has anyone looked at a bell curve with regard to winning numbers?

[mirage]

Has anyone looked at a bell curve average of numbers and how recently they previously won? After much obsessive number counting and recording manually, I looked about 4 years ago and found that indeed, there was a tendency to a bell curve, with additionally what seemed to be a certain tendency for specific average numbers hitting repeatedly. Does anyone know of an application that could crunch numbers (it would have to deal with a huge amount of data, I think) in a reasonable amount of time based on entering in data that would include updating all the numbers as to when they last won as of after each lottery draw to produce combinations that would equal certain pre determined averages? In theory, after running the program application, a set of the various combinations that fit the desired averages or range of averages was produced, a player could then select out preferred combinations using other "tools". Does this question make sense to anybody?

 

[Sheba]

TRY HERE

Sheba__ ~~~
$GOOD$LUCK$EVERYBODY!$©

 

[GillesD]

Bell curve

I use the Lotto 6/49 database to demonstrate the central limit theorem and effectively the distribution of averages for the 2106 draws approximates fairly well the bell-shape curve (normal distribution).

I use Excel to calculate this (and many other things) but I am sure many other programs are available, depending on what you want.

 

[thornc]

Usually combinations of Uniform variables are Normal variables themselfs (Gaussian, Belll Shaped...)!

The sum is another example, even the difference beetween the numbers can be normal!

 

[johnph77]

FYI - Full bell curve for sums in 6/49 lottery.

21 - 1
22 - 1
23 - 2
24 - 3
25 - 5
26 - 7
27 - 11
28 - 14
29 - 20
30 - 26
31 - 35
32 - 44
33 - 58
34 - 71
35 - 90
36 - 110
37 - 136
38 - 163
39 - 199
40 - 235
41 - 282
42 - 331
43 - 391
44 - 454
45 - 532
46 - 612
47 - 709
48 - 811
49 - 931
50 - 1057
51 - 1206
52 - 1360
53 - 1540
54 - 1729
55 - 1945
56 - 2172
57 - 2432
58 - 2702
59 - 3009
60 - 3331
61 - 3692
62 - 4070
63 - 4494
64 - 4935
65 - 5426
66 - 5940
67 - 6506
68 - 7097
69 - 7748
70 - 8423
71 - 9163
72 - 9933
73 - 10769
74 - 11637
75 - 12579
76 - 13552
77 - 14603
78 - 15690
79 - 16856
80 - 18059
81 - 19349
82 - 20673
83 - 22087
84 - 23540
85 - 25082
86 - 26663
87 - 28340
88 - 30051
89 - 31860
90 - 33706
91 - 35648
92 - 37625
93 - 39703
94 - 41809
95 - 44016
96 - 46253
97 - 48586
98 - 50944
99 - 53402
100 - 55875
101 - 58446
102 - 61031
103 - 63706
104 - 66388
105 - 69161
106 - 71928
107 - 74781
108 - 77624
109 - 80542
110 - 83440
111 - 86412
112 - 89348
113 - 92350
114 - 95311
115 - 98324
116 - 101285
117 - 104295
118 - 107235
119 - 110215
120 - 113119
121 - 116048
122 - 118889
123 - 121751
124 - 124507
125 - 127274
126 - 129930
127 - 132581
128 - 135109
129 - 137629
130 - 140008
131 - 142370
132 - 144587
133 - 146771
134 - 148800
135 - 150794
136 - 152617
137 - 154397
138 - 156004
139 - 157554
140 - 158923
141 - 160236
142 - 161354
143 - 162410
144 - 163273
145 - 164062
146 - 164654
147 - 165176
148 - 165490
149 - 165732
150 - 165772
151 - 165732
152 - 165490
153 - 165176
154 - 164654
155 - 164062
156 - 163273
157 - 162410
158 - 161354
159 - 160236
160 - 158923
161 - 157554
162 - 156004
163 - 154397
164 - 152617
165 - 150794
166 - 148800
167 - 146771
168 - 144587
169 - 142370
170 - 140008
171 - 137629
172 - 135109
173 - 132581
174 - 129930
175 - 127274
176 - 124507
177 - 121751
178 - 118889
179 - 116048
180 - 113119
181 - 110215
182 - 107235
183 - 104295
184 - 101285
185 - 98324
186 - 95311
187 - 92350
188 - 89348
189 - 86412
190 - 83440
191 - 80542
192 - 77624
193 - 74781
194 - 71928
195 - 69161
196 - 66388
197 - 63706
198 - 61031
199 - 58446
200 - 55875
201 - 53402
202 - 50944
203 - 48586
204 - 46253
205 - 44016
206 - 41809
207 - 39703
208 - 37625
209 - 35648
210 - 33706
211 - 31860
212 - 30051
213 - 28340
214 - 26663
215 - 25082
216 - 23540
217 - 22087
218 - 20673
219 - 19349
220 - 18059
221 - 16856
222 - 15690
223 - 14603
224 - 13552
225 - 12579
226 - 11637
227 - 10769
228 - 9933
229 - 9163
230 - 8423
231 - 7748
232 - 7097
233 - 6506
234 - 5940
235 - 5426
236 - 4935
237 - 4494
238 - 4070
239 - 3692
240 - 3331
241 - 3009
242 - 2702
243 - 2432
244 - 2172
245 - 1945
246 - 1729
247 - 1540
248 - 1360
249 - 1206
250 - 1057
251 - 931
252 - 811
253 - 709
254 - 612
255 - 532
256 - 454
257 - 391
258 - 331
259 - 282
260 - 235
261 - 199
262 - 163
263 - 136
264 - 110
265 - 90
266 - 71
267 - 58
268 - 44
269 - 35
270 - 26
271 - 20
272 - 14
273 - 11
274 - 7
275 - 5
276 - 3
277 - 2
278 - 1
279 - 1

Total possibilities - 13983816

gl

john

 

[GillesD]

Sum of numbers

johnph77, allmost perfect but if you add up all the numbers you posted, you get 13,983,216 not 13,983,816 as expected.

To get the proper total, verify these values:

- for a sum of 115, it should be 98324, not 98354 (copying error?);

- for a sum of 194, it should be 71928, not 71298 (inversion of 2 numbers).

 

[johnph77]

GillesD -

You are correct, of course. The post has been edited, and thank you for pointing those out. Had I taken the time and trouble to check the inverse sums I would have caught them, but.....

gl

john

 

[mirage]

Re: Bell curve - thanks! but there's more to the question

Thanks for the bell curve info re 6/49! Actually what i want is a way to associate, separate numeric values, with each of the numbers from 1 to 49, and produce a bell curve of the sums of these. Do you really think Excel can do that??

 

[johnph77]

mirage -

Not sure what you're asking. Position frequency possibly?

gl

john

 

[GillesD]

Question ???

As for the previous post, I am not sure exactly what you want.

Excel can do a lot of things. For example, the following list gives for number 1 to 49 the average sum and the number of times each number was included in the winning numbers. The data is valid for 2106 draws and does take into consideration the bonus number.

# 01: Avg. = 130.3 for 263 draws
# 02: Avg. = 132.0 for 247 draws
# 03: Avg. = 129.4 for 255 draws
# 04: Avg. = 134.7 for 250 draws
# 05: Avg. = 133.0 for 262 draws
# 06: Avg. = 133.4 for 241 draws
# 07: Avg. = 136.1 for 271 draws
# 08: Avg. = 138.2 for 249 draws
# 09: Avg. = 140.1 for 258 draws
# 10: Avg. = 140.8 for 235 draws
# 11: Avg. = 139.7 for 231 draws
# 12: Avg. = 144.2 for 256 draws
# 13: Avg. = 139.4 for 240 draws
# 14: Avg. = 139.7 for 249 draws
# 15: Avg. = 144.6 for 234 draws
# 16: Avg. = 142.8 for 257 draws
# 17: Avg. = 146.2 for 253 draws
# 18: Avg. = 143.8 for 249 draws
# 19: Avg. = 147.7 for 256 draws
# 20: Avg. = 149.2 for 274 draws
# 21: Avg. = 149.5 for 255 draws
# 22: Avg. = 149.9 for 240 draws
# 23: Avg. = 152.2 for 247 draws
# 24: Avg. = 150.1 for 235 draws
# 25: Avg. = 152.5 for 252 draws
# 26: Avg. = 155.2 for 259 draws
# 27: Avg. = 151.5 for 290 draws
# 28: Avg. = 154.5 for 241 draws
# 29: Avg. = 158.0 for 251 draws
# 30: Avg. = 155.8 for 258 draws
# 31: Avg. = 153.5 for 305 draws
# 32: Avg. = 159.4 for 272 draws
# 33: Avg. = 158.6 for 244 draws
# 34: Avg. = 159.7 for 296 draws
# 35: Avg. = 159.5 for 247 draws
# 36: Avg. = 163.2 for 256 draws
# 37: Avg. = 160.1 for 250 draws
# 38: Avg. = 163.6 for 268 draws
# 39: Avg. = 164.8 for 253 draws
# 40: Avg. = 164.6 for 274 draws
# 41: Avg. = 165.7 for 260 draws
# 42: Avg. = 165.6 for 260 draws
# 43: Avg. = 166.5 for 284 draws
# 44: Avg. = 165.8 for 275 draws
# 45: Avg. = 169.8 for 270 draws
# 46: Avg. = 172.0 for 270 draws
# 47: Avg. = 169.1 for 297 draws
# 48: Avg. = 170.0 for 237 draws
# 49: Avg. = 173.3 for 260 draws

So in this case, the sum of the 6 numbers increases as one specific number (#1 to 49) is involved. Which of course makes some sense.

 

[mirage]

Thanks gilles and johnph77 but this is what i'm really looking for

Thanks a bunch everyone. My approach is a long shot but worthwhile, i think. Actually i would like to produce a bell curve of only combinations of 6 numbers from 6 to 49 (if it turned out to be a 5 winner with the bonus well that's better than nothing). But i would like an app that would PRODUCE A LIST of all the combinations of 6 numbers that would fit inside a certain central area of the main hit zone of the bell curve. I think I remember reading that a majority of winning combinations fall in the sum range of 130 to 170(is this correct?). That's a lot of numbers. I would chop it down by trying to guessimate where it might hit next and chose a sum range that was smaller, say, 150 to 158. (I know, I'm asking a lot). Then it would nice to take this list that was produced and crunch some more: each of the numbers from 1 to 49 would have assigned to them another numerical value. The numbers 1 to 49 could be represented by, say, combinations of letters of the alphabet, maybe, in Ecel, with 1 being represented as AA, 2 represented as AB, 3 represented as AC, and so on, simply as a way to ID or tag the numbers 1 to 49. Then, AA would have an (associated) assigned value of say, 6, and AB would have an assigned value of say 15, and AC would have a value of say 5, ... and so on, and have the program app crunch away to come up with another LIST (theoretically also looks a bit like a bell curve, but in reality is more chaotic or random, if you will), of ALL OF THE COMBINATIONS OF 6 WHICH ARE EQUAL TO, a pre-specified sum range of the, previously mentioned, associated ASSIGNED VALUES ( i.e. maybe the range 40 to 50). What do you think? Am I asking for something too large to be done by a PC and a PC program? I don't speak math very well. Thanks!

 

[Maggie]

Hi mirage,

Here is a link with some Bell curve info in it. You will have to scroll down to almost the bottom of the page to get to it.

CLICK HERE

I realize it is not what you're looking for, but you may want to have a look at it anyways.

 

[Beaker]

Re: Thanks gilles and johnph77 but this is what i'm really looking for

<snip>
The numbers 1 to 49 could be represented by, say, combinations of letters of the alphabet, maybe, in Ecel, with 1 being represented as AA, 2 represented as AB, 3 represented as AC, and so on, simply as a way to ID or tag the numbers 1 to 49. Then, AA would have an (associated) assigned value of say, 6, and AB would have an assigned value of say 15, and AC would have a value of say 5, ... and so on, and have the program app crunch away to come up with another LIST (theoretically also looks a bit like a bell curve, but in reality is more chaotic or random, if you will), of ALL OF THE COMBINATIONS OF 6 WHICH ARE EQUAL TO, a pre-specified sum range of the, previously mentioned, associated ASSIGNED VALUES ( i.e. maybe the range 40 to 50). What do you think? Am I asking for something too large to be done by a PC and a PC program? I don't speak math very well. Thanks!

This I don't get what statistic will you generate from 'another LIST' that has Normal distribution? Sum? Not sure

You may have something else here. Say you like the 9. GIve me a list of combinations with sum between 140-160 with the 9 and repeaters and every other filter you can think of.

Lotwin does this

 

[johnph77]

mirage -

The program that generated the bell curve can be further restricted to only allow (or list) those draws adding up to the sums you want included. Of course, looking at the midpoint, 150, there are 165,772 different draws (of 13,983,816) that meet this requirement. Perhaps I'll fool around in this area a little longer when I get the time, and do a positional analysis on the possible draws.

gl

john

 

[GillesD]

Distribution of the sum

1 - Sum between 130 and 170

There are 6,416,196 combinations with a sum of 130 to 170 (these values included) or 45.9% of the 13,983,816 combinations.

2 - Obtaining all combinations with a sum meeting specific criteria

I have already posted a VBA macro that generates all possible combinations in an Excel sheet. Using this macro and inserting some appropriate IF ... THEN ... ENDIF statements in the section where combinations are inserted into cells, you could control which combinations are inserted in a sheet. This could be done by verifying if the sum of variables A, B, C, D, E and F that loop through all possibilities meet whatever criteris you want.

 

[Bertil]

standard deviation for bell curve

The frequency curve for the sum of the drawn integers in a lotto
game forms a bell curve, which has a variance of :

n(N+1)(N-n)/12. The std.dev. is the square root of variance. Thus for the lotto part of Powerball 5/53 it is 32.86. A normal distribution table can then be used to determine how far a given sum deviates from the mean, by calculating: (sum-mean)/std.dev.