Tottenham Report: One size does not fit all By Andrew Tottenham, Managing Director, Tottenham & Co November 15, 2021 at 10:00 pm I was at a conference last week organised by Clear Concise Media. The theme was “Reputation Matters”. A presentation by Oliver Rowe from YouGov detailed the results of polling that his firm carried out. The results were shocking. The gambling industry in the UK is held in such low esteem by the general public and by politicians that only 5% of the former thought the industry was trustworthy! John O’Reilly, CEO of Rank Group, gave the keynote speech. He took us on an entertaining trip down memory lane, describing his life in the gambling industry and the changes that have occurred during that time and speculated what might be the outcome of the current review of the 2005 Gambling Act. Obviously, the two big issues are affordability checks and maximum bet limits for RNG games. A one-size-fits-all approach to maximum bet limits is ridiculous and shows no understanding of “utility”. Each person’s view of how much to risk and for what outcome is different and will depend to some extent on their relative wealth. Let me explain. In the 16th century, Western Europe was first coming to grips with the idea that the future could be predicted. Until then, all was in the “lap of the gods”; whatever happened was God’s will. Specialists were hired to look at birds’ entrails and such like to see what the future might hold. Then in 1520, Gerolamo Cardano wrote a paper that showed an understanding of the probability of different numbers being rolled with dice. He also demonstrated that he understood how to calculate the probability that two things might happen if they were not connected — i.e., rolling a total of 6 followed by a total of 7. He did make some mistakes in the actual calculation, but he certainly understood the principle. Cardano’s paper was not published until 1663, long after his death in 1576, by which time many other famous mathematicians had gotten into the act. By the time that Pascal and Fermat wrote to each other discussing how to split the pot in an unfinished game in 1652, the concept of expectation was well understood. Expectation is simply the average payoff over a series of similar bets. For example, betting one chip on a single number on a European roulette table, on average, one can expect to lose one chip every 37 spins or approximately 2.7% of your stake each spin. In fact, Pascal’s Wager, a famous argument about whether to believe there is a God is all about expectation. He concluded that, in the absence of proof, you lose very little by acting as though God exists (perhaps some of life’s luxuries) and gain a great deal at death. Alternatively, one loses little by not believing there is a God during life, apart from being arrested by the Spanish Inquisition, but stand to be condemned to purgatory at death if God does exist. If humans were completely rational, nobody would bet on a game where the odds are against them, where the expectation is that they will lose. Similarly, you would expect them to make bets where the expectation is positive, where if you were to make a series of bets, on average you would come out ahead. But they don’t. Obviously, people will make bets where the expectation is negative (casino games, bets with a bookmaker, etc.), but not make a bet where the expectation is positive. Part of that has to do with the enjoyment that people get from increasing risk in their lives. Some like to increase risk by leaping out of an aircraft with a parachute strapped to their back; others go snowboarding, engage in parkour stunts, etc. And some like to gamble. However, there are times when expectation will be positive, even highly so, and people will not risk making the bet. In the beginning of the 18th century, Swiss-born mathematician Daniel Bernoulli realised that whether people made a bet where the expectation was positive depended on a number of things: first, wealth, or lack of it, of the bettor relative to the size of the bet; secondly, the potential winnings relative to the wealth of the bettor. The St. Petersburg Paradox, which Bernoulli explored, describes a game in which the initial stake is one ducat, a gold coin worth about £120 at today’s price of gold, and the expectation is infinitely positive. Therefore, you would expect people to be willing to risk enormous amounts to play this game. However, as Bernoulli wrote, “Any fairly reasonable man would sell his chance, with great pleasure, for twenty ducats”. Imagine a game where the stake is £50, with a 50% chance of winning £500 or losing £50, i.e, the expectation is that you will win, on average, £225 per game. At what price would you sell your chance to play the game? £50? £100? £225? The price will certainly depend on your circumstances and your appetite for risk. If all you have is £50, the price you will accept will be relatively low. On the other hand, if you’re a billionaire, you probably won’t sell at any price or you won’t even play the game; a win of £225 for Elon Musk will have a negligible impact on his life. Also, what premium do you put on winning more? Is winning £1,000 twice as satisfying as winning £500? Or is winning £1,000 one-fifth as satisfying £5,000? Probably not. There is a curve there somewhere, and each person’s curve will be different. Some people are quite satisfied with playing low-volatility slot machines, preferring to spend as much time as possible without losing too much money; time playing the game is more valuable than winning big. Others prefer the high-volatility machines, enjoying the big wins when they happen and being prepared to accept long periods of losses. Time playing the game is less valuable than winning a lot. The idea that a regulation should be promulgated that limits the amount that someone may bet at one time is trying to shoehorn everyone into the same size box, showing no understanding of human nature and why people gamble. In the effort to protect a very few, many will be turned off what is, for them, a very normal pastime.