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Average of the UK lottery
15-12-2019, 03:00 PM
Post: #1
Average of the UK lottery
Some of you may know that every lottery result has an identifying number calculated from how many changes in numbers there have been working from right to left compared with sequence 1,2,3,4,5,6. The number is called the Lexicographic or CSN number.

Starting from the right, imagine each ball number increases like a car odometer except instead of each digit going up to a max of 9 and the one on its left going up by 1, it goes up to its allowable maximum in its sorted position, thats 59 in the last position, 58 in second last etc.
Then the the digit to its left can go up by 1 whilst the current digit resets to its next allowable minimum value according to where it is, sorted in ascending order.

if
1,2,3,4,5,6 is given number 1 then
1,2,3,4,5,7 is number 2
1,2,3,4,5,59 is number 54.
1,2,3,4,6,7 is number 55
Because there are 45,057,474 combinations in the lottery this means that :-
54,55,56,57,58,59 has a CSN value of 45,057,474.

So they could run a lottery using just numbers between 1 and 45,057,474 instead and the odds of winning a jackpot prize would be just the same. Just not as much fun choosing a number to play. A lot harder to work out how to pay consolation prizes too.

Anyway the point Im getting to is that the mid point of the lottery range can be easily found, as its half of 45,057,474. This is 22,528,737.
These numbers can convert in reverse and its possible to work out what ball numbers correspond to CSN 22,528,737.
They are 7,9,25,27,43,5,8
I find it surprising that the mid point of a 59 ball lottery starts with a 7, but its a fact.

One thing I've done out of interest is to change all the 430 lotto draws since we had 59 balls to CSN numbers. One can then find the average CSN number drawn for the lottery so far. That average is 23,433,970 which in turn converts to ball numbers 7,14,26,34,56,57.
Comparing this with the mid point set, they do look to be in the same ball park. I really should not be surprised because if the lottery is fair in its spread of results over the range possible, then over time the average result will get closer and closer to the mid point value. All this tells us is that the results so far are fairly and widely spread across the range (I have a graph to prove it). It does nothing to help predict what the future results are likely to be unfortunately, just an interesting curiosity that I thought I would share.
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