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,
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Good job on this, Sam.
I think asking the question would you rather have a 100% chance of receiving $5 vs 80% chance of $6.25 misses a larger point in how we evaluate the choice. Those two numbers are only the same when played infinite times, and the question asked is a 'one-time' ask, not an infinite one. This doesn't take into account upside - $5 isn't much to most people, but I wont say no if you want to give it to me. However the 20% risk of not having $5 is not worth an extra $1.25 because $1.25 is basically nothing. Now in the example of 100% get $5 and 1% get $500 the mental math changes because again $5 is not very much money, but $500 is quite a lot - so you're willing to risk not getting very much to get much more. I imagine that if you changed the starting numbers you'd see something different. If I said you have a 100% chance of receiving $50k or a 1% chance of receiving $5m the vast majority would choose the first option because its a significant amount of money no matter how you look at it - and it is also a sure thing in this one-time play scenario.
I feel that the video is making the wrong conclusions, because it's making the point that the expected value ("worth") should be the only thing we base our decision on. Also, our net worth is not the same as our utility (which presumably is what we optimize on).
However, if you look at probability in general, it's important to look at both the expected value and the overall spread. For example in a normal distribution both the mean and standard deviation are both important to characterize the shape. For dice throwing, if you roll the dice a couple times the spread is pretty huge. If you roll the dice a million times, however, the std deviation is tiny. Both situations still have the same mean.
Since most events in our lives are finite; e.g. we get cancer once or twice, get into a car crash a few times; it makes sense to try to reduce the spread even though the expected value is lower as a result. It may even maximize utility (which does not have a linear relationship to net monetary worth), because your utility may be roughly the same by paying the insurance cost, but it will definitely decrease if you suddenly have to pay out of your pocket millions of dollars for medical costs.
It's true that humans have proven to be loss-adverse, and that's a fascinating topic by itself, but even for 100% logical self-interested people it makes sense to buy insurance.
Awesome ! Thank you !
In the video, he says at 200/1 odds, a one dollar bet earns you 300 dollars. At 200/1 odds, a 1 dollar bet will pay you 200 dollars, plus your one dollar back.