# Playing Lotto with LINQ

30 Jan 2009 in

You know, they are once again going craazy in Germany - The Lotto jackpot has swollen to a whopping 35 million. That’s a lot of money, certainly enough to devote some of my time to the subject.

I was looking around the Internet whether I could get my hand on all the lotto drawings that happened in Germany. I found a file here, which seems to contain all Saturday drawings. I cross-checked a few drawings with a different source here and it looks like these could really be the numbers. You can find other statistical analysis here as well.

I took the file since it was quickly readable by a machine. I read each line into a structure called Drawing, containing the Date of Draw and an array of int containing the numbers. Drawing itself implements IEnumerable<int> which enumerates the contained numbers.

Once the file is read I have an array of Drawings. The first analysis I did was to see whether all Drawings had all 7 numbers (the 6 out of 49 and the Zusatzzahl, the additional number).

The used LINQ query looks like this:

var result = from d in drawings group d by d.Numbers.Count() into g select g; foreach (var a in result) Console.WriteLine("{0} entries have {1} numbers", a.Count(), a.Key);

Which gave me…

``` 36 entries have 6 numbers 2519 entries have 7 numbers ```

Ergo, a few entries had the Zusatzzahl missing, but I can live with that. Next was a quick check which number is drawn most (and least)…

var result = from d in drawings from n in d group d by n into numbers orderby numbers.Count() descending select numbers;

The most popular number so far has been 32 (420 times), the least popular 13 (313 times).

Next question: Given your numbers, how lucky would you have been so far if you would have played every Saturday with the same numbers since 1955?

This query is a little bit lengthy because it contains the following information:

• I want to see the numbers that were drawn
• I do not want to see where I only would have had one or two correct numbers
• If the combination was drawn only once I want to see which date that happened (better matches are more likely to have happened only once)

It’s late, so maybe there is a more elegant solution, but I came up with this (please note that nums are the numbers typed in to be matched):

var result = from drawing in drawings let matches = drawing.Where(d => nums.Contains(d)) where matches.Count() > 2 let matchedNums = string.Join(",", matches.OrderBy(i => i).Select(i => i.ToString()).ToArray()) let elem = new {matches, matchedNums, drawing.DayOfDraw} group elem by elem.matchedNums into m orderby m.Key.Length descending let date = m.Count() > 1 ? "Various" : m.FirstOrDefault().DayOfDraw.ToString("dd.MM.yyyy") select new { Numbers = "[" + m.Key + "]", Hits = m.Count(), DrawDate = date };

That provides a bit more fun. The output looks e.g. like this:

``` Enter your numbers:7,13,16,19,32,43 Numbers: [7,13,16,32,43] were drawn 1 times on 28.10.1978 Numbers: [13,16,19,32] were drawn 1 times on 20.08.1977 ... ```

For the seriously awesome numbers 5,7,23,42 I can say that they were never drawn together. My wife played Lotto on Wednesday (1: 140’000’000 ain’t deterring her) with 7,13,16,19,32,43 . That one had 5 hits once…even so, it’s 31 years ago.

I didn’t get further today but I may try to pull off some other LINQies, see what else those numbers can tell us ;) So far, I can only say that if you win the Jackpot you are one lucky guy!

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