![[UK National Lottery Logo]](/Lottery.gif){kind=small}
Pos No. Wins Sales Percentage 1 07 84,850,053 40,277,712,170 0.21066% 2 05 79,021,162 39,102,822,575 0.20209% 3 09 87,460,970 43,426,370,985 0.20140% 4 11 85,237,439 42,770,138,105 0.19929% 5 03 79,822,826 40,251,870,625 0.19831% 6 27 82,544,939 42,233,510,280 0.19545% 7 12 78,740,187 40,489,169,075 0.19447% 8 17 79,241,455 40,901,628,525 0.19374% 9 08 72,119,215 37,250,412,130 0.19361% 10 13 65,734,294 34,096,529,910 0.19279% 11 06 76,552,397 39,900,975,235 0.19186% 12 44 90,123,900 46,998,419,565 0.19176% 13 23 87,046,501 45,473,424,665 0.19142% 14 04 75,420,330 39,490,708,935 0.19098% 15 19 74,092,202 38,853,490,875 0.19070% 16 18 77,976,143 40,989,763,735 0.19023% 17 10 76,445,217 40,214,109,360 0.19010% 18 02 75,792,037 39,983,721,705 0.18956% 19 14 75,094,928 39,864,056,915 0.18838% 20 28 77,731,623 41,357,900,220 0.18795% 21 29 73,487,480 39,327,684,450 0.18686% 22 22 72,586,606 39,085,325,510 0.18571% 23 21 64,176,834 34,697,469,420 0.18496% 24 24 75,776,193 41,072,240,170 0.18449% 25 15 72,310,527 39,278,523,860 0.18410% 26 25 83,231,914 45,530,699,285 0.18280% 27 42 74,500,540 40,983,636,870 0.18178% 28 16 66,431,393 36,574,228,035 0.18163% 29 33 77,209,813 42,686,748,880 0.18088% 30 30 80,335,544 44,597,383,685 0.18014% 31 32 74,307,725 41,419,521,480 0.17940% 32 01 69,793,395 39,123,663,385 0.17839% 33 38 79,285,003 44,574,819,575 0.17787% 34 31 78,631,488 44,425,601,085 0.17700% 35 26 71,697,574 40,601,477,415 0.17659% 36 43 78,253,672 44,506,719,155 0.17582% 37 48 75,654,390 43,261,517,405 0.17488% 38 20 58,239,724 33,471,501,995 0.17400% 39 47 74,567,321 43,000,756,520 0.17341% 40 39 69,432,501 40,247,166,005 0.17252% 41 37 64,363,501 37,336,122,870 0.17239% 42 45 70,094,119 40,812,877,185 0.17175% 43 40 78,344,403 45,794,253,835 0.17108% 44 36 64,746,747 37,849,970,000 0.17106% 45 34 67,894,525 40,104,236,595 0.16930% 46 49 67,838,920 40,496,975,985 0.16752% 47 41 59,280,436 35,684,141,030 0.16613% 48 35 69,560,068 42,031,279,890 0.16550% 49 46 63,266,165 38,613,960,715 0.16384%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 2003 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}