![[UK National Lottery Logo]](/Lottery.gif){kind=small}
Pos No. Wins Sales Percentage 1 23 620,505 819,789,110 0.07569% 2 10 708,266 961,083,950 0.07369% 3 03 870,896 1,232,350,400 0.07067% 4 21 319,795 458,188,310 0.06980% 5 07 826,197 1,185,149,830 0.06971% 6 11 921,756 1,332,043,560 0.06920% 7 29 1,070,952 1,590,758,770 0.06732% 8 08 681,739 1,039,528,730 0.06558% 9 47 475,158 725,284,830 0.06551% 10 24 514,245 786,377,790 0.06539% 11 19 710,634 1,090,881,620 0.06514% 12 31 763,246 1,179,191,720 0.06473% 13 20 801,847 1,249,995,850 0.06415% 14 01 467,351 732,500,920 0.06380% 15 25 896,265 1,408,622,970 0.06363% 16 17 509,828 820,629,930 0.06213% 17 44 493,304 803,112,300 0.06142% 18 05 376,231 612,624,410 0.06141% 19 26 666,022 1,091,385,030 0.06103% 20 27 574,932 942,733,700 0.06099% 21 06 530,506 873,302,960 0.06075% 22 35 266,527 441,010,580 0.06044% 23 49 545,361 913,325,740 0.05971% 24 22 715,630 1,204,348,000 0.05942% 25 41 582,815 985,237,490 0.05915% 26 33 642,242 1,090,052,560 0.05892% 27 45 663,030 1,138,537,740 0.05824% 28 14 549,765 946,119,490 0.05811% 29 48 773,165 1,336,960,460 0.05783% 30 09 597,223 1,037,279,100 0.05758% 31 36 273,280 476,966,900 0.05730% 32 32 389,742 680,448,760 0.05728% 33 18 453,235 792,140,950 0.05722% 34 57 252,137 441,077,520 0.05716% 35 04 530,552 930,146,070 0.05704% 36 15 724,977 1,280,570,070 0.05661% 37 56 440,483 778,081,550 0.05661% 38 28 623,093 1,104,425,280 0.05642% 39 40 496,694 893,368,340 0.05560% 40 46 417,261 750,868,480 0.05557% 41 12 421,933 762,813,330 0.05531% 42 13 454,891 823,074,060 0.05527% 43 30 247,513 451,843,620 0.05478% 44 02 585,894 1,070,530,780 0.05473% 45 39 339,406 620,365,980 0.05471% 46 38 505,405 928,441,620 0.05444% 47 16 477,172 882,925,130 0.05404% 48 53 632,410 1,174,586,010 0.05384% 49 55 331,196 619,715,120 0.05344% 50 50 583,861 1,120,691,310 0.05210% 51 34 725,221 1,394,206,890 0.05202% 52 42 500,602 974,159,750 0.05139% 53 43 648,695 1,275,704,070 0.05085% 54 59 488,464 966,371,600 0.05055% 55 51 289,437 587,678,200 0.04925% 56 52 412,803 838,954,900 0.04920% 57 37 711,502 1,478,634,170 0.04812% 58 54 347,945 729,471,080 0.04770% 59 58 454,402 953,077,430 0.04768%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}