![[UK National Lottery Logo]](/Lottery.gif){kind=small}
Pos No. Wins Sales Percentage 1 03 925,122 1,305,201,220 0.07088% 2 08 1,034,821 1,464,176,250 0.07068% 3 09 497,788 705,910,840 0.07052% 4 07 583,882 861,290,170 0.06779% 5 01 526,510 784,132,080 0.06715% 6 11 952,108 1,445,338,940 0.06587% 7 19 1,041,571 1,599,275,500 0.06513% 8 31 621,838 954,941,820 0.06512% 9 43 769,387 1,196,481,040 0.06430% 10 05 661,859 1,031,136,870 0.06419% 11 16 1,262,088 1,973,155,970 0.06396% 12 12 554,905 872,134,030 0.06363% 13 44 563,180 889,046,770 0.06335% 14 24 899,648 1,443,923,300 0.06231% 15 02 548,199 911,533,930 0.06014% 16 23 880,625 1,464,538,860 0.06013% 17 27 441,769 739,475,080 0.05974% 18 15 472,100 807,703,240 0.05845% 19 06 573,014 987,782,680 0.05801% 20 21 587,416 1,024,199,650 0.05735% 21 10 775,723 1,353,036,330 0.05733% 22 25 346,883 606,578,860 0.05719% 23 28 633,728 1,113,947,610 0.05689% 24 26 547,883 964,373,070 0.05681% 25 20 596,551 1,064,001,910 0.05607% 26 38 749,599 1,352,856,490 0.05541% 27 29 802,981 1,459,634,020 0.05501% 28 45 598,792 1,089,604,250 0.05495% 29 37 826,475 1,518,780,640 0.05442% 30 22 581,147 1,069,767,890 0.05432% 31 14 666,485 1,239,728,150 0.05376% 32 49 566,786 1,056,569,800 0.05364% 33 32 440,770 826,904,790 0.05330% 34 30 534,765 1,012,575,080 0.05281% 35 42 684,220 1,300,424,510 0.05262% 36 50 356,619 678,496,930 0.05256% 37 55 369,071 706,631,550 0.05223% 38 40 545,876 1,049,229,690 0.05203% 39 17 526,810 1,020,773,750 0.05161% 40 18 558,712 1,083,145,440 0.05158% 41 04 456,800 885,870,840 0.05157% 42 36 656,981 1,286,820,920 0.05105% 43 34 644,874 1,266,001,220 0.05094% 44 13 367,603 721,822,940 0.05093% 45 58 648,517 1,285,620,650 0.05044% 46 57 263,555 523,273,470 0.05037% 47 46 589,514 1,187,515,480 0.04964% 48 41 563,902 1,150,126,490 0.04903% 49 33 188,555 384,833,700 0.04900% 50 35 392,926 814,279,000 0.04825% 51 53 416,552 864,585,810 0.04818% 52 47 546,906 1,146,125,910 0.04772% 53 54 943,748 1,995,230,020 0.04730% 54 56 257,260 546,002,100 0.04712% 55 48 293,533 630,755,710 0.04654% 56 39 501,914 1,097,615,980 0.04573% 57 51 467,484 1,030,139,530 0.04538% 58 52 511,795 1,163,111,100 0.04400% 59 59 447,575 1,026,695,050 0.04359%Notes:
Firstly, I needed to work out how many winning tickets used a particular number (let's say using the number 1 as an example) in each prize tier for a single draw. Camelot don't release the figures for this, so for a particular prize tier, it has to be estimated thus:
Winning tickets using the number 1 in a prize tier = ( Number of combinations in that tier that use the number 1 / Total combinations in that tier ) * Number of actual prize winners in that tier [yes, this last figure is indeed released by Camelot]
This assumes an even distribution of combinations of course, which isn't the case in real life, but it's the best we can do. I then wrote a combinations program that generated all 14m tickets and calculated the first two figures in the RHS of the above equation for each tier (we know the third figure from Camelot as I said) by assuming that the 6 numbers drawn were 1 to 6 and we were looking at winning tickets using the number 1. This resulted in the following table:
Tier Uses 1 Combs Ratio 6-match 1 1 1.000 5+bonus 5 6 0.833 5-match 210 252 0.833 4-match 9,030 13,545 0.667 3-match 123,410 246,820 0.500 2-match 617,050 1,851,150 0.333 1-match 962,598 5,775,588 0.167 0-match 0 6,095,454 0.000
After this, it was simply a question of using the above table for each draw, multiplying the ratio by number of winners in the tier for a particular draw and then doing this for all 104 draws to get a total for a particular number. I then totalled the sales for every draw where a particular number appeared, divided the figure from the previous sentence by that total and then sorted on the percentage figure as shown in the main table on this page. You can wake up now...
![[Numerical Analysis]](/nav/Analysis.gif){kind=small}