The Magic Economics of Gambling

This video was made possible by Squarespace. Build your beautiful website for 10% off at squarespace.com/Wendover. According to conventional economic rules, casinos shouldn’t be able to exist. That’s because conventional economic rules assume humans are rational. Conventional economic rules would predict that, if someone offered you a deal where you gave them $100 and they gave you $94.80 back you wouldn’t take that deal but for some strange reason, perfectly intelligent people head to the roulette table every day and, in essence, take that exact deal. Just look: an American roulette table has 38 numbers on it—double-zero, zero, and one through thirty-six. The best odds on the table are in the red, black, even, and odd boxes.

If you put a $5 chip in the red box, for example, and the ball falls on a red number you double your money, you gain $5, but of course the ball can fall on zero or double zero which are neither red nor black and, for these purposes, neither even nor odd. Now, if the zero and double zero didn’t exist then playing roulette would make perfect sense. If you came in with $100 and played infinite times you would leave with $100 because it would be a 50% chance of doubling your money each time. In reality, because of those zeroes, the odds of doubling your money are actually 47.4%. That means that for every dollar you play you can expect to lose 5.2 cents but for some reason people still do it while this small gap in between fair odds and the odds casinos and other gambling institutions offer earn them worldwide close to half a trillion dollars per year.

But consider this. For the same reason gambling shouldn’t work insurance also shouldn’t. Insurance is essentially the exact opposite of gambling. Insurance companies are basically gambling companies but the roles are flipped—the insurance companies are the gamblers and you’re the casino. If you pay a car insurance company, for example, $1,500 a year to insure your vehicle they’re gambling that you’re not going to cause more than $1,500 in coverable damage in any one year but of course it takes money to run the insurance company so they need a margin. MetLife, one of the world’s largest insurance companies, for example, takes in $37.2 billion from the people who hold insurance policies with them but then pay back in insurance claims just $36.35 billion. Of course there are other sources of revenue and other expenses at MetLife but just looking at the balance between what comes in and what goes out for insurance the odds are pretty decent compared to the roulette wheel. For every dollar you give them you can expect to get about 97.7 cents back but that’s still that’s losing money. According to the same conventional economic rules that say that casinos shouldn’t be able exist insurance companies too just shouldn’t work as a concept because people get back less than they put in but here’s why they do. Just consider this: would you rather, with 100% certainty, receive $5 or would you rather have an 80% chance of receiving $6.25. Feel free to think about it for a second but chances are that you said you’d rather have that sure $5. When surveyed with this question over three quarters of respondents said that they wanted the certain $5 over the 80% chance of $6.25. But here’s the strange thing: these two options are worth the exact same amount. If you took the 80% gamble infinite times you would receive an average of $5 each time as 80% of $6.25 is $5. Therefore, in theory, people should have no preference between these two options because they’re worth the exact same amount. But here’s the thing: people, in general, dislike losing a given amount of money more than they like winning it. That is, the negative effect of losing $5, for example, is greater than the positive effect of winning $5. Because the second option comes with the chance of loss, which is a negative experience more powerful than the positive experience of certainly gaining $5, this option is worth less overall even if it’s worth the same in a dollar amount. This is why insurance works. Insurance is a worthwhile gamble for the insurance company since the odds are in their favor and they make money while the gamble is worth it for you because the monetary amount you get back plus the absence of monetary loss makes the deal worth more than the money you put in overall. Of course it is a bit more complicated than this since insurance companies often have preferential rates for healthcare and it helps smooth out economic shocks so, despite being a gamble, it is absolutely worth it in most cases but insurance, at it’s most basic level, is loosing to avoid loss. This principle of hating losing can be used to make the same amount of money worth more. In one experiment 150 teachers in Chicago Heights were split up into three groups. One group received nothing, one was told that they would receive a bonus at the end of the year corresponding to how well the students test scores were, and the third group was given the exact same deal for a bonus with the only difference being that they were given the bonus payment upfront at the beginning of the year and told that they would have to pay back the corresponding amount if their students did not score the test scores necessary. The group that was promised the bonus if test scores improved performed largely the same as the group offered no bonus but, the group given the bonus up-front overall performed much better with test scores improving up to 3 times as much as the traditional bonus group. It’s clear that the fear of loss is far more powerful than the promise of gain so this explains why insurance works but, for this same reason, gambling still shouldn’t work but something interesting starts changing when you change the odds. Now, remember that three quarters of people preferred a sure $5 to an 80% chance of $6.25 but now think whether you’d prefer an 100% chance of receiving $5 or a 25% chance of winning $20. Once again the options are worth the exact same amount since 25% of $20 is $5 but, with this change in the odds, those surveyed on average had no preference between the two options. Half preferred the sure $5 and the other half preferred a 25% chance of $20. But let’s change the odds again. Would you prefer an 100% chance of receiving $5 or a 0.5% chance of winning $1,000. Still with these numbers 0.5% of $1,000 is $5 so the two options are worth the exact same amount but, with these options, for the first time people prefer the gamble. Only 36% of respondents said they would take the $5 while 64% preferred the half percent chance of winning $1,000. What we’ve begun to understand is that humans like low-probability risk. We like a small chance of winning big over a certain gain. In fact, you can see this at the racetrack. The best horse might have 2/1 odds where you get $3 if they win for each dollar you bet while the bottom might have 200/1 odds where you get $300 if they win for each dollar you bet but, as it turns out, on average, the chance of the top horse winning is actually better than 2/1 and the chance of the bottom horse winning is worse than 200/1 because people prefer betting on the underdog which inflates the odds. You could therefore make more money betting on the horse that’s likeliest to win. Crunching the betting data from 8,000 tennis matches it was found that the bets on the best athletes with the best odds actually made money on average with 103% of the money won back while the bets on the worst athletes with the worst odds won just 81% of the money back. Evidence for this phenomenon has been found time and time again but the question of why we do it is tougher. The simple answer for why this is is that people overweight the impact and chances of extremely low-probability events. This has been used to explain why people are so afraid of terrorism and plane crashes despite the chances of dying of either being monumentally small. It really doesn’t matter if you know that the odds are not in your favor like with the lottery or in the casino. People still love risk if it comes with large returns and this is why gambling works as a concept. Everyone just has some arbitrary point where, given two options with the same value, they’ll start accepting the risk over the sure money. What that means is that in a gambling transaction with someone who bets and someone who accepts the bet both parties actually find what they’re doing worthwhile. The casino finds what they do worthwhile because they make money while the bettor finds what they’re doing worthwhile because they have the possibility of winning lots of money. Now, the explanation for why people prefer these low-probability bets moves further away from economics into psychology but one explanation with the lottery, for example, is that a bet doubling one’s money does little to change one’s quality of life but, a bet multiplying a person’s money by a factor of thousands can be truly life-changing so people are betting for monumental change rather than for another cup of coffee. To summarize, what this all means that a 5% chance of $100 is worth more to most people than $5 despite both having a monetary value of $5. Therefore, by offering gambles people can make money more powerful. Almost everywhere in the world there is an issue of low-savings rates: people don’t put enough money into banks. About half of Americans could not immediately come up with $2,000 if an unexpected expense came up according to one survey. A big reason for this lack of savings is that banks are not incentivizing enough. With how tiny savings accounts’ interest rates are many people just don’t see a reason to put their money in banks and banks are unwilling or financially can’t increase their interest rates so how do you make the same amount of money go further? You turn it into a gamble. Economists created a concept for what’s called a “prize-linked savings account.” A normal savings account with $2,000 in it at a bank that offered 1% annual interest would earn $20 a year but, with a prize-linked savings account, instead of being given the $20 in interest it would be entered into a gamble with, for example, a 0.4% chance of winning $5,000. As always that gamble is still worth $20 monetarily but to the gambler it’s worth more. These prize-linked savings accounts have been incredibly successful so far at getting people to save. In Michigan’s trial of the system 56% of those using it were first time savers. These same principles are the ones that make lotteries work. In fact, lotteries are just such easy ways of making money that in many countries privately runs lotteries are illegal. In the US, for example, all lotteries have to be state-run and their profits usually go to funding education. Because the states are guaranteed to make money from the lottery it is essentially a form of taxation. In fact, all forms of gambling are set up in a way that they’re guaranteed to make money for whoever’s running them. In a casino, at the racetrack, or with any form of gambling it’s never a good deal for the bettor but, the reason why people engage in these deals is a fascinating study of behavioral economics and its principles, if applied correctly, can sometimes, just maybe be used for good. What’s always a good deal, though, is Squarespace. That’s because if you’re running any sort of business your first impression counts immensely and Squarespace helps you build the perfect first impression. No matter how small your business is it’s absolutely crucial to have a website but of course it’s expensive to hire someone to create one and complicated to code one yourself. 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