![[UK National Lottery Logo]](/Lottery.gif){kind=small}
Pos No. Wins Sales Percentage 1 29 787,004 1,075,776,050 0.07316% 2 06 760,283 1,074,400,110 0.07076% 3 19 906,838 1,298,240,110 0.06985% 4 13 830,710 1,217,031,520 0.06826% 5 25 483,611 708,523,600 0.06826% 6 15 394,379 579,640,040 0.06804% 7 07 691,264 1,019,946,990 0.06777% 8 12 870,359 1,294,792,500 0.06722% 9 11 1,009,040 1,504,069,770 0.06709% 10 09 696,366 1,040,957,200 0.06690% 11 03 742,609 1,120,942,850 0.06625% 12 24 533,718 808,109,150 0.06605% 13 20 649,345 986,703,680 0.06581% 14 30 546,869 836,376,960 0.06539% 15 01 543,747 833,247,090 0.06526% 16 51 374,047 576,748,730 0.06485% 17 26 509,785 798,768,990 0.06382% 18 02 668,100 1,047,964,960 0.06375% 19 17 712,423 1,120,867,160 0.06356% 20 05 392,596 624,834,010 0.06283% 21 31 574,567 915,351,830 0.06277% 22 35 758,980 1,209,519,010 0.06275% 23 21 288,228 459,837,080 0.06268% 24 08 596,834 954,938,880 0.06250% 25 14 533,556 854,012,360 0.06248% 26 28 503,096 811,742,490 0.06198% 27 44 543,900 889,752,660 0.06113% 28 45 471,843 773,522,620 0.06100% 29 10 551,516 917,431,200 0.06012% 30 16 545,265 917,487,800 0.05943% 31 04 487,421 822,423,130 0.05927% 32 47 563,996 954,483,150 0.05909% 33 46 230,436 390,819,710 0.05896% 34 33 907,157 1,545,622,520 0.05869% 35 32 543,536 932,979,470 0.05826% 36 41 688,206 1,185,900,770 0.05803% 37 39 633,128 1,097,394,530 0.05769% 38 27 659,186 1,147,613,690 0.05744% 39 40 440,406 768,883,040 0.05728% 40 18 521,601 921,949,110 0.05658% 41 37 539,409 971,153,320 0.05554% 42 23 356,584 645,238,400 0.05526% 43 43 470,925 868,132,800 0.05425% 44 49 387,973 724,722,120 0.05353% 45 22 392,648 733,662,530 0.05352% 46 42 553,342 1,046,882,070 0.05286% 47 48 434,189 848,595,100 0.05117% 48 36 576,855 1,131,325,990 0.05099% 49 34 445,322 878,842,700 0.05067% 50 38 734,568 1,465,658,840 0.05012% 51 54 526,621 1,057,984,020 0.04978% 52 59 488,081 999,664,460 0.04882% 53 52 403,518 829,535,240 0.04864% 54 53 294,034 614,500,350 0.04785% 55 55 360,512 761,191,070 0.04736% 56 57 463,724 983,564,750 0.04715% 57 56 251,036 534,902,150 0.04693% 58 50 261,519 563,145,410 0.04644% 59 58 291,653 632,454,340 0.04611%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}