# Equipartition

#### Virbatem

##### Member
Equipartition pertains to equilibrium or the commonly held but false belief that (in the realm of random numbers) eventually all the occurances of every number will balance out or catch up.

For example, a few numbers have been drawn a mere 100 times over a 1000 draw lottery while at the other end of the scale, a few numbers have been drawn 140 or more times.

Those who hold the belief that those few low appearing numbers will soon have a long run and catch up to the frequency of the more comonly appearing number will be waiting a long time.

Several in-house tests and reference to two different lotteries have shown that numbers which have multiple appearances within the first 15 to 20 draws remain the most frequently draw numbers.

ref: http://www.peterwebb.co.uk/probability.htm#Equipartition

Further testing has revealed the following results which list how many times each number has been the most frequent over 900 lottery draws for a 6/45 game.

Number - Most frequent - Occurances
#19 - 453 - 136
#41 - 167 - 129
#08 - 149 - 139
#25 - 58 - 139
#29 - 48 - 120
#07 - 14 - 133
#01 - 5 - 132
#26 - 3 - 135
#44 - 3 - 113
#33 - 1 - 128
#27 - 1 - 109 *
#05 - 0 - 133
: - : - :
#13 - 0 - 104

#19 was the most frequently drawn number; 453 times over 900 draws from a 6/45 lottery. Its total times drawn was 136.
#19 was drawn 3 times in the first 6 lottery drawings and 4 times in the first 15 draws.

Conversely, #13 was not drawn until the 29th lottery draw and after 900 draws has appeared the least number of times for all 45 numbers.

Please note there is ALWAYS an exception to every rule and #27 is the exception here.

Next time the top 6 numbers from the list all have a skip period nearing 6 I am going to play them. If I do not comment on the result then I suggest you get pen and paper and try it yourself as I will be on a tropical island somewhere....

#### thornc

##### Member
The so called law of averages... usually says that with a big sample size everything will average out!
The question is: what's a big sample size!

In a 6/49 lotto when you have close to 14M possible combinations, I don't think a sample size of 2K is big enough! (canadian numbes!)

I did some quick calculations on a web page somewhere and to get 1% margin of error at 99% confidence interval you need close to 17K sample! (note that I didn't do an long search so I might ended up using the wrong formula!)

#### Virbatem

##### Member
Yes, point taken. I have yet to create a random database of such magnitude to test for the existance of a "law of averages". Maybe soon.

Additionally to equipartition, a quick calcuation for two lotteries shows the ratio of numbers drawn in each game as:

46% : 54% for 6/49
44% : 55% for 6/45

where the first % represent the percentage of numbers drawn which fell into the lower half of the Times Drawn count. Therefore most of the time, in each lottery draw, the larger percentage of numbers drawn are more frequently occuring numbers. This does makes absolute logical sense when you think about it - but it's nice to have some concrete methematical evidence to back it up.

thornc said:
The so called law of averages... usually says that with a big sample size everything will average out!
The question is: what's a big sample size!

In a 6/49 lotto when you have close to 14M possible combinations, I don't think a sample size of 2K is big enough! (canadian numbes!)

I did some quick calculations on a web page somewhere and to get 1% margin of error at 99% confidence interval you need close to 17K sample! (note that I didn't do an long search so I might ended up using the wrong formula!)

#### thornc

##### Member
Sorry but I don't consider your numbers significant!
What's the margin of error? What's the sample size?

With a 5% margin of error (a typical one), the values you give might as well be equal!

46+5 = 51; 54-5 = 49! So in the worst possible scenario it can be the other way around!

#### Grandmaster

##### Member
I did a experiment with 2 lotteries to test Virbatem theory:

Georgia Lotto South 6/49

First 20 draws 9/12/01 TO 11/17/01
07 28 41 11 14 16 19 20 45 46 02 05

10 12 13 15 17 24 31 34 35 42

ALL HISTORY available lottostrategies.com
36 44 42 20 26 17 45 49 09 31 01 19

07 28 40 12 24 34 41 03 11 27

13/22 numbers repeat

Quebec 6/49

First 20 draws 10/03/01 TO 12/08/01
18 43 21 02 42 47 04 26 29 46 01 03

12 13 22 25 28 36 45 48 07 08

ALL HISTORY Available lottostrategies.com
43 26 47 40 46 01 29 07 48 04 13 30

02 34 37 44 20 31 36 18 35 45

14/22 numbers repeat

Does anyone has the software Lottoeval of Virbatem? I would appreciate if you could send me a copy...

#### CMF

##### Member
Re numbers occurrence evening out.

Virbatem

All the many long runs sometimes 10,000 draws or more I've done have seen all the numbers fall into about 5% over/under the average - in fact you don't need to go anywhere near that to see it. For an exercise I've combined all the 6/49 Draws from around the world together - from memory I think it's around 17,000 Draws and they all work out to the same kind of range indicated above.

I always remember reading a newspaper article where a Professor said eventually they would all be the same. I disagree - there might be a miraculous point where they are all the same but this would change for the next draw.

An interesting thing I have observed is that your highest numbers tend to be closer together. So in 6/45 game 44 and 45 can be the same. For those that work by the history it's not a bad idea to monitor the top numbers.

If they were computer drawn I could theorise about it as I saw the effect before I completed my own RNG but why it should happen with Ping Pong balls I haven't a clue.

Regards
Colin

#### tomtom

##### Member
Any combination in a 6/49 has a mathematically proven chance of 1/ 13983816 to appear in the very next draw. Many people can’t accept this even in a case of a fairly small confirmed databases containing four or five repeats, two all odd or even numbers in a row, or even knowing about some repeating all numbers combinations especially in those 5/xx lotteries . Present lottery databases mostly contain a few hundreds or thousands draws. In case of any 6/49 database containing 7 millions unique combinations, there are something like 50% chances that the very next draw will be a repeated combination, any one of these 7 millions. Of course, chances for a real 7 millions unique combinations tend to 0, since repeated combinations will start to appear much earlier. Therefore, since it is necessary a bit less then 3000 years in order to get any chance to see all combinations appeared in a 6/49 , which will eventually start to tend to infinite at some point because of repeating combinations, in my opinion waiting for a situation where limits tend to get near either 0 or infinite seems a bit too much…..optimistic?

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