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