Measuring Turquoise Underwear
Evil Nigel
1) I hypothesised a potential mathematical mechanism to explain a small
amount of predictability in lottery draws based on past data. I
implemented a spreadsheet to generate predictions, ranking each of the
49 balls of the UK lottery. I checked the rankings of the drawn balls,
and no predictive effect was apparent. However, it seemed to my visual
inspection that the rankings of the drawn balls tended to be widely
dispersed.
2) For each of the approx 14 million possible 6/49 combinations, I
calculated the population standard deviation. Then I calculated the
average of the 14 million standard deviations, obtaining a result of
just over 12.
3) I calculated the population standard deviations of the ball rankings
of successive lottery draws, and using a formula hoicked from a stats
book, evaluated the probability that these came from a population with
the mean calculated in 2), using a 2-tailed t-test. Currently p = 0.000808.
I'm a long way from certain that the above tests are statistically valid
- do any math gurus have any comments? The population standard
deviations of the 14 million combos are not a normal distribution - the
minimum is probably found in 44 cases; 1-6, 2-7 ... 44-49. I guess the
maximum is probably only found in one case: 1,2,3,47,48,49.
I once found a web site that allowed you to type in a p value and
returned you an equivalent number of standard deviations, and vice
versa. Unfortunately I can't remember the URL and a quick google didn't
disclose it. If anyone knows of a website offering this facility, I'd be
grateful. Most sites just seem to offer a table, usually giving up at 3
SDs. As long-term subscribers and correspondees know, I've had a number
of healthy-looking systems keel over and die after reaching 3.5 SDs or
so, so I'm not going to blow any trumpets until at least 4 SDs.
Evil Nigel
Stig Holmquist
wrote:
>To recap:
>
>1) I hypothesised a potential mathematical mechanism to explain a small
>amount of predictability in lottery draws based on past data. I
>implemented a spreadsheet to generate predictions, ranking each of the
>49 balls of the UK lottery. I checked the rankings of the drawn balls,
>and no predictive effect was apparent. However, it seemed to my visual
>inspection that the rankings of the drawn balls tended to be widely
>dispersed.
>
>2) For each of the approx 14 million possible 6/49 combinations, I
>calculated the population standard deviation. Then I calculated the
>average of the 14 million standard deviations, obtaining a result of
>just over 12.
Please explain the formula used for std.dev. and what book you used
The std.dev. for sums in the 6/49 game is 32.8, and the std.dev. for
49 integers is 14.14. Where does 12 come from?
Stig Holmquist>
Evil Nigel
> Please explain the formula used for std.dev. and what book you used
> The std.dev. for sums in the 6/49 game is 32.8, and the std.dev. for
> 49 integers is 14.14. Where does 12 come from?
>
> Stig Holmquist>
>
Do you have Excel?
A B C D E F G
1 2 3 4 5 6 =STDEVPA(A1:F1)
1 2 3 47 48 49 =STDEVPA(A2:F2)
=AVERAGE(G1:G2)
The value in G3 = 12.36, a little higher than I calculated the average
population standard deviation of the 14M combinations.
Stig Holmquist
wrote:
>Stig Holmquist wrote:
Your calculation of std.dev.for F1 and F2 is based on treating the
data as a population, but they are just samples from a 14 million
large population. Thus if you treat each set as a sample you'll get
1.871 for F1 and 25.211 for F2 with a mean of 13.541.
But there are 43 sets of samples with std.dev. of 1.871 and only one
with 25.211. Also, there is a distribution curve for the std.dev. of
all possible combinations. The shape of that curve is not known.
Thus it seems to me that any calculation based on 12 is poinless.
Evil Nigel
> On Sat, 05 May 2007 18:42:08 +0100, Evil Nigel <use...@nospam.com>
> wrote:
>
>
>>Stig Holmquist wrote:
>>
>>
>>> Please explain the formula used for std.dev. and what book you used
>>>The std.dev. for sums in the 6/49 game is 32.8, and the std.dev. for
>>>49 integers is 14.14. Where does 12 come from?
>>>
>>>Stig Holmquist>
>>>
>>Do you have Excel?
>>A B C D E F G
>>
>>1 2 3 4 5 6 =STDEVPA(A1:F1)
>>1 2 3 47 48 49 =STDEVPA(A2:F2)
>> =AVERAGE(G1:G2)
>>
>>The value in G3 = 12.36, a little higher than I calculated the average
>>population standard deviation of the 14M combinations.
Make that 'a little lower' - my calculated average is approx. 12.72.
>>
>
> Your calculation of std.dev.for F1 and F2 is based on treating the
> data as a population, but they are just samples from a 14 million
> large population. Thus if you treat each set as a sample you'll get
> 1.871 for F1 and 25.211 for F2 with a mean of 13.541.
Since I didn't really know what I was doing and I needed a measure of
diverseness, I assumed I could use either population standard deviation
or sample standard deviation provided I was consistent throughout. I
leaned towards population rather than sample because the combo
1-2-3-4-5-6 is a complete population - there are no more members, the
values of which are unknown.
>
> But there are 43 sets of samples with std.dev. of 1.871 and only one
> with 25.211. Also, there is a distribution curve for the std.dev. of
> all possible combinations. The shape of that curve is not known.
That's what I said. However the stats book didn't specify that the
distribution had to be normal. Apart from the end bits, which are rather
small in comparison to 14 million, it probably is very bell-curve-ish.
>
> Thus it seems to me that any calculation based on 12 is poinless.
>
I'm open to suggestions for better methods of analysis.
BTW, I owe you substantial thanks. You're the first person to have a
good read of what I'm trying to calculate and make intelligent feedback.
Evil Nigel
Stig Holmquist
wrote:
Is your average based on an actual computer generated
complete set of all 14 million combinations? If so. you might have
or be able to extract the frequencies for all possible s.d.'s and
construct a distribution curve, which would be very interesting to
look at. Please post this curve or a table with the data.
Stig Holmquist
Stig Holmquist
wrote:
My memory is not what it used to be so I just recalled that I
corresponded some time ago with Harry Schneider, who wrote the
book "Lottery Numbers". It is about the UK 6/49 game and has
stats for about 52 draws. He was the first to calculate the std.dev.
for the numbers and came up with 14.1.
I then modified a formula by J.E Freund from his book "Mathematical
statistics" (1962) on p. 184 where he claims the variance for the
mean is (N+1)(N-n)/12n. I suspect this is a misprint and should not
include the n in the denominator. The revised formula would yield
50x43/12=179.17 ,which equals 13.4 as std.dev. Keep in mind that the
formula for the variance of 49 integers taken one at a time is
(N^2-1)/12 and thus close to the above formula.
His book is now available with a co-author.
Stig Holmquist
Evil Nigel
> On Sun, 06 May 2007 11:44:12 +0100, Evil Nigel <use...@nospam.com>
> wrote:
>
>>Apart from the end bits, which are rather
>>small in comparison to 14 million, it probably is very bell-curve-ish.
>>
>>
> Is your average based on an actual computer generated
> complete set of all 14 million combinations? If so. you might have
> or be able to extract the frequencies for all possible s.d.'s and
> construct a distribution curve, which would be very interesting to
> look at. Please post this curve or a table with the data.
>
> Stig Holmquist
>
I'm expecting snorts of derision from Duncan Smith when I admit this,
but I'm still using spreadsheet macros rather than a real programming
language. I can loop the 14 million combos but I can't save information
about more than a tiny fraction of the individual combos. (The official
limit for my spreadsheet is 1 million rows, but performance becomes
intolerable approaching 10% of that).
The distribution won't be 'normal' because the variances of the 49
combos comprise a set of discrete values, some of which are repeated
many times. For example:
3 5 7 28 33 39
4 6 8 29 34 40
47 45 43 22 17 11
all have the same variance.
Sorry,
Evil Nigel
Stig Holmquist
I've just carried out a std.dev. for the old PB /53 with 302 draws.
It yields numbers from 3.21 to 23.70.This range can then be divided up
into units 20 units of 1 and the frequencies within each class can
then be graphed. The result is a broad tripple peak from 10 to 20
with a small shoulder peak on each side.
I suspect there are too few data to yield a smooth curve. Can you
generate a graph based on your simulation?
Stig Holmquist
Evil Nigel
Cruncher running at the moment. I've arbitrarily chosen integer ranges
for the bins. I don't know about a graph - I've only ever tried the
graphing facility a couple of times and each time they've looked like sh*t.
I'll post the bincounts here if/when it finishes.
Evil Nigel
Evil Nigel
Wow. I admit my spreadsheet is slow - 2 hours just to generate and cycle
through 14 million combos, but adding processing to calculate the
population SDev's and putting them into bins, albeit using crap quality
programming, the macro got just over 5% of the way through in 21 hours.
1 3
2 68
3 417
4 1333
5 3052
6 5744
7 9743
8 15116
9 22278
10 31202
11 42496
12 55908
13 72210
14 90973
15 112116
16 111481
17 90214
18 62232
19 29725
20 8053
21 1208
22 98
23 1
The combo being processed when the macro was terminated was:
1 7 9 18 36 48
The distribution is somewhat skewed. The average SDev so far is 14.84.
Since that drops to 12.72 over the full range of combos, that would
suggest the 5% sample is not representative of the whole distribution.
Evil Nigel
Evil Nigel
> I once found a web site that allowed you to type in a p value and
> returned you an equivalent number of standard deviations, and vice
> versa. Unfortunately I can't remember the URL and a quick google didn't
> disclose it.
Found one:
http://www.fourmilab.ch/rpkp/experiments/analysis/zCalc.html
Evil Nigel
Stig Holmquist
wrote:
If you tested the last 500 draws of UK649 I'm sure you would get a
cumulative mean that approaches the theoretical limit. But you must
use the sample s.d not the population form.
Stig
Evil Nigel
I'm happy that I already know the mean, what I'm not certain about is
the shape of the distribution.
Since I'm relatively arbitrarily using the population standard deviation
throughout, I don't understand why you think I should use the sample
standard deviation of each combo in the last 500 draws. The mean of the
sample standard deviation sample and the mean of the population standard
deviation population will almost certainly be different and non-convergent.
Evil Nigel
John Griffin
s.d. frequency
2: 385
3: 4008
4: 17658
5: 51401
6: 112400
7: 208995
8: 351353
9: 539383
10: 764322
11:1015862
12:1284690
13:1530424
14:1701592
15:1755043
16:1621714
17:1289115
18: 865629
19: 499579
20: 245578
21: 93947
22: 25502
23: 4649
24: 555
25: 32
Maximum variance at: 1 2 3 43 48 49
Average s.d.: 13.9376251501268
Since you say the average should be 12.72, I wonder if I got this
right. Where did that number come from?
Stig Holmquist
wrote:
It is debatable if one should calculate the sample or the population
std.dev.. There is a simple conversion factor between them.
I'm still puzzled about your knowing the mean. Where did you get it
from? Can the method be applied to 'small lottos' like 3/10? Also,
I was hoping that the mean std.dev after 500 draws would converge
to a value with very little spread and wonder what that value would be
and how it relates to your "known value"?
Stig
Evil Nigel
Are you using sample standard deviation? As that has more degrees of
freedom, it will be larger.
Evil Nigel
Evil Nigel
I looped through all approx 14 million combos, calculated the population
standard deviation for each, kept a running sum of the population
standard deviations then divided by approx 14 million. That was
acceptably quick - it was the sorting into bins to show what the
distibution looked like that made the macro unacceptably slow.
The important thing is that I'm using the standard deviation of a combo
as a measure of its 'clumpiness' to test whether the 'clumpiness' of my
system comes from the same population.
Evil Nigel
Evil Nigel
> John Griffin wrote:
>
>> Maximum variance at: 1 2 3 43 48 49
Sample standard deviation of that combo = 25.21
Population standard deviation of that combo = 23.01
They are in proportion sqrt(6):sqrt(6-1), as are the mean you calculated
and the mean I calculated.
Evil Nigel
John Griffin
Yes.
This oughta do it:
Sample standard deviation ,frequency, cumulative proportion,
Population s.d.,...
1: 0 . 0 .
2: 385 .00003 719 .00005
3: 4008 .00031 7431 .00058
4: 17658 .00158 30557 .00277
5: 51401 .00525 83875 .00877
6: 112400 .01329 179586 .02161
7: 208995 .02824 328996 .04514
8: 351353 .05336 536645 .08351
9: 539383 .09193 800448 .14075
10: 764322 .14659 1104192 .21971
11:1015862 .21924 1420396 .32129
12:1284690 .31111 1705899 .44328
13:1530424 .42055 1894023 .57872
14:1701592 .54223 1899713 .71457
15:1755043 .66774 1637695 .83169
16:1621714 .78371 1166599 .91511
17:1289115 .87589 686199 .96418
18: 865629 .9378 336256 .98823
19: 499579 .97352 126475 .99727
20: 245578 .99108 32436 .99959
21: 93947 .9978 5168 .99996
22: 25502 .99963 490 1.
23: 4649 .99996 18 1.
24: 555 1. 0 1.
25: 32 1. 0 1.
Maximum variance at: 1 2 3 43 48 49
Average s.d.: 13.9376251501268
Average s.d.: 12.7232528212385
Evil Nigel
Thanks. Did you write a prog specially, and if so, in what language? How
long did it take to run.
Your average Population SD is the same as mine, so if Stig accepts that
we're not sock puppets fronting for the same person, that ought to
convince him that your distribution is genuine. I notice he's been in
some of the math newsgroups asking if there's a theoretical way to
calculate the average, and the typical reply is (to paraphrase) "I don't
know, that looks difficult".
Below are the Turquoise version 3 rankings of the drawn UK lottery balls
since I began recording the stats. None of the data is retro generated.
By my calculation, the average Population Standard Deviation of the sets
of Turquoise Rankings is 13.4474058610064 and the probability that this
comes randomly from a population with mean 12.7232528212385 is
0.000703827297979179
Evil Nigel
Draw B1 B2 B3 B4 B5 B6 PSDev
1188 47 32 23 44 8 35 13.1244047484067
1187 13 32 26 27 47 48 12.2667119564381
1186 38 41 15 13 48 47 14.3255792979629
1185 14 22 7 44 42 20 13.7163730223733
1184 26 15 22 13 12 47 12.0381338531629
1183 2 1 43 44 11 24 17.7145577296063
1182 26 10 5 15 36 41 13.2591687354659
1181 32 7 3 4 39 8 14.3845982448822
1180 34 39 11 36 45 46 11.6535640709422
1179 22 35 27 43 11 49 12.7856256093404
1178 6 20 14 31 42 15 11.9117122568038
1177 4 2 36 16 44 9 15.9973956213712
1176 49 16 31 46 23 11 14.2672897060218
1175 33 31 1 7 48 2 17.9226734116934
1174 33 42 4 39 8 36 15.1437555888007
1173 9 2 20 17 25 4 8.43438728592
1172 21 27 4 37 26 14 10.4363148029688
1171 36 13 33 37 43 9 12.7769323391806
1170 36 8 41 16 20 7 13.0085442007252
1169 48 29 10 6 44 20 15.8578757159407
1168 38 1 27 3 2 43 17.6540835691538
1167 44 20 12 23 24 38 10.8691714904536
1166 19 5 7 14 44 48 17.0432456481218
1165 44 24 5 37 46 4 17.1820319584798
1164 23 33 17 18 46 42 11.3345587572795
1163 46 2 41 5 1 30 18.8097197096489
1162 25 13 21 12 42 6 11.6821326059167
1161 7 42 39 29 9 3 15.7665257217097
1160 9 8 44 35 48 11 16.9648329067974
1159 41 9 32 38 13 22 12.1025708930881
1158 43 33 9 22 15 10 12.4096736459909
1157 6 5 15 49 44 28 17.3469497799085
1156 4 23 38 15 39 25 12.2746350930146
1155 29 25 39 28 49 11 11.7815769553806
1154 18 13 7 44 40 29 13.6554832291729
1153 45 26 46 20 1 2 18.0523928854013
1152 8 42 28 4 39 31 14.4875425414005
1151 13 12 1 21 23 31 9.52919490594854
1150 47 22 35 17 21 12 11.8274633328068
1149 47 15 21 23 5 11 13.3499895963339
1148 27 17 32 26 16 18 5.99073358520381
1147 5 6 40 37 47 1 18.9619502044372
1146 41 12 10 37 43 7 15.502687938978
1145 38 11 8 45 5 33 15.8184140236062
1144 9 27 1 29 42 16 13.5973853695808
1143 40 3 42 21 16 20 13.5973853695808
1142 19 3 7 49 46 38 18.2847842025366
1141 39 5 49 35 44 16 15.6702123647242
1140 21 5 48 14 19 20 13.1582251420505
1139 21 6 30 42 43 28 12.6315302143309
1138 48 30 32 2 40 27 14.2643689738531
1137 12 19 15 36 32 10 9.89388138643722
1136 16 34 15 42 18 39 11.2792828771258
1135 30 8 25 22 46 42 12.6809130410848
1134 35 44 32 19 21 2 13.4752860204648
1133 44 42 41 7 6 5 18.1972220102105
1132 23 8 46 14 40 30 13.4463956343533
1131 14 39 9 27 49 36 14.0118997046558
1130 6 10 19 28 14 18 7.03364928200306
1129 41 15 44 46 43 18 12.8419884233972
1128 1 38 32 21 29 34 12.2667119564381
1127 28 49 5 6 34 25 15.4137384606504
1126 19 42 6 8 32 44 15.192286054296
1125 12 6 49 18 9 40 16.2958754154404
1124 3 15 49 21 34 9 15.5608126037456
1123 2 21 44 24 8 25 13.4370962471643
1122 17 39 12 34 20 37 10.5316981853197
1121 33 1 13 26 19 36 11.9814671704076
1120 29 41 44 42 38 45 5.33593686452738
1119 39 8 22 24 49 30 13.0085442007252
1118 2 48 9 32 49 27 17.7709188157381
1117 17 42 7 21 20 35 11.5998084275369
1116 35 23 29 11 24 17 7.75492674942123
1115 35 18 14 39 37 2 13.7527774972508
1114 35 39 19 13 11 12 11.310025051549
1113 40 18 46 38 19 36 10.5895650944167
1112 11 35 18 20 19 4 9.47657931721967
1111 2 22 16 44 5 38 15.6035964515307
1110 7 10 42 49 5 40 18.42778698958
1109 6 17 7 13 31 8 8.63455589799241
1108 42 23 44 39 37 22 8.77021474461525
1107 32 23 46 15 43 8 13.8974418109553
1106 19 18 12 6 28 33 9.08600878029268
1105 46 39 19 18 45 48 12.5620681241408
1104 44 12 26 29 4 8 13.8774397254441
1103 27 31 16 36 32 25 6.36177822799744
1102 15 41 7 47 40 44 15.4236470683457
1101 39 49 27 35 3 33 14.1891977691952
1100 14 38 5 20 15 1 11.8988794990677
1099 46 28 31 36 35 13 9.97914491994847
1098 33 4 36 32 1 35 14.9303940559741
1097 29 41 6 13 15 3 13.2465928533424
1096 49 11 35 24 17 5 14.8520481191428
1095 20 2 33 41 14 35 13.4835290467873
1094 3 2 24 29 4 41 15.0489940601431
1093 24 47 38 22 23 27 9.22707369044427
1092 11 14 16 20 43 9 11.3639292891539
1091 3 49 14 25 33 1 16.9156403629567
1090 8 15 45 49 21 25 15.0157324903656
1089 8 5 38 12 7 6 11.5421931287872
1088 17 10 36 29 16 9 9.84462628374824
1087 11 29 1 20 47 38 15.61694236683
1086 9 5 22 46 1 30 15.6994338185242
1085 11 26 35 41 14 10 12.0473602456675
1084 8 27 28 45 21 10 12.4018367815238
1083 2 11 31 12 34 43 14.6448701674758
1082 37 47 4 20 19 17 14.0712472794703
1081 49 38 33 27 5 37 13.5615879109589
1080 23 28 26 21 40 3 10.9962114688045
1079 4 39 25 2 21 19 12.5918845116827
1078 49 5 47 28 3 4 19.8382346884887
1077 46 49 1 25 37 26 16.0485374896143
1076 48 27 36 16 30 41 10.2632028788938
1075 46 21 28 45 3 19 15.0665191733194
1074 22 37 46 18 16 9 12.7758452644912
1073 15 27 41 43 7 16 13.4711626158332
1072 49 30 44 15 29 40 11.2657297440808
1071 25 42 46 35 18 6 13.9004396413287
1070 10 11 27 23 34 48 13.1497781983829
1069 17 39 43 11 9 31 13.3666251038423
1068 47 26 1 12 5 42 17.6580167503476
1067 35 2 33 48 41 28 14.4846662217517
1066 38 47 4 35 12 27 14.9378341431711
1065 13 24 16 37 1 18 10.915076220022
1064 13 46 6 32 20 11 13.7558068546422
1063 31 46 17 42 14 3 15.4569294061488
1062 47 8 6 15 14 30 14.3178210632764
1061 32 48 30 7 42 15 14.2594997574716
1060 46 40 41 4 6 11 17.8854379003951
1059 44 27 22 48 34 21 10.3869576339219
1058 22 45 15 31 49 1 16.6774964814534
1057 11 16 44 37 3 20 14.3226704524292
1056 42 26 31 12 41 20 10.7651701746368
1055 45 8 30 14 24 25 11.7851130197758
1054 39 42 15 26 49 10 14.2993783858678
1053 17 7 23 45 43 20 13.7648909266373
1052 17 26 19 32 23 14 5.98377435700542
1051 7 43 48 1 36 46 18.9509601046725
1050 26 28 48 25 44 14 11.6678570821248
1049 46 18 10 24 7 41 14.6818103636968
1048 5 15 31 46 18 4 14.7582368715086
1047 47 11 28 44 5 14 16.1804065324563
1046 23 44 35 8 33 13 12.6227308191743
1045 4 12 14 21 49 18 14.1499901845274
1044 39 10 26 22 48 15 13.1866936299017
1043 46 2 6 29 26 8 15.5750869446476
1042 47 34 32 5 33 12 14.2526800598655
1041 45 44 20 4 1 8 18.0800688297608
1040 35 12 25 48 38 2 15.7020876177518
1039 10 35 27 8 41 12 12.8765506078125
1038 17 33 4 47 21 22 13.3666251038423
1037 44 12 17 39 9 27 13.2245562832516
1036 8 4 47 9 38 43 18.0869811988869
1035 37 24 27 12 33 44 10.1775897605147
1034 21 44 39 18 11 41 12.7671453348037
1033 16 43 20 2 49 6 17.6225865171817
1032 22 34 31 44 14 7 12.4588210606872
1031 20 27 7 44 40 3 15.326991442115
1030 7 19 13 24 23 17 5.84284938098603
1029 36 30 37 35 2 27 12.0749971244533
1028 22 41 23 43 37 9 12.1712320201732
1027 43 21 5 49 2 17 17.7051467721175
1026 21 39 18 42 26 10 11.3284303119776
1025 41 45 18 24 9 34 12.7115433104456
1024 40 46 6 32 10 45 16.1288216832132
1023 44 43 34 2 35 22 14.456832294801
1022 19 27 1 29 10 3 10.9607886983049
1021 34 14 5 3 41 30 14.599276998841
1020 29 14 7 24 44 16 11.9814671704076
1019 32 3 37 26 49 46 15.2032525759749
1018 37 22 4 20 34 15 11.1504857891185
1017 29 3 32 5 14 23 11.1902735543963
1016 44 24 14 40 11 47 14.3643076176102
1015 14 29 18 3 24 33 9.95685135416257
1014 30 33 8 20 14 47 12.9571944837179
1013 42 48 41 38 49 14 11.6856987619721
1012 22 1 2 38 27 35 14.6220913536866
Stig Holmquist
wrote:
If you return to the math post you'll find a simple formula for the
sample variance for any lotto: N(N+1)/12. It works for 3/7 and 5/7
and does not depend on n in n/N. Remarkable.
Stig Holmquist
Evil Nigel
That's certainly an aesthetically pleasing result.
I've tried it for myself and the average combo sample variance for a 3/7
lottery is, as the formula predicts, 4.6666r. And the average combo
sample variance for a 3/6 lottery is, as the formula predicts, 3.5.
However I don't see how to get from those figures to the average combo
sample standard deviation, which I calculate to be 2.05425287 and
1.790827048 respectively.
It's not the end of the world if there's no easy formula - I was using
the standard deviation as a measure of the dispersion of the individual
numbers and the variance should be equally as good.
Evil Nigel
John Griffin
I just added some stuff to a VB6 program I used to tabulate sums
a few years ago. Running it in the VB environment, it takes about
one minute. If I compile it to a .exe, it will probably take
about ten seconds.
> Your average Population SD is the same as mine, so if Stig
> accepts that we're not sock puppets fronting for the same
> person, that ought to convince him that your distribution is
> genuine. I notice he's been in some of the math newsgroups
> asking if there's a theoretical way to calculate the average,
> and the typical reply is (to paraphrase) "I don't know, that
> looks difficult".
That sounds like a reasonable answer.
> Below are the Turquoise version 3 rankings of the drawn UK
> lottery balls since I began recording the stats. None of the
> data is retro generated.
>
> By my calculation, the average Population Standard Deviation
> of the sets of Turquoise Rankings is 13.4474058610064 and the
> probability that this comes randomly from a population with
> mean 12.7232528212385 is 0.000703827297979179
I don't believe your analysis is meaningful. I think you should
treat the history as one sample of size 6*drawings and compare it
using the standard deviation of the universe (14.29?). Don't ask
me why I think that until tomorrow.
>
> Evil Nigel
> [ editor screwed up your data! ]
Evil Nigel
>
> I just added some stuff to a VB6 program I used to tabulate sums
> a few years ago. Running it in the VB environment, it takes about
> one minute. If I compile it to a .exe, it will probably take
> about ten seconds.
>
I really really MUST ditch spreadsheet macros and adopt a real
programming language.
I'm guessing Microsoft make you pay extra for free-standing VB, although
since I have Office I can run VB inside Excel.
>>By my calculation, the average Population Standard Deviation
>>of the sets of Turquoise Rankings is 13.4474058610064 and the
>>probability that this comes randomly from a population with
>>mean 12.7232528212385 is 0.000703827297979179
>
>
> I don't believe your analysis is meaningful. I think you should
> treat the history as one sample of size 6*drawings and compare it
> using the standard deviation of the universe (14.29?). Don't ask
> me why I think that until tomorrow.
>
Well, as far as usefulness is concerned, it's in the chocolate fireguard
category. There seemed to be some mileage in choosing numbers at the
extreme ends of the system's rankings, particularly the bottom end, but
that doesn't seem to be panning out.
>
>>Evil Nigel
>
>
>>[ editor screwed up your data! ]
>
>
I copied and pasted from a spreadsheet so it should be tab-delimited, if
your newsreader supports tabs.
Evil Nigel
nikb...@yahoo.co.uk
> John Griffin wrote:
>
> > I just added some stuff to a VB6 program I used to tabulate sums
> > a few years ago. Running it in the VB environment, it takes about
> > one minute. If I compile it to a .exe, it will probably take
> > about ten seconds.
>
> I really really MUST ditch spreadsheet macros and adopt a real
> programming language.
>
> I'm guessing Microsoft make you pay extra for free-standing VB, although
> since I have Office I can run VB inside Excel.
>
I believe you can dowwnload the express edition for free from here:
http://msdn.microsoft.com/vstudio/express/downloads/default.aspx
Ta
Nik
Evil Nigel
Thanks, Nik.
It's good to know you're still around, even though predominantly as a
lurker.
I'm toying with a new idea at the moment - I think it might be possible
to use historical draw data to pull off a sort of mathematical con trick
which guarantees that you'll never get a 6 match jackpot but might
increase the number of 3 match prizes to a worthwhile level.
(Ducks as the pig flying overhead gets dangerously close)
Evil Nigel
Nik Barker
>
> - Show quoted text -
Hi Nigel
Well I know there's those that would advocate that the only way to
guarantee a no 6 match jackpot is to not buy a ticket...
The UK Lotto Test I did here (now a scarily long time ago) sort of
found what you're looking for - though the intention was to get as
many of the 6 drawn numbers as possible - an unsurprising goal I know.
I've just started testing it again on "paper" (an excel spreadsheet
keeps tabs on it) and it seems to be performing as positively as it
did before. So if it keeps performing that way throughout a year cycle
I will by then have enough money to play it for real. I'll then make
as much money as I can before they ban me from placing bets, and then
I'll just write the book about how I did it...and hopefully the sales
of the book will keep me in an even more luxurious style of living
than I'll have been used to thus far...
...which way was the pig flying so I know to look out for it.
Ta
Nik
Gerry
> (Ducks as the pig flying overhead gets dangerously close)
Look, up in the sky ! It's bird, it's a plane, no wait.....
It's Nick UK !!
Stig Holmquist
wrote:
I lack the ability to calculate the variance for the data set
above.Would you please do it . I'm looking for a formula
that would predict the variance for all 14 million sets but
have not found one yet. I expect it to be around 9.
We now know the formula for the mean std.dev. as 14.3.
Stig H.
John Griffin
Every number appears with equal frequency (1712304) in the
13983816 sets, so the variance is the same as the variance of the
numbers 1 through 49, which is 200. The standard deviation is
14.14.
I'm not sure that's the data set you were referring to. I posted
an update to the frequency distribution, including a tabulation
of both sample and population standard deviations. Let me know
exactly what you're referring to.
Nick UK
He/she/it, a.k.a.. Gerry/Sherry/Griffuck-the-Gremlin, wrote..
>
> Look, up in the sky ! It's bird, it's a plane, no wait.....
>
> It's Nick UK !!
>
Look! Look! Look!.. up in Usenet..
Is it Gerry?
Is it Sherry?
Is it Griffuck-the-Gremlin?
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Bolted/jammed into his shit-dribbling commode, an infestation by
Gerry/Sherry/Griffuck-the-Gremlin, of more than..
**THREE HUNDRED AND FIFTY NEWSGROUPS**
In just 3.5 years!
Look up in the sky? Nah, look here.. .
rec.gambling.lottery Griffuck/Gerry/Sherry/ has posted 1,119 articles.
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alt.english.usage he/she/it has posted 55 articles.
99% of subscribers to the above newsgroups, are now advising
He/she/it, a.k.a.. Gerry/Sherry/Griffuck-the-Gremlin..
> "You are way beyond help, you sick Bastard!"
http://rglsheepman.bravehost.com/Gerry.html
Stig Holmquist
wrote:
>Stig Holmquist <stigf...@hotmail.com> wrote:
Your mean s.d =13.94 differs from the theoretical 14.29
because you based your calculation on the truncated or
abreviated class values. I did the same for 301 sets of the old
PB 5/63 game and got 14.49 as amean while the mean was 14.97
when based on the actual s.d. values.
Also, the max. variance must be for 1-2-3-47-48-49. Typo in 43?
Stig Holmquist
Evil Nigel
> The std.dev. for sums in the 6/49 game is 32.8
For the system (versions A, 0 and M) that I currently use for the
pick-16 trial, I've been recording the sums of the rankings of the drawn
numbers. They are somewhat larger than 32.8, possibly giving credibility
to my theory that a little turquoisishness does unusual things to the
volatility.
Do you happen to have a few more decimal places available for that 32.8?
It seems intuitive to me that if the standard deviation of the sums is
larger than expected, then the standard deviations of the combos should
be smaller than expected, and perhaps I should be recording the
individual rankings too.
Evil Nigel