Lotteries, goes the saying, are a tax on people who are bad at math. How bad? So bad that that Britain’s National Lottery is able to market using data that I would like to think is an argument against playing the lottery.

From a suspicously press release-ish BBC Article:

Medway Towns has one top prize-winning ticket for every 6,119 adults who are eligible to play the Lottery, compared with Ilford in second place with one in every 6,839.

That’s not so bad, too many people probably think (The ones who don’t know about Base Rate Fallacy, which is to say, most of them. After all, their reasoning goes, that’s much better than stated odds from an old IHT article:

The chances of [winning the lottery] actually happening are slim — about one in 3 million, on average, according to industry figures

I don’t recall what the frequency of drawings is for the National Lottery, but even if there were a drawing every single day, the average elapsed time to win the lottery (assuming buying a ticket for every single drawing) would be every 16 years and 9 months. And during that time, you’d have spent over £6,000 (plus time value of money, ignoring the time involved to purchase a ticket and then see if it won) to do it. If you lived in Ilford, you’d be looking at waiting almost 19 years (on average) to see any money back, and the queue length just goes up and up from there.

Another thing which is not mentioned is the period of time over which that rate of winning accumulated. I get the impression that’s since the National Lottery was founded in the mid-1990’s. Without knowing the effective time period, we’re missing a key variable whose omission further distorts the data.

Of course, I still haven’t answered my original question. Fortunately, as I sought data on how much the average payout was (since all I can seem to get from public sources is averages), I found this page at the UK Treasurer’s Web site, which I realized actually tells me all I really needed to know:

For every £1 spent on the National Lottery…50p returned as prizes

At the risk of putting myself in tax peril for my math skills, I’ll argue from that fact that the tax rate on poor math skills (the part that the government doesn’t give back) is effectively 50%.

That would be the mathematician’s answer, yes.

The entertainer’s answer is different: compared to any other form of entertainment, gambling pays out big time.

That’s pretty bad. It reminded me of a story I came across a few weeks ago that’s a few months old.

http://www.manchestereveningnews.co.uk/news/s/1022757_cool_cash_card_confusion

Apparently you’re not allowed to “trick” people with negative numbers…

–jason