## Lottery: How to use past results/sales to figure out chance of split w ur pick?

Now, most lottery corporations publish their numbers picked and the number of people who matched them. They also publish their total sales as well.

e.g. numbers A B C D E F G

Match all 6: A B C D E F G = 2 winners
Match 5 of 6: A B C D E F, A B C D E G, A B C D F G, etc = 10 winners
Match 4...
Match 3...

Some number combinations have resulted in a 10 way split while other numbers have resulted in 0 winners. So obviously, it is better to pick the ones with no splits than the ones with.

Is there any way to use that information to mathematically determine which numbers will least likely be picked by someone else (and thus least chance of a split jackpot)?

What I have so far is:

1. Use a random number generator

2. Filter it against commonly picked combinations (1 2 3 4 5 6), prime numbers, odds only, even only, dates etc

3. ???
(filter it against past lottery results)

4. Profit?
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 Use the lottery history to compute stats on the set of available numbers usage the pick the ones with the lowest usage. Or break the history in periods like yearly periods, then do number stats in each period to get an idea of number trending.
 Recognitions: Gold Member Science Advisor Staff Emeritus Unless something (and probably illegal) numbers coming up in a current lottery are completely independent of previous lotteries. You cannot gain any information from past values.

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## Lottery: How to use past results/sales to figure out chance of split w ur pick?

You're right that the only useful information is the patterns others tend to select. Yes, if you can avoid those then you've definitely improved your own average winnings, though whether by enough to make it positive is unclear.
There seems no merit in using a random number generator. As far as the lottery's number generator is concerned, all sequences are equally likely anyway. So having found a selection that's good at avoiding split pots, stay with it.
 Recognitions: Science Advisor It is very hard to be purely random; you may want to apply a Chi^2 to test for randomness, as a goodness-of-fit test.

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In general, the other players will have some probability distribution which depends on all 6 numbers at the same time. (1 2 3 4 5 6) will have a high probability, for example - much higher than the individual probabilities of "1 is used", "2 is used", ... would suggest.
Let's use 1 to N as range for the six numbers.

Of course, it is impossible to find this distribution - it has (N choose 6)-1 degrees of freedom.

As a toy model, you could assume that all numbers are independent. For each pick, each number has a probability pi of getting picked ((N-1) degrees of freedom). Using these pi, you can evaluate the probability of all possible combinations - might be a bit tricky for ~4 numbers, but it is possible. For each published result, you can compare this prediction with the calculation, and adjust your numbers accordingly (this is quite nontrivial). The required computing time depends on the amount of input data... the process will find some optimal values for those probabilities. Deviations from the prediction now come from random fluctuations and correlations between those numbers.

The next best model would be to add correlations between two numbers each, this already gives ~N(N+1)/2 degrees of freedom. And so on :).

 though whether by enough to make it positive is unclear
I would doubt that.

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 Quote by HallsofIvy Unless something (and probably illegal) numbers coming up in a current lottery are completely independent of previous lotteries. You cannot gain any information from past values.
I think the OP is referring to numbers used by the general public, not outcomes of the
lottery.
 So, to look at this from the long view, what the OP is saying is: I know I won't increase the odds of me actually winning, I just want to decrease the odds of having to share it with others. I think, if I were to win the lottery big time, but had to share it with others, I would not look a gift horse in the mouth.
 Let me illustrate the problem: Lotto 649: In both drawings the prizes and sales are roughly the same. about \$3.1million jackpot and about 11million in sales. However, the number of winners is vastly different. In the May drawing, we have a total of 60 winners that matched 5 or 6 of the numbers drawn. In the june drawing, we have a total of 143 that matched that amount. We can conclude that the may numbers 05, 32, 37, 38, 39, 42 or any combination revolving that set is a "better" pick than the latter combination. However, is there any way to mathematically determine any more information?

 Quote by techcrium We can conclude that the may numbers 05, 32, 37, 38, 39, 42 or any combination revolving that set is a "better" pick than the latter combination.
How exactly can we conclude that? Sure, it would have been a great pick for you - if you had a time machine.

I may be misunderstanding, but it sounds like what you're doing is tantamount to this:

I roll a die 6 times, the results were 1,3,5,6,5,2.

I can conclude that 5 is a "better" pick than any other.

No. The point of a fair, random lottery is that results of one draw/roll have no effect on the next draw/roll.

 Quote by DaveC426913 How exactly can we conclude that? Sure, it would have been a great pick for you - if you had a time machine. I may be misunderstanding, but it sounds like what you're doing is tantamount to this: I roll a die 6 times, the results were 1,3,5,6,5,2. I can conclude that 5 is a "better" pick than any other. No. The point of a fair, random lottery is that results of one draw/roll have no effect on the next draw/roll.
It is a better pick because if you take a look at the statistics, the may 5 drawing shows that there are much less winners than the june 30 drawing.

If you rolled a 5 and you found out 400 other people picked 5 and you had to split the jacpot 400 ways...

If you rolled a 2 and you found out 9 other people picked 2 and you had to split it 9 ways...

and knowing that the chance of drawing a 5 and a 2 are equal...

Then is it not safe to conclude that a 2 is a better pick than a 5?
 using the lottery history can determine the most commonly selected numbers which would be the ones to avoid if you're trying not to share the prize when you win. why is this so? because many people get tired of selecting numbers and so use common sets of numbers like birthdays for family members that means that numbers in the range of 01 - 12 are the most common especially in the last few years (months, days and years) then would come 13-31 block followed by 32-NN for whatever the lottery uses. my feeling though is you should just enjoy playing the lottery and whatever you win is a gift that you can share with others through gifts, dinners and goodtimes. In the end you'll be happier. As an aside you should watch Waking Ned Devine and Irish comedy about a fellow winning the lottery in a small village.

 Quote by techcrium Then is it not safe to conclude that a 2 is a better pick than a 5?
No.

It is safe to conclude that 2 was a better pick than 5.

It tells you nothing about the next series of rolls, which is as likely to be 5,5,5,5,5,5 as any other specific sequence (the odds are exactly 1 in 66 or 1 in 46,656).

You are making the classic mistake of assuming that, if you toss a fair coin and get heads 4 times in a row, your best bet is on heads. It isn't. Regardless of what's happened in the past, the odds of the next roll being heads are 50:50.

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 Quote by DaveC426913 You are making the classic mistake of assuming that, if you toss a fair coin and get heads 4 times in a row, your best bet is on heads. It isn't. Regardless of what's happened in the past, the odds of the next roll being heads are 50:50.
DaveC, techcrium is doing nothing of the sort. He has made it abundantly clear that all he is trying to do is avoid the selections others make.

 Quote by haruspex DaveC, techcrium is doing nothing of the sort. He has made it abundantly clear that all he is trying to do is avoid the selections others make.
That's what I'm trying to determine. I specified exactly that in post 9, but then he seemed to go back on it in his next post.

Thing is, if he were only interested in not having to share, then he need not worry about what the winning numbers are at all; he need only worry about what numbers people are picking. Yet he keeps bringing up the issue of which numbers won in the last lottery, suggesting he thinks that this has anything to do with the winners of the next lottery.

If the issue here is about not having to share, (and we assume the lottery is fair*), then it is very simple: just bet what other people aren't betting - winning numbers are irrelevant.

* if we don't assume this, then that's a whole nother discussion

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