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Old Dec 31, 2007, 01:32 AM
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Euromillions statistics
How do you calculate the probability of winning the Euromillions?

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Old Dec 31, 2007, 01:37 AM   #2  
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Try this: Euromillions, Euromillónes, Euromilhoes: Software, Strategy, Systems, Odds

Good piece on Wiki too: EuroMillions - Wikipedia, the free encyclopedia

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Ion Saliu agrees: Refers to the best resources.
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Old Dec 31, 2007, 04:19 AM   #3  
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I love the fact that bookies are willing to give better odds of Elvis crash landing in a UFO on top of the Loch Ness Monster than you winning the Euromillions! Ha ha!

Also, quite like the graphic at the bottom of that story!

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Old Jan 24, 2008, 03:05 AM   #4  
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The euro millions probability has to be calculated in two parts, firstly the probability of getting 5 balls out of 50. Order doesnt matter so:
P(A) = 50!/5!(50-5)! = 2,118,760
Then we need to calculate the probability of getting the 2 balls out of 9 so:
P(B) 9!/2!(9-2)! = 36
Because the two are independent we need to multiply them together so:
P(A) * P(B) = P(A&B)
2,118,760 * 36 = 76,275,360
Therefore the chances of winning the euromillions is 1 in 76,275,360

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Ion Saliu agrees: Correct formulas, although they are not in the simplified form.
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Old Jan 26, 2008, 03:52 AM   #5  
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Thank you, I learned this in school but had forgotten how to use probabilities formulas.
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Old Feb 9, 2008, 11:00 AM   #6  
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The lotto games are covered by the numerical sets named COMBINATIONS. The sets and combinations are very well covered at my website, including unique software:

Combinatorics, Permutations


The fundamental formulas of probability are presented here:

Probability Theory


The most comprehensive formula to calculate the probability (or odds) of lotto games is known as hypergeometric distribution probability. It covers multiple prizes, not only the jackpot (the first prize in a lotto game).

Here is a text format of the hypergeometric formula for the case ‘m of k in s from n’:
Code:
                                C(n, k)

P(m of k in s from n) = ---------------------------- 

                            C(s, m) * C(n-s, k-m)
An example: ‘4 of 6 in 12 from 49’. You want to know the odds of winning 4 numbers of the 6 drawn by the lottery in a 49-number game. S=12 is a pool of numbers; e.g. you play a system or lotto wheel which comprises 12 numbers. The default for s is 6 for lotto 6 games. It is the general case when you don’t play lotto wheels or pools of numbers.

C() represents the formula of combinations:

Code:
             n*(n-1)*(n-2)*(n-3)*...(n-k+1)

C(n, k) = ------------------------------------- 

                       1*2*3*...k
For k=6 and n=49 (the most common lotto game), the formula reads:

C(49, 6) = [49 * 48 * 47 * 46 * 45 * 44] / [1 * 2 * 3 * 4 * 5 * 6]

Euromillions (like the Powerball) is a two-in-one lotto game. You calculate first the odds for the first part (game): the 5 regular numbers. Then, you calculate for the second part: The Star numbers. Finally, you multiply the two results and get the final odds for Euromillions.

I wrote the most comprehensive software for calculating odds and probability and also analyze combinations and lexicographical order. The main software titles:

OddsCalc.EXE
PermuteCombine.EXE
LexicographicSets.EXE

A different member (Curlyben) already pointed to my web page that deals specifically with the game of Euromillions. The page also runs two (free) ActiveX controls that calculate the odds and also generate Euromillions combinations (1000 at a time).

Best of luck!
Parpaluck,
EuroAmerican At-Large
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Old Feb 9, 2008, 08:22 PM   #7  
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Quote:
Originally Posted by Ion Saliu
disagrees: Mockery has never solved problems or challenges.
Who was I mocking?

I'm sorry if my little interjecture of fun somehow offended your awesome website!

Some people need to grow a sense of humour!

Anyone else fancy chucking some reds my way, I seem to be on a roll at the minute!
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Old May 7, 2009, 04:43 PM   #8  
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Quote:
Originally Posted by Internet Junkie View Post
How do you calculate the probability of winning the Euromillions?
I realize now that this thread has some popularity, based on the consistent referrals I get from here. Appears also to be popular in Google searches. Returning the favor, here is some more useful resources. You can download for free the results of the Euromillion lotto game. You get every draw, from the beginning of the game. The file is also ready for immediate statistical analysis, using the software offered on the same website. You get also statistical reports ranking the Euro Millions numbers by frequency, from the hottest to the coldest, including the percentages of hitting.

Euromillions, Euromillónes, Euromilhões History File: Results, Drawings, Past Winning Numbers;

Euromilionen Lotto Numbers Ranked by Frequency.

Ion Saliu,
Statistician At-Large
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Old May 7, 2009, 04:49 PM   #9  
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Code:
                The Euromillions Numbers Ranked by Frequency 
                File: LOTTERY\EUROMILLIONS.DAT
                Draws Analysed:  273  |  Date: 05-02-2009
                Frequency norms based on probabilities:  10.00% &  22.22%

 =======================================================================
         R E G U L A R   Numbers       |       E U R O   S T A R S
 =======================================================================
 Rank  Regular #  Hits   Percentage    |    Star #   Hits   Percentage
 =======================================================================
   1      50       44      16.12%              1      69      25.27%
   2      37       37      13.55%              5      68      24.91%
   3      12       35      12.82%              6      68      24.91%
   4      19       35      12.82%              3      64      23.44%
   5      14       33      12.09%              7      61      22.34%
   6      21       33      12.09%              8      60      21.98%
   7       3       32      11.72%              2      53      19.41%
   8      36       32      11.72%              9      52      19.05%
   9       7       32      11.72%              4      51      18.68%
  10       9       32      11.72%
  11      25       31      11.36%
  12       1       31      11.36%
  13       4       30      10.99%
  14      11       30      10.99%
  15      44       30      10.99%
  16      45       30      10.99%
  17      15       30      10.99%
  18       8       29      10.62%
  19      26       29      10.62%
  20      29       29      10.62%
  21      49       29      10.62%
  22      16       29      10.62%
  23      23       28      10.26%
  24      10       28      10.26%
  25      40       28      10.26%
  26      41       28      10.26%
  27      35       27       9.89%
  28      38       27       9.89%
  29       6       26       9.52%
  30       5       26       9.52%
  31      47       25       9.16%
  32       2       25       9.16%
  33      42       25       9.16%
  34      17       24       8.79%
  35      48       24       8.79%
  36      22       24       8.79%
  37      30       24       8.79%
  38      33       23       8.42%
  39      34       23       8.42%
  40      13       23       8.42%
  41      27       23       8.42%
  42      31       23       8.42%
  43      20       22       8.06%
  44      18       22       8.06%
  45      32       22       8.06%
  46      24       21       7.69%
  47      43       21       7.69%
  48      39       19       6.96%
  49      28       17       6.23%
  50      46       15       5.49%
 =======================================================================


         The Euromillions Numbers Ranked by Frequency - By Position
         File: LOTTERY\EUROMILLIONS.DAT
         Draws Analysed:  273  |  Date: 05-02-2009

    ==================================================================================================================================================
    Rank |    Position 1     |    Position 2     |    Position 3     |    Position 4     |    Position 5     |    Star pos_1     |    Star pos_2     |
         | Number Hits   %   | Number Hits   %   | Number Hits   %   | Number Hits   %   | Number Hits   %   | Number Hits   %   | Number Hits   %   |
    ==================================================================================================================================================
      1  |   1    31  11.36% |  11    18   6.59% |  21    15   5.49% |  37    19   6.96% |  50    44  16.12% |   1    69  25.27% |   8    55  20.15% |
      2  |   2    24   8.79% |   9    14   5.13% |  19    14   5.13% |  35    14   5.13% |  49    24   8.79% |   3    50  18.32% |   9    52  19.05% |
      3  |   3    24   8.79% |  12    14   5.13% |  22    13   4.76% |  38    13   4.76% |  48    20   7.33% |   2    44  16.12% |   6    45  16.48% |
      4  |   4    21   7.69% |   8    12   4.40% |  25    13   4.76% |  40    13   4.76% |  47    18   6.59% |   5    35  12.82% |   7    45  16.48% |
      5  |   7    21   7.69% |  10    12   4.40% |  14    11   4.03% |  44    12   4.40% |  45    17   6.23% |   4    31  11.36% |   5    33  12.09% |
      6  |   5    20   7.33% |  13    12   4.40% |  27    11   4.03% |  45    12   4.40% |  44    16   5.86% |   6    23   8.42% |   4    20   7.33% |
      7  |   6    19   6.96% |  16    12   4.40% |  30    11   4.03% |  34    10   3.66% |  42    16   5.86% |   7    16   5.86% |   3    14   5.13% |
      8  |   9    15   5.49% |  19    12   4.40% |  16    10   3.66% |  25    10   3.66% |  41    15   5.49% |   8     5   1.83% |   2     9   3.30% |
      9  |   8    14   5.13% |  15    11   4.03% |  31    10   3.66% |  41    10   3.66% |  38    12   4.40% |   9     0   0.00% |   1     0   0.00% |
     10  |  12    13   4.76% |  20    11   4.03% |  32    10   3.66% |  43    10   3.66% |  43    11   4.03% |
     11  |  10    10   3.66% |  21    11   4.03% |  26     9   3.30% |  36    10   3.66% |  40    10   3.66% |
     12  |  14    10   3.66% |  18    10   3.66% |  24     9   3.30% |  31    10   3.66% |  36     9   3.30% |
     13  |  11     9   3.30% |   7    10   3.66% |  29     9   3.30% |  39     9   3.30% |  46     9   3.30% |
     14  |  15     9   3.30% |  23    10   3.66% |  33     9   3.30% |  29     9   3.30% |  37     8   2.93% |
     15  |  17     4   1.47% |  14     9   3.30% |  36     9   3.30% |  19     8   2.93% |  39     7   2.56% |
     16  |  16     3   1.10% |   4     9   3.30% |  18     8   2.93% |  42     7   2.56% |  35     6   2.20% |
     17  |  13     3   1.10% |  17     8   2.93% |  23     8   2.93% |  26     7   2.56% |  34     5   1.83% |
     18  |  20     3   1.10% |   3     8   2.93% |  15     8   2.93% |  30     6   2.20% |  33     4   1.47% |
     19  |  22     3   1.10% |  26     8   2.93% |  12     8   2.93% |  23     6   2.20% |  26     3   1.10% |
     20  |  25     3   1.10% |  29     8   2.93% |  37     8   2.93% |  32     6   2.20% |  30     3   1.10% |
     21  |  23     2   0.73% |  24     6   2.20% |  34     7   2.56% |  33     6   2.20% |  32     3   1.10% |
     22  |  21     2   0.73% |   5     6   2.20% |  13     7   2.56% |  46     6   2.20% |  23     2   0.73% |
     23  |  26     2   0.73% |   6     6   2.20% |  17     7   2.56% |  47     6   2.20% |  31     2   0.73% |
     24  |  19     1   0.37% |  28     5   1.83% |  28     6   2.20% |  27     5   1.83% |  29     2   0.73% |
     25  |  24     1   0.37% |  27     5   1.83% |  35     6   2.20% |  17     5   1.83% |  18     1   0.37% |
     26  |  27     1   0.37% |  25     4   1.47% |  20     4   1.47% |  49     5   1.83% |  24     1   0.37% |
     27  |  28     1   0.37% |  30     4   1.47% |  10     4   1.47% |  20     4   1.47% |  25     1   0.37% |
     28  |  29     1   0.37% |  36     4   1.47% |  40     4   1.47% |  21     4   1.47% |  21     1   0.37% |
     29  |  32     1   0.37% |  33     3   1.10% |   9     3   1.10% |  22     4   1.47% |  27     1   0.37% |
     30  |  33     1   0.37% |  22     3   1.10% |   8     3   1.10% |  28     4   1.47% |  28     1   0.37% |
     31  |  35     1   0.37% |  32     2   0.73% |  39     3   1.10% |  16     4   1.47% |  22     1   0.37% |
     32  |  18     0   0.00% |  37     2   0.73% |  11     3   1.10% |  48     4   1.47% |  13     0   0.00% |
     33  |  30     0   0.00% |  34     1   0.37% |  41     3   1.10% |  24     4   1.47% |  14     0   0.00% |
     34  |  34     0   0.00% |   2     1   0.37% |  38     2   0.73% |  18     3   1.10% |  15     0   0.00% |
     35  |  31     0   0.00% |  31     1   0.37% |  42     2   0.73% |  14     3   1.10% |  16     0   0.00% |
     36  |  36     0   0.00% |  40     1   0.37% |  44     2   0.73% |  10     2   0.73% |  17     0   0.00% |
     37  |  37     0   0.00% |  35     0   0.00% |   6     1   0.37% |  15     2   0.73% |   1     0   0.00% |
     38  |  38     0   0.00% |  38     0   0.00% |   7     1   0.37% |  13     1   0.37% |  19     0   0.00% |
     39  |  39     0   0.00% |  39     0   0.00% |  45     1   0.37% |   6     0   0.00% |  20     0   0.00% |
     40  |  40     0   0.00% |   1     0   0.00% |  47     1   0.37% |   7     0   0.00% |   2     0   0.00% |
     41  |  41     0   0.00% |  41     0   0.00% |   1     0   0.00% |   8     0   0.00% |   3     0   0.00% |
     42  |  42     0   0.00% |  42     0   0.00% |   2     0   0.00% |   9     0   0.00% |   4     0   0.00% |
     43  |  43     0   0.00% |  43     0   0.00% |  43     0   0.00% |   1     0   0.00% |   5     0   0.00% |
     44  |  44     0   0.00% |  44     0   0.00% |   3     0   0.00% |  11     0   0.00% |   6     0   0.00% |
     45  |  45     0   0.00% |  45     0   0.00% |   4     0   0.00% |  12     0   0.00% |   7     0   0.00% |
     46  |  46     0   0.00% |  46     0   0.00% |  46     0   0.00% |   2     0   0.00% |   8     0   0.00% |
     47  |  47     0   0.00% |  47     0   0.00% |   5     0   0.00% |   3     0   0.00% |   9     0   0.00% |
     48  |  48     0   0.00% |  48     0   0.00% |  48     0   0.00% |   4     0   0.00% |  10     0   0.00% |
     49  |  49     0   0.00% |  49     0   0.00% |  49     0   0.00% |   5     0   0.00% |  11     0   0.00% |
     50  |  50     0   0.00% |  50     0   0.00% |  50     0   0.00% |  50     0   0.00% |  12     0   0.00% |
    ==================================================================================================================================================
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