The British Gazette

The above image is of the Andromeda spiral galaxy. What has it to do with winning the National Lottery? Answer: the numbers concerning both are astronomic.
The other day, we were in the Co-Op and a lady was having a discussion with the check out lady about the different types of voluntary taxation offered by the operator Camelot. The assistant explained to that lady that she understood very little about the lottery and asked for her colleague to come over to help the lady whilst she got on with dealing with other customers. When eventually we were able to pay for our goods we commented about the variety of “games” available to those punters who presumably “feel lucky.” The lady responded that she never played the lottery but both her two adult sons did each of whom spent £40 every week! £20 on Wednesdays and £20 on Saturdays.

Thus, on the basis of pro bono publico, the British Gazette offers this explanation as to how to calculate the odds of winning the Wednesday or the Saturday lottery.

As you may or may not know the draws for the Wednesday and Saturday Lotto comprise a random draw of six numbers in the form of balls. There are 49 balls, numbered 1 to 49.

Thus when the first ball is drawn it is 1 ball drawn from 49 balls. When the second ball is drawn it is from 48 remaining balls. When the third ball is drawn it is from 47 remaining balls. When the fourth ball is drawn it is from 46 remaining balls. When the fifth ball is drawn it is from 45 remaining balls, and when the sixth ball is drawn it is from 44 remaining balls.

The formula therefore is:
(49 x 48 x 47 x 46 x 45 x 44) divided by (6 x 5 x 4 x 3 x 2 x 1)
or: 10,068,347,520 divided by 720
Which equals 13,983,816.
Thus the odds of winning are: 1 in 13,983,816

Where two or more people either select of have a random selection presented to them in the form of a “Lucky Dip” ticket, the odds of these identical tickets are exactly the same as they comprise in effect the same entry. The difference being that should these tickets become the winning tickets the prize is shared equally between the multiple holders.

At this point many consider that they can increase their chances of winning the lottery by the simple expedient of buying more tickets! This of course is correct. However, where they go wrong is to make this erroneous calculation:

If I buy two tickets, I double my chances. Thus, odds of 1 in nearly 14 million, become 2 in 14 million, in other words, 1 in 7 million!

Err…. No!

Each lottery ticket must be viewed as a discrete random draw of six numbers that have been entered into the draw. Thus each ticket whatever the numerical selection of numbers has exactly the same chance of corresponding to the numbers drawn by the lottery machine. Thus the odds of one ticket winning are 1 in 13,983,816. The odds that one of the two lottery tickets purchased are 1 in 13,983,816 minus 1 or 1 in 13,983,815! So for a doubling of your stake you have increased your chances of winning the lottery by approximately 0.000007152 percent!

If you thought odds of nearly 14 million to 1 were long, these are nothing when compared to the odds of winning the Euromillions draw!

Up to Friday 6th May 2011 the draw for this exercise in futile hope was once a week late on a Friday night and comprised two random draws, one of five numbers out of a selection of 50 and a second of two numbers out of a selection of 9.

The formula for the two draws was slightly more complex, being in two parts:
Firstly:
(50 x 49 x 48 x 47 x 46) divided by (5 x 4 x 3 x 2 x 1)
or: 254,251,200 divided by 120
Which equals 2,118,816.
Secondly:
(9 x 8) divided by (2 x 1)
Or: 72 divided by 2
Which equals 36.
The first part is then multiplied by the second part:
2,118,816 x 36
Which equals 76,275,360
Thus the odds of winning are: 1 in 76,275,360!!!!

From Tuesday 10th May, 2011, a second weekly draw was lauched together with revisons includiung the addition of two extra numbers (10 & 11) in the second set of numbers, to make winning the jackpot even less likely:

Firstly (unchanged):
(50 x 49 x 48 x 47 x 46) divided by (5 x 4 x 3 x 2 x 1)
or: 254,251,200 divided by 120
Which equals 2,118,816.
Secondly:
(11 x 10) divided by (2 x 1)
Or: 110 divided by 2
Which equals 55.
The first part is then multiplied by the second part:
2,118,816 x 55
Which equals 116,534,880
Thus the odds of winning are: 1 in 116,534,880!!!!

These are hardly prudent investments! It is because so many disregard or are of ignorant of this that many regard lotteries as a tax on fools!