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,
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100 Comments

  1. if i could choose not to pay insurance, i would choose that opttion, unfortunatly its the law that you MUST have insurance.. sooooo yeah

  2. There are so many oversimplifications and incorrect definitions in this video. Suggest that you familiarize yourself with "expected value", "utility", and the time va,ur of money and then revise / rescript.

  3. I was in a casino once, just for fun

    I won about 150 CHF^^

    But this was the first and only time, I went to a casino^^

  4. I don't think the $5 example works. There's value to reducing risk. It is completely rational to prefer the lower risk, all else equal.

    The more risk, the bigger the required payoff.

  5. Let's not forget that the odds for winning the lottery jackpot is around 1 in 45 million, and if you buy 2 tickets, the odds become around 1 in 22.5 million, for a small price. so people are more likely to buy 2 tickets.

  6. I rarely downvote, but this simplification of insurance is nonsense. If my losses could destroy me, removing my ability to meet the opportunity costs for recovering, but the premiums are manageable, then the insurance is worthwhile. Only the wealthiest entities (such as New York City) can self insure.

  7. 5 dollars is equally to a 5 percent chance of 100 only if the bet is done multiple times. The whole point is it's a one time thing

  8. this video states odds of 200/1 gives you 300 back for every dollar bet. but its actually only 201. i wouldnt want to be the videos author if im paying out 50% above the odds.

  9. I like your channel so I'm a little surprised that you made a video I have so many issues with

    0:18 – no they do not make that exact deal. They would be if something you assumed a bit later was actually true: that they had an infinite number of trials, but since that's not true your statement is illogical. On average over trillions of attempts by millions of people, people lose 5 cents on the dollar, but individuals only take a ridiculously small fraction of those attempts. The smaller the sample size the higher the variation, so people are actually betting that the variation will be in their favor.

    1:22 – the reason people still do it is, besides the reason I mentioned earlier, because it's fun. It's entertainment, and the 5 cents on the dollar people lose on average is essentially the cost of admission for this grown-up amusement park

    1:36 – insurance shouldn't work. At least in the form that it does. It "works" how it does in the US because not having insurance is literally a criminal offense

    2:25 – even ignoring the first thing I said, people who want insurance don't want it to make money. They want it to prevent too much loss at any one point in time. With insurance there's only so much you're liable for until the insurance company has to pay for everything, so if you royally screw up and t bone some guy's million dollar Lamborghini, you don't have to come up with a million dollars all of a sudden and go bankrupt. Even ignoring that, people use insurance for the same reason people buy cars on payment plans despite it literally costing more money: it amortizes the cost. If something unrelated and drastic happened that cost you a lot of money, and now you lost a bunch more money to pay for some accident not covered by insurance, you could get hit with too much at a single point in time and go bankrupt as well.

    2:42 – again, the two things are not the same, but not because of the negative effects of losing or whatever, but because there is not an infinite number of trials but instead only one. You even said at 3:13 your theory relies on an infinite number of trials, which isn't the case in the real world. How could you miss something so obvious

    7:29 – terrible explanation. The real reason is because the amount of reporting the media does on, say, terrorism, is astronomically high in proportion to the number of people who actually die of it. With plane crashes it's the same deal, but made even worse by the fact that you're trusting your life with an extremely complex machine when you have no clue how it works

    9:23 – this is a bit, well, petty, but this is also not true. You're losing money here due to inflation

  10. I think it's kind of the same thing with the chance of crashing in a airplane and the low Chance of winning it big at the casino. There's still a chance of it happening.

  11. The point is that people who play will never achieve average results. You need enough examples to average out stuff. One single person will never play so much to have enough to average out. On the casino's side it's averaged out because it's many to one relationship.

  12. The point that the fear of loss is stronger than the promise of gain, is also the reason why religions work.

  13. Insurance companies screw you over. Expensive premiums and on top of that you still have to pay a deductible or co-pay

  14. I'd rather have a normal savings account tbh because then I can get away with doing less work to figure out its interest rate.

  15. I very much liked the video, but there is a small mistake in it.

    The two "behavioral" features mentioned are indeed necessary to explain lotteries. Conventional economics does not explain those.

    But rational agents may use insurances and the insurance business may be explained in a conventional economics framework. This is because a rational agent does not need to be risk neutral. In fact most agents are risk-averse and this is not a "behavioral" feature. A rational agent with consistent preferences may prefer $10 100% of the time to 30$ 50% of the time, there is no contradiction. That is why, regarding assets and investments, riskier assets are more profitable than safer assets. A "utility function" is compatible with those choices and they are "classic/conventional" economics.

    Lotteries are not explained in this way, because if agents were consistent and risk-loving (instead of risk-averse, like most people are) they would go to the stock market and "gamble" in the riskier assets – where you are payed (in expectation) to have a risky behavior – instead of going to the casino – where you pay (in expectation) to have a risky behavior.

    In a world of risk-averse agents insurances make sense, but in that same world – where you are payed if you are willing to have risky decisions – paying to do so does not make sense. And therefore, only agents who behave in an inconsistent/irrational manner make casinos and lotteries work. And one may explain that using "prospect theory" (loss aversion, etc.) like you did in this video.

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  17. One big problem with this video
    You keep saying "if you took this deal infinite times", yet if this ever were to happen it wouldn't, it would be once, and that's how the general amount of people would think

  18. Would you rather have 6.25 at an 80% chance? Or get $5 guaranteed and not get arrested and have your car impounded by the government

  19. The reason why car insurance works is because you don't want risk going completely broke due to potential car accident expenses every time you drive a car

  20. I'm not sure what your saying about the 80% of 6.25 = 5.00. Are we talking about a series of one-off rolls of a ten-sided dice in which the outcome isn't effected by previous outcomes? Say you need numbers 1-8 to win 6.25 and numbers 9-10 yield you 0. And say you roll the dice 20 times in row and every roll you get between 1-8, the next roll is still in your favor as you would still have an 80% chance of rolling between 1-8 because it is not effected by previous outcomes.

  21. I don't know how it works in the US but, here in Europe, vehicle insurance is not a voluntary option. If you want to drive a car on public roads, then you have to buy insurance. It's nothing to do with me making a intelligent choice about whether insurance is an economically viable gamble: it's the law!

  22. I will teach anyone the secrets of making money gambling if they deposit 4 dollars worth of bitcoins into my bitcoin walllet. Im dead serious. I will hold your hand the whole way. something unfortunate happened to me that depleted my bitcoin account. I just need one adventurous stranger to help me out.

  23. I personally would always take the $5 even if you have me a chance to win a thousand dollars. I just really hate probability

  24. 100% for getting X is not 25% for getting X*4. Maybe it is mathematically, but not practically. The first option is surety, while the other is a chance of getting 4 times more 1/4 of the time, which in practical terms may mean never. Get a 100 sided die, throw it 100 times and look a the distribution. Chances are that there will be results that occur multiple times and such that do not occur at all. So yeah, 100% for getting X is the same as 100% for getting X*4 every fourth time.

  25. I gambled once in my life. My dad gave me $50 to gamble as a "lesson" to show its a waste of money. I was down to $10 and feeling bad about it and then I won $394. Im never gambling again.

  26. This totally fails to explain tail risk. Tail risk of death or baskrupcy is “more expensive” to buy because if it happens you’re out of business for good. Don’t believe me? Google why put options are “overpriced” and you will see it’s because this downward tailrisk is actually correctly priced and that there is a value to not dying no matter the “risk”

  27. I have a gambling problem the sad part about it is that i have 120 iq and I already have watched this video thrice
    Is really hard to fight this things

  28. u miss one important fact: when i have the chance to win 100Dollars with an input of 5 then i hope that i get these 100 dollars faster than spending 100 Dollars

  29. Well, there is also the entertainment factor – people think gambling is fun, and maybe they're okay with paying for that through gambling.

  30. The horse racing gamble is wrong i think. With 2:1 odds you win $2 for every $1 you bet. So if you win, you get $2 plus your original $1 back…so $3. If you bet 200:1. If you win you get $200 plus your original $1… so $201, not $300. Come on guys, are you or are you not degenerate gamblers who should know this?

  31. If you can swing the advantage to you favor $100 bet with a 1% edge is worth $1 per bet and the longer you play the more you win it's that easy folks just gain the edge over the house and play a lot to win the same way the casino does

  32. I think your study lead you to make a bad premise where the gambled $6.25 is equal to $5. Winning a prize happens only once, and cannot be averaged out over time and therefore it's obvious these two choices aren't equal. One is either $6.25 or $0 and the other is always $5.

  33. The 80% option doesn't only come with a "chance of loss", depending on the number of tries you are able to take for example 1 try you have 20% to loose everything and end up with 0$ instead. Even if you are unlcuky because of the nature of the probability there is a certain random factor involved and if you are unlucky this certainly happens because you can't ramp up the sample size to infinty when applying this to reality. So optiopns considering probability are not "woth the exact same". Only if you are able to run enough cycles you are able to achieve these results due to the law of large numbers. Since this doesn't usually apply for many ppl it is totally reasonable to pick the 100% chance chance choice over the other.

  34. gambling should be banned 100% and the government should shut down all the casinos

    why?

    1. it exploits the poor for money
    2. the profits from casinos do not generate any material wealth

  35. Insurance doesn't exist only because people have loss aversion. It's actually logical, if you grant that there's decreasing marginal utility of money. Spending that extra 3 cents on the dollar to make sure that an accident doesn't leave you in abject poverty is a huge win, because the marginal utility of the universe where your $100,000 accident coverage pays out and you avoid abject poverty is worth a lot more than the universe where you risked abject poverty for the long-run benefit of +$3,000. In other words, though it's negative EV in terms of money, it's positive EV in terms of utility.

    It's important that loss aversion and the decreasing marginal utility of money are kept as separate ideas. If people had a ton of money like banks themselves, then insurance would be illogical, as you say, and would only exist because of loss aversion. But it exists for a very logical reason, not just couched in human psychological biases.

  36. A 1:15 the video claims a fair 50-50 would let you leave with the money you came in with after infinite time.
    Wrong!
    With a finite stake playing on a fiar 50-50 proposition you will with certainty go broke. In finite time. You may be rich from time to time, but you will at some point hit zero — at which point you're out of the game. The end.
    So much for Wendover's knowledge of "magic economics."

  37. The reason people buy into low probability big wins is because most people that gamble can't afford too. Gambling feeds off the poor.

  38. Now explain how people buy loot boxes in videogames when it's cheaper to buy a game without loot boxes and it's way more fun.

  39. if you go see a movie you will loose the 10$ but get 2 hrs of entertainment. if you gamble 10$ you could win more, break even or loose all the 10$ all the while you are entertained and prob get a free drink.

  40. This is a stupid explanation of gambling hes leaving out so many factors juat by saying essentially you lose 94 cents for every dollar you play. Btw playing black or red is a suckers play on roulette. You play 3 numbers every spin they pay out like 38x

  41. I didn't hear mention of entertainment being a motivation for patrons. I know I will lose money gambling but the thrill of winning has a value to consumers.

  42. This video is filled with inaccuracies. Behavioral economics is difficult to grasp intuitively, but you made some pretty incorrect analogies there

  43. 2 to 1 odds does not pay out $3 for $1 bet:
    https://youtu.be/7cjIWMUgPtY?t=397

    It would double the bet, so it would pay $2
    Reference: https://en.wikipedia.org/wiki/Odds

  44. 7:30 Think the issue about plane crashes might also depend on what you use as the denominator for calculating its probability. If it's all the flights in the world then the probability is probably low, since the stakes are high (there's quite a lot of delay in evacuation after an emergency occurs in aviation, compared to other transport modes, due to things like the need to dump fuel and find a diversion airport, and during that delay the aircraft might no longer still be in 1 piece e.g. SR111), leading to a highly-regulated industry. However if the denominator is only the planes that have been in an accident than I imagine the probability is higher. I don't recall seeing as frequently, among other transport modes, accidents with a ~100% fatality rate e.g. JA123, AF4590, QZ8501, MS604, JT610

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