Property rules

In order to have an improved chance at the jackpot it is necessary to ensure that the sets of numbers that you enter have realistic properties. Apparently many thousands of people buy lottery tickets with the numbers 1,2,3,4,5,6. Let us examine the properties of this set.

[snip lots of pseudomathematical garbage]

So the overall property of the set 1,2,3,4,5,6 can be described as ‘15 0 5 4 6’.

Of these only the 0 representing pairs with the same end digit is acceptable.

Every other property is so low in likelihood that each on its own is a good reason for not using this set of numbers. Together they combine to make 1,2,3,4,5,6 even more unlikely.

If these properties were mutually exclusive then we could calculate the probability of them occurring together by multiplication. They are not mutually exclusive, however, it is useful to find out what kind of number we get. Let us be generous here and allow less than 1% (<1%) be 1% and <<1% be 1 tenth of 1% and <<<1% be 1 tenth of 1 tenth of 1% then,

<1%=1%=0.01

<<1%=0.1%=0.001

<<<1%=0.01%=0.0001

Remember a probability of 20% means 1 chance in 5 which is 0.2

Multiplying the properties of 1,2,3,4,5,6 we get

Properties number = 0.0001 x 0.2 x 0.0001 x 0.001 x 0.0001 = 0.0000000000000002

For non mathematical people this means 2 divided by 10,000,000,000,000,000

In a 6/49 lottery there are roughly 14,000,000 different ways of picking 6 of the numbers. We will round of the actual number (13,983,816) to make the words easier by calling this 14 million.

If all sets were equally likely then classical probability theory states that the probability of any of the sets is 1/14,000,000 = 0.00000007.

Classical probability number = 0.00000007

Our properties number ( 0.0000000000000002) for the set 1,2,3,4,5,6 is a heck of a lot smaller than the classical probability number. In fact 357,556,192 times smaller.

So the properties number for 1,2,3,4,5,6 is roughly 360 million times smaller than the classical probability number. That is why 1,2,3,4,5,6 and sets like it not a very good idea if you want to win the jackpot.

For comparison now consider another set of numbers. Let us pick the very first draw of the UK national lottery. The drawn numbers were 3,5,10,14,22,30.

The properties of this set are 2 1 0 1 1

Let us calculate the properties number as in the above,

2 pairs with same first digit = 0.38

1 pair with the same end digit = 0.4

0 pairs of consecutive numbers = 0.49

1 pair of consecutive odd/even = 0.38

1 symmetrical triple = 0.35

Properties number = 0.38 x 0.4 x 0.49 x 0.38 x 0.35 =0.0099058 = 0.01

This does not mean that the probability of this set is 0.01. These properties are not mutually exclusive. We can only use the properties number for comparing the properties of the sets of 6 that we pick.

This property number of 0.01 is very much bigger than the properties number for the set 1,2,3,4,5,6. In fact it is 50,000,000,000,000 (50 million million) times bigger.

Compared to the classical probability number it is 139,838 times bigger. Its properties are such that it is likely to come up. It did it was the first draw in the UK lottery.

Conclusion

The bigger the property number the more likely the set is to come up.