Following up on my Lottery Winners Counter JavaScript toy, and on Andy‘s recent blog post about trying to rig the lottery using statistics, I decided to write a new software toy to help demonstrate exactly how impossible it is to do as he suggests and guarantee a profit through the strategic purchase of large numbers of lottery tickets. Even at it’s most statistically optimistic, using obscene rounding (i.e. 49.999% is "unlikely", 50.001% is "likely"), you stand to lose over £2M every time you play. Try out my calculator now.

If that’s not in itself enough to convince you, have a look through this stunning Times article on why "our national gamble stinks". It compares the National Lottery to casinos, which have a significantly higher payout rate, and argues that if you’re doing it for the charities, you should just give one a quid – they get to claim 28p gift aid that way too.

Just my £13.9M worth.

Two things:

1. I think the one way it might be profitable to enter the lottery with 13.9 million tickets might be on a sufficiently big rollover week. If the prize fund is only provided by you and your fellow competitors, then you and they will only get half or so back on average, but if there are some non-players beefing up the fund, ie those whose ticket money was nabbed last week and hung on to, it might work.

2. I had a fiddle with this calculation in Excel following Andy’s post. One thing confused me. I assume you got your data on prize fund etc from Wikipedia’s Lottery article: any idea why the percentages of the prize fund used for the various prizes don’t add up to 100? (2 10 16 52 = 80)

Sorry to be picky but you can’t have proven exactly how impossible something is as there are no degrees of impossibility. Something is either possible or it is not. Possible things can have degrees of probability but impossible things are all equally impossible.

Statto,

1. Yes. This is reflected somewhere in the “Interesting numbers” bit of my page. The rollover point at which is becomes worthwhile if you have sufficient money to buy all the ticket combinations and nobody else will play is about £7M. Owing to the increase in ticket sales on rollover weeks, though, I’d suspect that the real rollover value required is much higher.

2. So I see – I hadn’t noticed that before, just used the numbers unquestioningly. Will fix it when I know better what they mean.

Matt In The Hat,

I think you’ve demonstrated exactly how right you are.