Lottery

Cycling Software

Thirteen Point Six Million Chances Of Winning The National Lottery

If you look in a good stats book you might find something like this:

number of combinations = n!/((n-r)!r!)
where:
n = number of balls in basket
r = number of balls in winning line

This comes out at about 100million possible 7 ball combinations or about 15million 6 ball combinations all of which are equally likely (or equally unlikely) if your lottery has 50 balls to choose from. My spreadsheet says that the 'exact' numbers are 99,884,400 or 15,890,700 respectively but these will only be approximate because calculating machines truncate when the numbers get too big.

i.e. 50! gets quoted on my pocket calculator as 8.06517512 x1067 or approx 8 with 67 zeros afterwards so everything after the 1st 10 digits gets lost. So you will need to try it on a very big bit of paper if you want the exact value.

n! (n factorial) is 1+2+3+4+5...etc.....up to +n

Putting it another way: If you buy a Ł1 lotto ticket every week on an indefinite basis. Then (averaged over millions and millions of years) you might expect all 7 numbers to come up approximately once every 1,923,077 years.

Applying the same formula for 6 balls we get a mere 15,890,700 combinations. However the punters only need to guess 6 balls correctly out of 7 chosen numbers so this reduces the number of possible combinations to approximately 13,620,600. I.e. 15,890,700 x (6/7) = 13,620,600 or about 13.6 million.

On this basis, if you buy a Ł1 lotto ticket every week on an indefinite basis. Then (averaged over millions of years) you might expect either 6 correct numbers or 5 correct numbers and the bonus ball to come up approximately once every 13,620,600 / 52 = 261,935 years. And even then you aren't guaranteed a win because each ticket has exactly the same chance of winning.

Don't let the mathematics stop you though. Remember that the lotto ticket you buy today is as likely to be a winner as any other ticket, so you could win tomorrow if 13,620,600 people all buy tickets then the likelihood is that one of these people will get the 6 required numbers... It could be you as they say. And if you win with my lotto number generator, then please send me a donation.

I guess you could send in ~13.6 million entries, each with a different line. Then you would be sure to win, but it would cost Ł13.6 million to win about a million which you could well be sharing with someone else. Also if you can fill in 1 line per second it will take about 157 days, working 24 hours per day, to fill in all your entries.

Best bet is spend your lotto money on a statistics book and read the chapter on probability. Or better still just send your money to me (I'm currently between jobs and very short of cash and your chances of winning are about the same if you send your money to Camelot as they would be if you send it to me)...