![[UK National Lottery Logo]](/Lottery.gif){kind=small}
Pos No. Wins Sales Percentage 1 08 822,257 1,081,954,270 0.07600% 2 07 341,109 450,448,000 0.07573% 3 05 940,815 1,313,767,060 0.07161% 4 11 668,498 961,309,500 0.06954% 5 17 908,268 1,351,126,470 0.06722% 6 12 638,839 963,247,650 0.06632% 7 04 746,056 1,128,419,640 0.06612% 8 10 435,749 661,204,630 0.06590% 9 09 685,254 1,045,354,800 0.06555% 10 25 859,218 1,371,431,700 0.06265% 11 16 319,689 519,122,540 0.06158% 12 24 294,934 479,986,730 0.06145% 13 01 701,655 1,143,233,940 0.06137% 14 33 461,561 760,510,410 0.06069% 15 15 738,476 1,220,025,210 0.06053% 16 37 451,743 750,493,280 0.06019% 17 34 546,289 911,371,710 0.05994% 18 31 832,488 1,396,019,920 0.05963% 19 19 532,234 895,162,150 0.05946% 20 38 736,715 1,241,305,000 0.05935% 21 28 243,234 417,519,380 0.05826% 22 20 479,665 826,486,360 0.05804% 23 27 474,627 824,534,250 0.05756% 24 43 725,673 1,268,146,880 0.05722% 25 44 383,732 674,182,430 0.05692% 26 23 376,498 663,298,010 0.05676% 27 13 392,290 692,811,270 0.05662% 28 42 738,612 1,305,386,420 0.05658% 29 45 808,909 1,432,826,370 0.05646% 30 14 239,439 427,369,720 0.05603% 31 06 552,813 998,532,330 0.05536% 32 29 353,784 639,556,890 0.05532% 33 26 752,380 1,362,301,910 0.05523% 34 03 676,871 1,226,583,290 0.05518% 35 18 597,339 1,088,992,360 0.05485% 36 39 427,686 780,542,300 0.05479% 37 49 400,038 733,906,570 0.05451% 38 21 200,961 371,445,370 0.05410% 39 47 441,614 820,196,320 0.05384% 40 32 664,926 1,236,804,270 0.05376% 41 35 526,341 993,599,440 0.05297% 42 02 194,815 367,888,980 0.05295% 43 22 734,357 1,393,080,970 0.05271% 44 30 372,318 719,180,710 0.05177% 45 41 504,457 981,373,020 0.05140% 46 36 490,381 963,432,540 0.05090% 47 48 579,344 1,160,213,750 0.04993% 48 46 706,210 1,414,631,600 0.04992% 49 54 495,959 1,002,403,220 0.04948% 50 55 519,546 1,055,434,350 0.04923% 51 40 683,632 1,390,400,210 0.04917% 52 51 535,669 1,111,322,960 0.04820% 53 56 490,808 1,085,622,500 0.04521% 54 52 542,574 1,210,100,190 0.04484% 55 59 375,462 852,932,220 0.04402% 56 53 324,474 754,236,930 0.04302% 57 58 452,417 1,111,172,270 0.04072% 58 57 101,937 251,863,830 0.04047% 59 50 154,838 417,795,260 0.03706%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}