Chapter 5: The Whittle Theory
The elimination of certain patterns in an attempt to increase the chance of picking winning lotto numbers... does it work? How effective?
[Editors note: The following chapter, this whole book actually, was written for the Texas Lottery and the 6 from 50 system they used at the time of this writing.]
What if it was possible to eliminate certain sets of numbers? For example, although any set of pick-six numbers has an equal chance to occur as any other set, there has never been a draw where the six numbers were sequential. There has never been a 1, 2, 3, 4, 5, 6, nor a 12, 13, 14, 15, 16, 17, nor any other set of six sequential numbers. In fact, there has never even been five or four sequential numbers in a set!
There have been, however, cases where three sequential numbers were drawn. However, for our purposes, three sequential digits so rarely show up as to make them highly unlikely to appear.
This indicates that the probability of three or more sequential numbers appearing in a lotto event is highly unlikely. Therefore, can we be confident that by eliminating picks with sequential numbers we would improve our chance to win? Let's examine this theory closely.
How many possible combinations are there that involve six sequential numbers? Starting with the set "1 2 3 4 5 6" and ending at "45 46 47 48 49 50", there are exactly 45.
So we subtract 45 from our total possible combinations figure of 15,890,700 to get 15,890,655. That shouldn't even be considered an improvement!
Now let's calculate how many combinations of five sequential numbers are possible. We have to pick six numbers, five of which must be sequential. Starting at 1 through 5 for the first five numbers, we skip picking 6 since we already eliminated that pick, and begin at 7. Since 1-5 can show up with all numbers after 6, that is 44 picks. Starting with 2-6, we combine that with the numbers 8 through 50 to get 43 more picks. We continue until we begin with 46 through 50, combined with numbers 1 through 44. In all, this gives us an additional 1,980 picks we can eliminate based on picks with five sequential numbers. We are now down to 15,888,675 possible combinations! Still not very impressive.
Our next elimination is that of four sequential number patterns. Starting with "1 2 3 4," we now must add two more numbers. There are 46 numbers left. We'll eliminate the 5 because we've already eliminated that pattern, leaving us with 45 numbers available for the fifth number. When we multiply the options for picks number five and number six, our combinations for the starting numbers 1-4 are 1,980. In all, sets of four sequential number patterns total 89,100 combinations. Subtracting this from our total combinations, we are left with 15,799,575. In all, we've eliminated only 0.57344% (91,125) of the total combinations, leaving us with a 1 in 15,799,575 chance of winning the jackpot. Still an extremely slim, very unlikely chance of winning.
Finally, let's eliminate all patterns including three sequential numbers, which total 4,098,600 combinations. That would bring us to 11,701,020 possible combinations, having eliminated a little over 26% (4,189,680) combinations as unlikely to occur.
The conclusion we draw is simply don't pick sets of numbers with three, four, five, or six sequential numbers. It has never happened (except for the three sequential digits), and although it could happen, it most likely won't. By eliminating these sets, you will increase your chances to pick the winning set of lotto numbers by 26%! This is nothing to get excited about, however, because you still only have a 1 in 11,701,020 chance to win, which is a 0.0000002386817131619% chance of winning. That puts it in better perspective. In other words, you haven’t really come close to increasing your chance of winning!
Our final elimination will be of "all odd," "all even," "all high," and "all low" digits.
All odd describes a set of numbers where all numbers are odd, such as "1 3 5 7 9 11." All even, then, would describe a set of numbers which are all even.
All high refers to numbers 26 to 50. In recent Texas lotto drawings, no winning numbers have been "all high." All low refers to numbers 1 to 25, and no winning numbers have been composed completely by all low numbers.
There are 177,100 combinations of all odd numbers. There are also 177,100 combinations of all even, all high, and all low digits. We can, therefore, eliminate a total of 708,400 combinations from our current total, bringing us to 10,992,575.
Our little experiment here has "whittled" away 31% of the possible combinations! Our chance to win has been increased by 145%! These percent figures sound impressive, but don't let them fool you. The math shows that we still only have a 0.000009097050% chance to win the jackpot.
We still have not eliminated other "unlikely patterns," such as TWO sets of three sequential numbers (such as 1-2-3-48-49-50). No doubt we could still shave some picks off our list, but there would be too few to waste any more pages to this endeavor.
Our best chances finally arrive in the next chapter!