Debunking the "Gambling away £100 every 20 seconds" myth

"At the moment, a punter can walk into a high street bookmakers and gamble away £100 every 20 seconds for 13 hours."

Tom Watson - HuffPostUK - Oct 2013

I'm highlighting this claim about Fixed Odds Betting Terminals in particular because it is so mathematically wrong-headed. Also because the "gambling away £100 every 20 seconds" and "gambling away £18,000 per hour" narratives are now forming a core part of the campaign against FOBTs. I may come back to the political and moral arguments on this subject in a later post. But for now I just want to focus on the maths.

FOBTs, which are most commonly roulette have a house edge of between 2.7% and around 5%. This is in line with the standard odds yielded by a roulette table. If a table has a single zero then the odds of winning on a red or black bet are just less than 50/50 (because if it comes up zero the house wins). So with 36 numbers plus zero the chances of winning in a single spin are 18/37 or 0.486. This yields a house edge of just over 2.7%. If the roulette table has two zeroes (a zero and a double zero) then the odds are titled more in the house's favour as it becomes 18/38 or 0.474 yielding a house edge of 5.26%.

So as probability theory tells us, over the long term we would expect a punter on the first type of table to be about 2.7% down and a punter on the second type of table to be 5.26% down. For the rest of this piece I am going to focus on the second type of table as I wanted to pick the worst case scenario for this to be generous.

If someone was foolhardy enough to bet £100 on a red or black bet every 20 seconds for an hour on this sort of table they would be incredibly unlikely to lose (or "gamble away" to use Watson's term) £18,000. In fact we can calculate just how unlikely this is. We simply take the chance of them losing each time and multiply this number by itself the number of times they are going to play. From this we can see that the chance of this happening is (1-(18/38))^180

Which is one in 149,847,041,024,310,787,847,729,246,045,620,000,000,000,000,000,000*

Or to put it another way roughly the same likelihood as picking two random molecules of water from all the oceans of the world and them being the same one. In other words pretty much as close to impossible as you can theoretically get.

In actual fact someone who gambled £100 every 20 seconds for an hour would not have "gambled away £18,000". They would, on average gamble away 5.26% of £18,000 or £946.80. Now I'm not trying to claim this is not a large amount of money, it of course is, but it's only around a twentieth of the amount that the headlines and distortions of the campaign would have you believe.

More importantly though it is the most extreme interpretation of the possibilities. How many people who gamble on these machines seriously wager the maximum amount every 20 seconds for an hour (or more) at a time? I suspect very few. Far more likely is that they would wager smaller amounts, perhaps £5 or £10 a spin. So if someone did bet £5 for 180 spins they'd be on average down about £48. Now whether £48 spent in this way for an hour is a wise use of money is a different question. But of course losing £48 in an hour is not as scary or headline grabby as £18,000 in an hour.

As I said the politics and morality is for another post and I am not covering that here. I'm simply saying that if people want to campaign on this they should at least get the basic maths right.


*After the 32nd figure my calculator ran out of accuracy (because the number is so massive) so the final 19 digits are all zeroes meaning that it is rounded down.

Excellent AV vs FPTP post from an award winning mathematician

I don't often do a post which essentially just links to another blog post but I am making an exception here.

This is simply one of the best blog posts I have ever read from award winning mathematician Tim Gowers. He goes through all of the arguments for and against AV and FPTP and with intelligence and humour analyses each one from a mathematical perspective but in an accessible way. He is clearly in favour of a switch to AV but he is not afraid to point out its weaknesses as well as its strengths.

It is a very long post and will probably take 20 or 30 minutes to read in full but it is very much worth it. If you are still undecided about AV (and even if you think you aren't) I heartily recommend it.

Why is numeracy so undervalued in the UK?

Alison Goldworthy on Twitter has raised an interesting issue this morning. Paul Waugh retweeted something from Ed Richmond where he had tweeted:

At daughter's swim lesson. Why do 7 year olds need to learn butterfly? The swim equivalent of algebra; complex, elegant and utterly useless.

Ali responded:

I love algebra, I use it all the time. Why is being numerate useless and literate useful?!

I am fully in agreement with her on this one.

This little vignette from Ed sums up something I have thought for a long time. Literacy is very highly prized in this country. People generally are not happy to be unable to read or write (or be poor at it) and it is considered to be very important to overcome any problems associated with this.

Contrast this with the general attitude to numeracy and mathematical skills. I have lost count of the number of times I have heard people over the years say with a shrug of the shoulders "I'm no good at maths!" with them seeming almost proud of this fact, or at the very least happy to announce this to the world. There are people close to me who I have heard do this on occasion too.

It seems like once someone gets the idea that maths is not for them, or that they are not a "mathematical person" then they effectively write themselves off and our society tacitly (or in some cases blatantly) assents to this.

Now I am fortunate in that I was pretty good at all 3 Rs so I could be accused of being insensitive here but I don't think so. It would be insensitive if I was having a go at people for not being able to improve their skills at something that they were incapable of but the relative success of other countries (especially in Asia for example) when it comes to maths suggests to me that this is a cultural problem rather than an innate one. Countries like Japan encourage all children to push themselves at maths as the skill is very highly regarded in their society (a bit like literacy is for us) and the result is much higher levels of numeracy than we have.

Here is some evidence to back up what I am talking about. There was an "International Numeracy Study" done in 1996 (available within this document). Here is a summary of the findings:

The International context for Basic Skills within the United Kingdom can be demonstrated from findings of the International Numeracy Survey 1996 (Opinion Research Business). This found that comparing the percentage of respondents who managed to give the correct answer for all the tasks, Japan emerged top. 43% of respondents tested in Japan achieved a full set of correct answers. This was followed by France (40% getting them all correct) and the Netherlands (38%). Respondents in the UK performed least well. Only 1 in 5 people tested (20%) managed to accurately complete all twelve given tasks. Australia was second from bottom (at 33%) but Australians still performed significantly better than the UK.

When the results were reviewed for the proportion of respondents getting most answers right (10 -12 correct across the twelve tasks) the UK respondents do not improve their performance vis a vis other countries. Barely half (47%) were able to give the correct answer for 10 or more of the tasks, which compares very unfavourably with the rest of Europe (76% in the Netherlands, 68% in Denmark and 65% in France and Sweden).

At the other end of the scale almost a quarter of the UK respondents (22%) could only answer up to 5 questions out of the 12. This compares with a lower 14% in Australia, 10% in France, 7% in Sweden, 7% in Denmark, 5% in Japan and 4% in the Netherlands.

The following table provides a summary of the survey results.

Scores achieved across 12 numeracy tasks:

So out of 7 developed nations all of whom we will compete and trade with we came bottom at numeracy.

Like I say, for this to change will take a big cultural shift but it could start by people thinking twice before happily announcing to all and sundry that they are rubbish at maths. After all, would they be so keen to announce that they were virtually illiterate?