, it is
therefore not surprising to see winning numbers with sums 14-22 drawn every
other day.



List if all the 37 possible sums and the
corresponding distinct 4-digit numbers.
SumHow many have this sumList of distinct boxes having this sumOdds of winning with the sumProbability of the sum to be drawn

0	1	0000	1:10000	0.01%
1	4	0001	1:2500	0.04%
2	10	0002,0011	1:1000	0.1%
3	20	0003,0012,0111	1:500	0.2%
4	35	0004,0013,0022,0112,1111	1:286	0.35%
5	56	0005,0014,0023,0113,0122,1112	1:179	0.56%
6	84	0006,0015,0024,0033,0114,0123,0222,1113,1122	1:119	0.84%
7	120	0007,0016,0025,0034,0115,0124,0133,0223,1114,1123, 1222	1:83	1.2%
8	165	0008,0017,0026,0035,0044,0116,0125,0134,0224,0233, 1115,1124, 1133,1223,2222	1:61	1.65%
9	220	0009,0018,0027,0036,0045,0117,0126,0135,0144,0225, 0234,0333, 1116,1125,1134,1224,1233,2223	1:45	2.2%
10	282	0019,0028,0037,0046,0055,0118,0127,0136,0145,0226, 0235,0244, 0334,1117,1126,1135,1144,1225,1234,1333,2224,2233	1:35	2.82%
11	348	0029,0038,0047,0056,0119,0128,0137,0146,0155,0227, 0236,0245, 0335,0344,1118,1127,1136,1145,1226,1235,1244,1334, 2225,2234, 2333	1:29	3.48%
12	415	0039,0048,0057,0066,0129,0138,0147,0156,0228,0237, 0246,0255, 0336,0345,0444,1119,1128,1137,1146,1155,1227,1236, 1245,1335, 1344,2226,2235,2244,2334,3333	1:24	4.15%
13	480	0049,0058,0067,0139,0148,0157,0166,0229,0238,0247, 0256,0337, 0346,0355,0445,1129,1138,1147,1156,1228,1237,1246, 1255,1336, 1345,1444,2227,2236,2245,2335,2344,3334	1:21	4.80%
14	540	0059,0068,0077,0149,0158,0167,0239,0248,0257,0266, 0338,0347, 0356,0446,0455,1139,1148,1157,1166,1229,1238,1247, 1256,1337, 1346,1355,1445,2228,2237,2246,2255,2336,2345,2444, 3335,3344	1:19	5.40%
15	592	0069,0078,0159,0168,0177,0249,0258,0267,0339,0348, 0357,0366, 0447,0456,0555,1149,1158,1167,1239,1248,1257,1266, 1338,1347, 1356,1446,1455,2229,2238,2247,2256,2337,2346,2355, 2445,3336, 3345,3444	1:17	5.92%
16	633	0079,0088,0169,0178,0259,0268,0277,0349,0358,0367, 0448,0457, 0466,0556,1159,1168,1177,1249,1258,1267,1339,1348, 1357,1366, 1447,1456,1555,2239,2248,2257,2266,2338,2347,2356, 2446,2455, 3337,3346,3355,3445,4444	1:16	6.33%
17	660	0089,0179,0188,0269,0278,0359,0368,0377,0449,0458, 0467,0557, 0566,1169,1178,1259,1268,1277,1349,1358,1367,1448, 1457,1466, 1556,2249,2258,2267,2339,2348,2357,2366,2447,2456, 2555,3338, 3347,3356,3446,3455,4445	1:15	6.60%
18	670	0099,0189,0279,0288,0369,0378,0459,0468,0477,0558, 0567,0666, 1179,1188,1269,1278,1359,1368,1377,1449,1458,1467, 1557,1566, 2259,2268,2277,2349,2358,2367,2448,2457,2466,2556, 3339,3348, 3357,3366,3447,3456,3555,4446,4455	1:15	6.70%
19	660	0199,0289,0379,0388,0469,0478,0559,0568,0577,0667, 1189,1279, 1288,1369,1378,1459,1468,1477,1558,1567,1666,2269, 2278,2359, 2368,2377,2449,2458,2467,2557,2566,3349,3358,3367, 3448,3457, 3466,3556,4447,4456,4555	1:15	6.60%
20	633	0299,0389,0479,0488,0569,0578,0668,0677,1199,1289, 1379,1388, 1469,1478,1559,1568,1577,1667,2279,2288,2369,2378, 2459,2468, 2477,2558,2567,2666,3359,3368,3377,3449,3458,3467, 3557,3566, 4448,4457,4466,4556,5555	1:16	6.33%
21	592	0399,0489,0579,0588,0669,0678,0777,1299,1389,1479, 1488,1569, 1578,1668,1677,2289,2379,2388,2469,2478,2559,2568, 2577,2667, 3369,3378,3459,3468,3477,3558,3567,3666,4449,4458, 4467,4557, 4566,5556	1:17	5.92%
22	540	0499,0589,0679,0688,0778,1399,1489,1579,1588,1669, 1678,1777, 2299,2389,2479,2488,2569,2578,2668,2677,3379,3388, 3469,3478, 3559,3568,3577,3667,4459,4468,4477,4558,4567,4666, 5557,5566	1:19	5.40%
23	480	0599,0689,0779,0788,1499,1589,1679,1688,1778,2399, 2489,2579, 2588,2669,2678,2777,3389,3479,3488,3569,3578,3668, 3677,4469, 4478,4559,4568,4577,4667,5558,5567,5666	1:21	4.80%
24	415	0699,0789,0888,1599,1689,1779,1788,2499,2589,2679, 2688,2778, 3399,3489,3579,3588,3669,3678,3777,4479,4488,4569, 4578,4668, 4677,5559,5568,5577,5667,6666	1:24	4.15%
25	348	0799,0889,1699,1789,1888,2599,2689,2779,2788,3499, 3589,3679, 3688,3778,4489,4579,4588,4669,4678,4777,5569,5578, 5668,5677, 6667	1:29	3.48%
26	282	0899,1799,1889,2699,2789,2888,3599,3689,3779,3788, 4499,4589, 4679,4688,4778,5579,5588,5669,5678,5777,6668,6677	1:35	2.82%
27	220	0999,1899,2799,2889,3699,3789,3888,4599,4689,4779, 4788,5589, 5679,5688,5778,6669,6678,6777	1:45	2.20%
28	165	1999,2899,3799,3889,4699,4789,4888,5599,5689,5779, 5788,6679, 6688,6778,7777	1:61	1.65%
29	120	2999,3899,4799,4889,5699,5789,5888,6689,6779,6788, 7778	1:83	1.20%
30	84	3999,4899,5799,5889,6699,6789,6888,7779,7788	1:119	0.84%
31	56	4999,5899,6799,6889,7789,7888	1:179	0.56%
32	35	5999,6899,7799,7889,8888	1:286	0.35%
33	20	6999,7899,8889	1:500	0.2%
34	10	7999,8899	1:1000	0.1%
35	4	8999	1:2500	0.04%
36	1	9999	1:10000	0.01%

The second column is the total numbers that
have the sum value of the first column, while the third column lists only the
distinct boxes. For instance, there are 4 numbers that have sum of 1 and they
are 0001, 0010, 0100, and 1000. Since all four are simply different arrangements
of the number 0001, we have listed only 0001 in the third column.

Of the 10,000 4-digit numbers 5040 are non-repeating, 4320
one-repeating (doubles), 270 two-repeating (dual-doubles), 360
one-tripled, and 10 quadruples. Since a non-repeating number has 23 more
siblings, we can divide 5040 by 24 to obtain 210 distinct
non-repeating-digit numbers which are listed below.


4-digit, non-repeating-digit combinations (24-way) 0123, 0124,
0125, 0126, 0127, 0128, 0129, 0134, 0135, 0136, 0137, 0138, 0139, 0145,
0146, 0147, 0148, 0149, 0156, 0157, 0158, 0159, 0167, 0168, 0169, 0178,
0179, 0189, 0234, 0235, 0236, 0237, 0238, 0239, 0245, 0246, 0247, 0248,
0249, 0256, 0257, 0258, 0259, 0267, 0268, 0269, 0278, 0279, 0289, 0345,
0346, 0347, 0348, 0349, 0356, 0357, 0358, 0359, 0367, 0368, 0369, 0378,
0379, 0389, 0456, 0457, 0458, 0459, 0467, 0468, 0469, 0478, 0479, 0489,
0567, 0568, 0569, 0578, 0579, 0589, 0678, 0679, 0689, 0789, 1234, 1235,
1236, 1237, 1238, 1239, 1245, 1246, 1247, 1248, 1249, 1256, 1257, 1258,
1259, 1267, 1268, 1269, 1278, 1279, 1289, 1345, 1346, 1347, 1348, 1349,
1356, 1357, 1358, 1359, 1367, 1368, 1369, 1378, 1379, 1389, 1456, 1457,
1458, 1459, 1467, 1468, 1469, 1478, 1479, 1489, 1567, 1568, 1569, 1578,
1579, 1589, 1678, 1679, 1689, 1789, 2345, 2346, 2347, 2348, 2349, 2356,
2357, 2358, 2359, 2367, 2368, 2369, 2378, 2379, 2389, 2456, 2457, 2458,
2459, 2467, 2468, 2469, 2478, 2479, 2489, 2567, 2568, 2569, 2578, 2579,
2589, 2678, 2679, 2689, 2789, 3456, 3457, 3458, 3459, 3467, 3468, 3469,
3478, 3479, 3489, 3567, 3568, 3569, 3578, 3579, 3589, 3678, 3679, 3689,
3789, 4567, 4568, 4569, 4578, 4579, 4589, 4678, 4679, 4689, 4789, 5678,
5679, 5689, 5789, 6789

Of the 10,000 4-digit numbers 5040 are
non-repeating, 4320 one-repeating (doubles), 270 two-repeating (dual-doubles),
360 one-tripled, and 10 quadruples. Since a non-repeating number has 23 more
siblings, we can divide 5040 by 24 to obtain 210 distinct non-repeating-digit
numbers which are listed below.


4-digit, non-repeating-digit
combinations (24-way) 0123, 0124, 0125, 0126, 0127, 0128, 0129, 0134, 0135,
0136, 0137, 0138, 0139, 0145, 0146, 0147, 0148, 0149, 0156, 0157, 0158, 0159,
0167, 0168, 0169, 0178, 0179, 0189, 0234, 0235, 0236, 0237, 0238, 0239, 0245,
0246, 0247, 0248, 0249, 0256, 0257, 0258, 0259, 0267, 0268, 0269, 0278, 0279,
0289, 0345, 0346, 0347, 0348, 0349, 0356, 0357, 0358, 0359, 0367, 0368, 0369,
0378, 0379, 0389, 0456, 0457, 0458, 0459, 0467, 0468, 0469, 0478, 0479, 0489,
0567, 0568, 0569, 0578, 0579, 0589, 0678, 0679, 0689, 0789, 1234, 1235, 1236,
1237, 1238, 1239, 1245, 1246, 1247, 1248, 1249, 1256, 1257, 1258, 1259, 1267,
1268, 1269, 1278, 1279, 1289, 1345, 1346, 1347, 1348, 1349, 1356, 1357, 1358,
1359, 1367, 1368, 1369, 1378, 1379, 1389, 1456, 1457, 1458, 1459, 1467, 1468,
1469, 1478, 1479, 1489, 1567, 1568, 1569, 1578, 1579, 1589, 1678, 1679, 1689,
1789, 2345, 2346, 2347, 2348, 2349, 2356, 2357, 2358, 2359, 2367, 2368, 2369,
2378, 2379, 2389, 2456, 2457, 2458, 2459, 2467, 2468, 2469, 2478, 2479, 2489,
2567, 2568, 2569, 2578, 2579, 2589, 2678, 2679, 2689, 2789, 3456, 3457, 3458,
3459, 3467, 3468, 3469, 3478, 3479, 3489, 3567, 3568, 3569, 3578, 3579, 3589,
3678, 3679, 3689, 3789, 4567, 4568, 4569, 4578, 4579, 4589, 4678, 4679, 4689,
4789, 5678, 5679, 5689, 5789, 6789

Similarly, since twelve one-repeating numbers can be
represented by one number, there are 4320/12=360 distinct one-repeating-digit
numbers (doubles) as listed below.
4-digit, one-repeating-digit (doubles)
combinations (12-way) 0012, 0013, 0014, 0015, 0016, 0017, 0018, 0019, 0023,
0024, 0025, 0026, 0027, 0028, 0029, 0034, 0035, 0036, 0037, 0038, 0039, 0045,
0046, 0047, 0048, 0049, 0056, 0057, 0058, 0059, 0067, 0068, 0069, 0078, 0079,
0089, 0112, 0113, 0114, 0115, 0116, 0117, 0118, 0119, 0122, 0133, 0144, 0155,
0166, 0177, 0188, 0199, 0223, 0224, 0225, 0226, 0227, 0228, 0229, 0233, 0244,
0255, 0266, 0277, 0288, 0299, 0334, 0335, 0336, 0337, 0338, 0339, 0344, 0355,
0366, 0377, 0388, 0399, 0445, 0446, 0447, 0448, 0449, 0455, 0466, 0477, 0488,
0499, 0556, 0557, 0558, 0559, 0566, 0577, 0588, 0599, 0667, 0668, 0669, 0677,
0688, 0699, 0778, 0779, 0788, 0799, 0889, 0899, 1123, 1124, 1125, 1126, 1127,
1128, 1129, 1134, 1135, 1136, 1137, 1138, 1139, 1145, 1146, 1147, 1148, 1149,
1156, 1157, 1158, 1159, 1167, 1168, 1169, 1178, 1179, 1189, 1223, 1224, 1225,
1226, 1227, 1228, 1229, 1233, 1244, 1255, 1266, 1277, 1288, 1299, 1334, 1335,
1336, 1337, 1338, 1339, 1344, 1355, 1366, 1377, 1388, 1399, 1445, 1446, 1447,
1448, 1449, 1455, 1466, 1477, 1488, 1499, 1556, 1557, 1558, 1559, 1566, 1577,
1588, 1599, 1667, 1668, 1669, 1677, 1688, 1699, 1778, 1779, 1788, 1799, 1889,
1899, 2234, 2235, 2236, 2237, 2238, 2239, 2245, 2246, 2247, 2248, 2249, 2256,
2257, 2258, 2259, 2267, 2268, 2269, 2278, 2279, 2289, 2334, 2335, 2336, 2337,
2338, 2339, 2344, 2355, 2366, 2377, 2388, 2399, 2445, 2446, 2447, 2448, 2449,
2455, 2466, 2477, 2488, 2499, 2556, 2557, 2558, 2559, 2566, 2577, 2588, 2599,
2667, 2668, 2669, 2677, 2688, 2699, 2778, 2779, 2788, 2799, 2889, 2899, 3345,
3346, 3347, 3348, 3349, 3356, 3357, 3358, 3359, 3367, 3368, 3369, 3378, 3379,
3389, 3445, 3446, 3447, 3448, 3449, 3455, 3466, 3477, 3488, 3499, 3556, 3557,
3558, 3559, 3566, 3577, 3588, 3599, 3667, 3668, 3669, 3677, 3688, 3699, 3778,
3779, 3788, 3799, 3889, 3899, 4456, 4457, 4458, 4459, 4467, 4468, 4469, 4478,
4479, 4489, 4556, 4557, 4558, 4559, 4566, 4577, 4588, 4599, 4667, 4668, 4669,
4677, 4688, 4699, 4778, 4779, 4788, 4799, 4889, 4899, 5567, 5568, 5569, 5578,
5579, 5589, 5667, 5668, 5669, 5677, 5688, 5699, 5778, 5779, 5788, 5799, 5889,
5899, 6678, 6679, 6689, 6778, 6779, 6788, 6799, 6889, 6899, 7789, 7889, 7899

Again, since six dual-doubles numbers can be
represented by one number, there are 270/6=45 distinct dual-double-digit numbers
as listed below.
4-digit, dual-double-digit combinations (6-way)
0011, 0022, 0033, 0044, 0055, 0066, 0077, 0088, 0099, 1122, 1133, 1144, 1155,
1166, 1177, 1188, 1199, 2233, 2244, 2255, 2266, 2277, 2288, 2299, 3344, 3355,
3366, 3377, 3388, 3399, 4455, 4466, 4477, 4488, 4499, 5566, 5577, 5588, 5599,
6677, 6688, 6699, 7788, 7799, 8899

Finally, since four dual-doubles
numbers can be represented by one number, there are 360/4=90 distinct
one-tripled-digit numbers as listed below.
4-digit, one-tripled-digit
combinations (4-way) 0001, 0002, 0003, 0004, 0005, 0006, 0007, 0008, 0009,
0111, 0222, 0333, 0444, 0555, 0666, 0777, 0888, 0999, 1112, 1113, 1114, 1115,
1116, 1117, 1118, 1119, 1222, 1333, 1444, 1555, 1666, 1777, 1888, 1999, 2223,
2224, 2225, 2226, 2227, 2228, 2229, 2333, 2444, 2555, 2666, 2777, 2888, 2999,
3334, 3335, 3336, 3337, 3338, 3339, 3444, 3555, 3666, 3777, 3888, 3999, 4445,
4446, 4447, 4448, 4449, 4555, 4666, 4777, 4888, 4999, 5556, 5557, 5558, 5559,
5666, 5777, 5888, 5999, 6667, 6668, 6669, 6777, 6888, 6999, 7778, 7779, 7888,
7999, 8889, 8999