give me the awe of understanding over the awe of ignorance every time - Douglas Adams


I Bet You Won't Win The Lottery

We human beings are not all that good at assessing chance events. Many of us suffer from extreme optimism when it comes to betting. Some of the things people bet on have a large number of variables, such as horse racing for example and some of these variables are more predictable than others. These variables are worked out by bookmakers who understand the mathematics, which is why it is rare that the bookmakers lose. Of course the favourite doesn't always win but the odds are adjusted as each bet is placed so that in the long run the punters will always lose. You may get lucky (or you may have information the bookmaker doesn't know) but the more often you bet the more sure you are to lose.

The National Lottery has a fixed set of variables and as such the odds are absolutely predictable. If we for simplicities sake just consider the main prize this requires that you select six numbers that coincide with the six numbers randomly selected from forty-nine. So like the bookmakers do, lets do the mathematics, its really not that difficult.

The first number you select has six chances of being selected from forty-nine.

That is 49/6
The second number you select has five chances of being selected from the remaining forty-eight.

That is 48/5
The third number you select has four chances of being selected from the remaining forty-seven.

That is 47/4
And so on...
Until the sixth number you select has one chance of being selected from the remaining forty-four.

All these chances are multiplied together to give

the odds of correctly selecting the 6 winning numbers = (49 x 48 x 47 x 46 x 45 x 44) / (6 x 5 x 4 x 3 x 2 x 1)

Mathematicians would write this out as 49C6 =  (49!)/ (43!6!) = 13,983,816

That's almost 14 million to one against! So if I buy one lottery ticket each week for the next
269 000 years then I can quite reasonably expect to win the big prize at least once.

So if you think its worth £1 to dream what you'd do with the winnings and it give you a little thrill to watch the balls emerge from the machine then fine, there are many worse things you could do with £1. But I'll bet you a pound to a penny every week that you don't win!