The standard deviation figure tells us where the bulk of the sums occur, e.g 68% of all values lie in a range between one standard deviation less than the mean and one standard deviation more than the mean. 95% of all sums lie between 2 standard deviations plus and minus the mean.

If you had a ticket in which all the main balls added to between 61 and 70 , then in theory you had about 4 chances so far of a result falling in that category. In practice, it has happened 6 times.

Expected and actual results tables

It is possible to work out exactly how many lottery result lines will have a particular total, and therefore have sums falling within a particular range. One can then compare this with what actually happens during the history of the lottery.

Some lottery lines, for example have a very low sum say in the range 21 to 30. You may be interested to know that there are only 90 possible tickets with this sum, out of 13,983,816 possible combinations of six numbers from 49. On average then, in theory you may have to wait 155,376 draws or 1,494 years until the first result within this range happens. On the other hand it can happen in the next draw. Contrast that with sums in the range 140 to 150 where there are 1,638,159 possible tickets with this sum. On average, a result matches this criteria once every 8.5 draws. It is possible therefore to calculate when a result in a sum range is due , and when it is overdue. However, a huge number of draws are required before sufficient data can be collected about the higher and lower sum values. Hence only figures about mid range values are viable.

The table below shows the figures discussed above for all the sum ranges. You will recognise the column in red - "Actual No of draws matching sum" as those plotted in the chart above. Where sufficient data is available the difference between theory and reality is shown, and The number of times overdue of the laggards are shown.

For example at the time of writing, numbers in the 181 to 190 range were expected to have appeared 64.74 times by draw 935 at an average rate of every 14.44 draws. They had appeared 64 times, and were hence on target. However, numbers in the range 91 to 100 should have come out 30 times by this draw number, but had actually been drawn 21 times. They were last drawn 44 draws ago and were 44/30.81 =1.43 times overdue. An overdue figure of less than one means it is not overdue, whereas 2, 3 or 4 times overdue would suggest a result in this range must be due soon.

Distribution of Tickets across the sum ranges at draw 1533 Mainball_ sums adding to between Theoretical Number of different tickets within the range Group is expected to have matching sum every draws Theoretical   Actual Draws ahead/ behind on total count Last drawn how many draws ago Times Overdue % of tickets with this sum draws which should match sum to date   No of draws matching sum % of tickets 21 to 30 90 155,376 0.00064% 0.0099 0 0.00% -0.0099 Never   31 to 40 1,141 12,256 0.008% 0.1251 0 0.00% -0.1251 Never   41 to 50 6,110 2,289 0.044% 0.6698 0 0.00% -0.6698 Never   51 to 60 21,426 653 0.153% 2.3489 1 0.07% -1.349 1147 1.76 61 to 70 58,331 240 0.417% 6.395 8 0.52% 1.605 62 0.26 71 to 80 132,841 105.27 0.950% 14.563 15 0.98% 0.4371 28 0.27 81 to 90 261,351 53.51 1.869% 28.65 32 2.09% 3.3489 63 1.18 91 to 100 453,861 30.81 3.246% 49.76 36 2.35% -13.76 20 0.65 101 to 110 707,047 19.78 5.056% 77.51 76 4.96% -1.51 2 0.10 111 to 120 997,894 14.01 7.14% 109.40 105 6.85% -4.40 4 0.29 121 to 130 1,283,726 10.89 9.18% 140.73 147 9.59% 6.27 25 2.30 131 to 140 1,512,817 9.24 10.82% 165.85 148 9.65% -17.85 3 0.32 141 to 150 1,638,159 8.54 11.71% 179.59 175 11.42% -4.59 0 0.00 151 to 160 1,631,310 8.57 11.67% 178.84 182 11.87% 3.16 5 0.58 161 to 170 1,493,902 9.36 10.68% 163.77 168 10.96% 4.23 10 1.07 171 to 180 1,256,837 11.13 8.99% 137.78 154 10.05% 16.22 1 0.09 181 to 190 968,215 14.44 6.92% 106.14 101 6.59% -5.14 9 0.62 191 to 200 679,482 20.58 4.86% 74.49 85 5.54% 10.51 19 0.92 201 to 210 431,692 32.39 3.09% 47.32 47 3.07% -0.32 11 0.34 211 to 220 245,704 56.91 1.757% 26.94 29 1.89% 2.06 17 0.30 221 to 230 123,205 113.50 0.881% 13.51 12 0.78% -1.51 423 3.73 231 to 240 53,239 262.66 0.381% 5.836 6 0.39% 0.164 21 0.08 241 to 250 19,152 730 0.1370% 2.100 6 0.39% 3.900 678 0.93 251 to 260 5,288 2,644 0.0378% 0.580 0 0.00% -0.5797 Never   261 to 270 932 15,004 0.0067% 0.1022 0 0.00% -0.1022 Never   271 to 280 64 218,497 0.0005% 0.0070 0 0.00% -0.0070 Never   TOTALS 13,983,816 N/A 100.00% 1533 1533 100.00% N/A                      02-09-2010 12:55

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