![[UK National Lottery Logo]](/Lottery.gif){kind=small}
Pos No. Wins Sales Percentage 1 03 559,938 753,331,260 0.07433% 2 15 207,787 284,310,060 0.07308% 3 12 374,394 526,838,200 0.07106% 4 14 646,062 914,242,140 0.07067% 5 07 690,079 993,199,270 0.06948% 6 16 415,219 598,412,660 0.06939% 7 04 612,716 894,490,080 0.06850% 8 27 930,873 1,362,018,140 0.06835% 9 28 853,497 1,294,010,120 0.06596% 10 21 857,829 1,317,740,200 0.06510% 11 11 613,851 948,922,020 0.06469% 12 17 330,413 520,813,130 0.06344% 13 01 577,557 918,719,770 0.06287% 14 08 636,063 1,012,219,420 0.06284% 15 48 457,373 742,306,600 0.06162% 16 02 443,428 726,107,830 0.06107% 17 23 603,085 995,563,130 0.06058% 18 22 353,504 584,590,850 0.06047% 19 19 632,633 1,048,198,160 0.06035% 20 09 602,753 1,001,634,590 0.06018% 21 30 462,209 769,450,010 0.06007% 22 38 777,110 1,302,430,280 0.05967% 23 10 699,664 1,177,378,040 0.05943% 24 24 492,939 833,152,260 0.05917% 25 18 607,079 1,029,131,810 0.05899% 26 29 367,812 636,623,040 0.05778% 27 33 858,047 1,497,976,150 0.05728% 28 42 602,699 1,058,785,540 0.05692% 29 35 639,304 1,123,816,540 0.05689% 30 05 308,529 543,130,900 0.05681% 31 45 586,959 1,034,144,780 0.05676% 32 47 836,850 1,489,450,350 0.05619% 33 06 381,541 682,369,980 0.05591% 34 40 384,160 687,390,090 0.05589% 35 36 614,536 1,115,295,610 0.05510% 36 31 336,427 622,641,830 0.05403% 37 37 593,879 1,115,741,330 0.05323% 38 25 430,136 817,111,390 0.05264% 39 44 519,750 1,018,365,420 0.05104% 40 34 410,070 804,874,000 0.05095% 41 20 445,969 878,405,870 0.05077% 42 53 387,861 770,948,280 0.05031% 43 26 396,081 799,822,780 0.04952% 44 13 401,432 811,481,210 0.04947% 45 50 520,727 1,077,270,620 0.04834% 46 51 522,904 1,093,118,050 0.04784% 47 43 321,412 672,309,960 0.04781% 48 39 581,136 1,223,018,180 0.04752% 49 52 777,646 1,637,093,930 0.04750% 50 59 486,494 1,024,754,490 0.04747% 51 32 522,554 1,107,406,070 0.04719% 52 41 206,786 439,506,640 0.04705% 53 46 368,514 787,645,310 0.04679% 54 49 642,637 1,376,673,260 0.04668% 55 54 496,538 1,127,643,460 0.04403% 56 56 425,053 966,467,770 0.04398% 57 57 488,325 1,123,956,280 0.04345% 58 55 395,031 926,158,830 0.04265% 59 58 317,438 774,627,270 0.04098%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}