# The Magic Economics of Gambling

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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.

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You know there are no clocks at a casino.

“Not a plane video!” 0:00

7:32

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You don't make $20 on a savings account that pays 1% on a $2000 investment. You lose $40 of spending power because inflation went up by 3%.

I find gambling extremely boring. I was never a cards guy, and growing up playing deep, complex video games with story arcs and varied gameplay, casino games just feel ridiculously simple. Ooo, press a button and watch reels spin! Ooo, watch this ball spin around this wheel and see where it lands! Really? Give me something more complicated and maybe I'll be entertained enough to throw my money at a casino.

To the question at 3:00 I'd pick 6.25 because the amount is worth so little that not getting it would be totally acceptable. If you'd upped the amount to 50 vs 62.5 or 500 vs 625, I'd have taken the surefire money though, because at that point, it actually starts hurting when "losing" it. Same goes with the other deals you offer. 5 bucks is just barely worth my time, but give me a surefire 50 vs 200, or 500 vs 2000, I'd still take the sure fire money. Even, at 50 vs 10000, or 500 vs 100000, I'd still take the sure money, because I understand how percentages work. Yes it'd suck if I was then told I'd have gotten the larger amount, but I'd still have gotten a good amount of money. 5 vs 1000 I'd go for 1000 though, because again, 5 bucks is just not worth my time

I've heard of a gamble that's theoretically worth an infinite amount of money, but always makes the House money. Here's what it is:

The gambler pays a fee E to enter, and the jackpot starts at 1. For each round, they flip a fair coin. If they get heads, they proceed to the next round with double the jackpot. If they get tails, they get the winnings of the last round, or 0 if they get tails on round 1.

For each round, there is a 1/2 chance of dropping out, and 1/2 chance of advancing. Iterate through, and it becomes 1/2 chance of 0, 1/4 chance of 1, 1/8 chance of 2, and so on.

The expected value of this bet is:

0 × 1/2 + 1 × 1/4 + 2 × 1/8 + 4 × 1/16 + 8 × 1/32 + …

= 0 + 1/4 + 1/4 + 1/4 + 1/4 + …

= ∞

So we, as the house, could theoretically set E as high as we want, and it would always lose us money! But we know from common sense that no gamble could possibly have infinite value, and this still makes us money in practice…

You forgot about the time value of money. Insurance companies invest those premiums; that's why they can be profitable even if they have a negative combined ratio.

$6.25 has roughly the same utility to most people as $5. It's not risk aversion, it's just that you can buy roughly the same thing for the two amounts. However, having potential $20, $100, or $2000 even on the same expected returns, give you very different utilities. Also I'm not sure why it is so weird that rational ppl gamble. Pretty much any service we use includes a cut to the service provider as we know they'll run on a margin so that they stay in business. If you go for a $20 haircut, you only get $18 worth of time, products and tool usage, if you get a $10 burger, you only get $9 worth of food and service

Life is a gamble, but do not gamble

with that roulette table, why can’t you pay 10 dollars and double for every time you lose? you will eventually win and gain all your money back if you get a bad losing streak.

Insurance is bullshit and not a risk from the companies. If they start getting a loss they just jack their rates up. Also the people as a whole may get close to their return back but not the individual because 1 dude will sue for 4 million dollars because his neck hurts from an accident

The insurance explanation is flawed. I am forced to buy health insurance even in the US which has no national health insurance. I am forced to buy auto insurance. I am forced to buy homeowner's insurance. I don't have a choice to roll the dice. We're not true casinos for insurers either because they get pseudo infinite rolls and pseudo infinite bankroll. The $5 example is terrible because it's 2019 and that amount is like pocket lint. A much better video could have been done with the game show Deal or No Deal where players look at the number of high value briefcases left.

Can't wait for PETA to see this.

This is a smart ad.

8:09 Paying even money on a Banker bet??? Where is that casino? O_O

In all seriousness, if that happened at a real casino instead of a gaming expo, that dealer (and their supervisor) just cost the casino $75 for not taking out the commission. That'll probably get the dealer written up (and the supervisor, if they weren't fired)

Also, can we talk about why that dealer is only using her right hand? That looks incredibly uncomfortable, as well as being inefficient

Fear of missing out?

So essentially, gambling is more fun that just having money

Insurance makes money off a small chance of loss, while casinos make money off a small chance of enormous gain.

Is this based on the Barberis academic paper from Yale?

It follows it well. As someone who works in a Vegas style casino and specializes in gaming mathematics, I am a big proponent of letting people know the math behind the games. Having a basic understanding of what a casino does helps keep people from becoming problem gamers.

you forget that insurers are brokering their risks. otherwise they couldn't be profitable. risk mitigation is the lost art of economics…it isn't even considered in some fortune 500 portfolios. sounds dumb, is fact.

This is all you need to know: the house always wins.

If you play an infinite amount of times with 100$, you would leave with 0$, as there is a 100% chance that you had a consecutive losing streak that would leave you with 0$ and unable to continue betting

How ever if you only have 1 play would you take $5 or are you willing to take a chance on $100000?

Bruh u cant equate 5% chance of 100 and 100% chance of 5 cause im not gonna fucking do it infinite times

Don't play roulette period..total ripoff

perfectly intelligent poeple? LOL

have you seen the clientele in a casino?

Umm, insurance

DOESN'Twork. Not in America, anyway….3:13 yeah but we're not taking the bet infintie times are we? It's a one-time bet so 100% beats 80%, obviously though we have our limits and if the profits for the 80% were increased past say $10-20 then people would switch to that bet.

I think 5 dollars gets prefered, because it's easier to understand how much it actually is, while noone can calculate 80% times 6.25

Risk taking behavior and addiction also play a huge roll.

Most compulsive gamblers know full well they are losing money overall. But the rare few times they won big and that massive lump sum of money was so pleasurable it was like a drug. So it sticks in their minds and they are after that high.

Just to comment on the start, casinos make sense just like how going bowling loses you money. Of course, people gamble for fun, not to make money! They know they'll likely lose, but the rush of potentially winning is worth the average loss.

Remember kids… the house ALWAYS wins.

I get nothing back from my car insurance because I don't hit people. I guess that is their margin. Also if your going to gamble, the stock market is the way to do it. As long as you pick large caps or index funds you will likely do fine and if you pick very well you can double your money every couple years.

Well I don't think it's irrational to gamble. You know that you're almost certainly going to lose money, but if you enjoy it, how is it any different to paying for movie tickets or other entertainment?

Nobody would take a deal where they pay $100 and get back $94, but that's not what roulette is. Roulette is effectively paying $6 for entertainment. I personally don't enjoy gambling but I don't see why it would be considered irrational if you take into account the fact that people take pleasure out of it.

I’d take $5 100% over any of the other choices. First, The amount is added on top of your gross income, which means potentially more tax for the higher amounts. Second, there’s a diminishing return of money. The first dollar is worth more than the second dollar. This is less obvious in small quantity, but if you consider one million and two million, it’s easy to see that going from zero to a million gives you more benefit than going from one million to two million.

10:38 did he just say "a good dildo? "

Choose the best to bet https://gamblingappsstore.com

Financially it's best to look at gambling as entertainment that you pay for

More videos like this PLEASE

Win loss statements from casinos you play at as a tax write-off possibly and don't forget to claim the jackpots you hit through the year if you do anything over $1,199 Uncle Sam's a-knocken

I just would do the certain chance of the 5$ so I wouldn't have to carry around the $.25 in change

“Small chance of winning big?” What about losing big?

Shouldn't 0 and 00 count for even on roulette? 0 is an even number.

lottery is just a fancy word for stupidity tax…

What a Rad Freaking Video!! I like all yours but that one was The Tits!

Ok, say person 1 has $1m and person 2 has $40m. A coin toss is proposed. If person 1 wins he will get $1.25m & if person 2 wins he will get $1m. The person with $40m won't really be affected if they lose but the person with $1m will be broke. Thus, factors other than odds are at play. here.

Same in car insurance. Being uninsured might cost you say $50k in total car repairs if you crash into someone. This is a significant sum for most. Thus, paying $1k for insurance is seen as worthwhile even if it is most likely a money loser.

I don't really understand how the math behind the infinite rolls works. If one has $100 and plays roulette with a 50% chance, it only takes one fail to lose that $100. How is it made back? How exactly is the value gained/lost calculated?

It would also help to see a more in-depth explanation about how an 80% of $6.25 is equal to a 100% chance of $5.

you gambled on weather or not i would like this video…I did

People picked the 100% chance to win a $5 option because you left out the part about an infinite number of tries.

"In a casino, at a racetrack, or with any form of gambling it's never a good deal for the bettor" COMPLETELY FALSE

1. Legal means could include: holecarding, card counting, shuffle tracking, ace sequencing, matched betting, bonus hunting etc.

2. Illegal means countless, a few: Slot manipulation, signalling, match fixing so many more

Just completely wrong statement basically

Great video! I hadn't heard about the lottery savings accounts before. Neat concept!

You didn't mention games of skill like poker that are also found at casinos. There, it can be a profitable endeavor for the player… although the vast majority of players are still losing players, and the house is taking a cut.

Insurance is viable because the utility of money is not linear. Most folks would be homeless if they had a bad wreck and had to pay the medical bills. It is worth sacrificing expected value to be sure to avoid a scenario that ruins your life. On the other hand, a millionaire probably should shun insurance if his state allows him to do so. Of course, if you drive like I do, insurance is always the +EV move.

Wow, that was some really bad math skills you showing everyone. worth the exact same amount?? LMAO on that one. Plus how did you forget about the Deductible with insurance?? Back to school for you. You need to go.

Engineers like numbers… but those numbers never factor in the human cost. The lottery thing about it being "good", when you see people playing like $85(daily) to win $5(daily)… especially seniors. You will start to see the real world factor of "addiction".

My favorite game is the one they have at the bank. You put your card into the machine and press a button and money comes out every time. Best game by far.

This is whh poker is best. You are playing another peraon not the house

"conventual economics believes humans are rational"

and that's why conventional economics is thick

insurance works because humans don't live infinitely and the variance in the outcomes in a finite number of bets can be significant.

You shouldn't have made this video. You clearly aren't qualified.

There are loopholes like arbitrage bets, but they are rare and not intentional. If you seem them you know it's a accident, but a profitable accident for any statistician!

I would just like to say that according to traditional economic rules casino could exist. Someone isn't juste offering you a bad deal, but sells you an experience, a good time. So the pleasure you take in gambling justifies the bad deal you get from the house

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the idea of a prized based savings account disgusts me on a personal level

What this video touched upon for only 2-3 seconds is the concept of marginal value. It's the determining factor for a lot of these gambles and why people overwhelmingly prefer certain odds of similar value. Most people will always choose a 100% to get 100,000,000$ over a 10% chance to win Several Trillion, despite the Trillion deal having much higher EV.

buying a AWP in CSGO is basically gambling if you win the round like 2 times you get money back if you die ur enemy can take the AWP and kill ur team

And that's why the riskiest game I play is blackjack

Everyone: You can't loose money while running a Casino.

Trump: Hold my wall.

this is only true when you get the choice between $5 (100% chance) and $1000 (0.5% chance) an infinite amount of times. In most cases, you don't get this choice an infinite number of times and if you get the choice only once, then its a decision between $5 and $0.5, so it's pretty easy to choose now.

Well.. I don't get this concept of 100% chance of $5 being equal to 80% chance of $6.25.

The chance is a percentage of probability to win against others. Not the percentage of value of the money.

Can someone explain? Because at no point there is a probability of winning $5, it is always $6.25. So both amounts are never equal.

On may 5th, I woke up at 5 am. I had been dreaming of the number 5 all night. I had the 5 dollar special at the diner for breakfast. I filled my car up with gas, it topped off at exactly 5 dollars. I said I have to go to the race track, it was 5 miles away. I got there at 5pm, just in time for the 5th race. I bet 5 thousand on the #5 horse.

Sure enough, she came in 5th.

am sorry but the math is wrong. 100% chance to get $5 you can run that 100x and still get $5 each times. 25% chance of getting $20 doesn't mean you'll get the $20 after certain times but actually you get 25% chance each times you might get $20. So the math is not the same.

1. insurance it not a pure paying and giving calculations for most cases. If i buy a car, i might bot have the money to buy another one within the next 10 years. So its more like a credit where i pay interest regardless of me actually getting the money.

2. If i play the lottery, a large part of the value received, is dreaming about what I could buy if I won. And this value has to be included in the calculation. It’s basically like a cheap movie ticket where I for a few hours am introduced to an imaginary world where I’m a billionaire, rather than an imaginary world created by some movie director

Lol i thought the banking thing at the end was gonna be a sponser

A ton of useless information.

Umm…. pretty sure you messed up the horse betting odds. If you put up $1 with 200/1 odds you win $200 so the payout is $201. Not $300…

I wish I could live in New Zealand were insurance isn't mandatory

I never understood it honestly.

I've had the privilege to walk through Monaco, Macau and Las Vegas and I saw the same things.

Huge fancy halls filled with slot machines, or gambling tables of varies kinds. There's expensive carpets, chandeliers, majestic architecture and gardens.

Often times even free food for gamblers.

After putting 2 and 2 together one should come to realize that gambling is ridiculously lucrative for the house.

All this has been built using gambling money. How can anyone feel comfortable walking into and spending money to a business like that?

It baffles me.

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Introducing premium bonds in the U.K.! oh wait it’s been around for years

Private lotteries being illegal is the perfect example of how we are the slaves and the government is the master. "Do as I say, not as I do you pathetic, ignorant mutts!" That's my evil Gov't impression.

Gambling itself is pure magic especially after hard day at work.

The fact that surprised me most was: "About half of Americans could not immediately come up with $2,000" … Very sobering.

Humans are dumb

Economics is more complicated than quantum mechanics…

So, while I understand what was said, I can't relate to the phenomenon you are describing. You claim that "everyone just has some arbitrary point, where, given two options with the same value, they'll start accepting the risk over the sure money". In my own experience, as the chance of success diminishes and the reward increases, I become increasingly disinterested with the gamble. I suppose the aforementioned statement is true in the sense that I would shrug my shoulders in indifference given a choice between a 100% chance of getting $5 or a 99% chance of getting $5.05, since the potential negative reaction to the 1% chance loss is unlikely, and thus not worth the effort made to make a choice.

squarespace sucks

Funny, I'm the exact opposite.

I'd take the 80% chance at $6.25 over the 0.5% chance at $1000 any day.

I would propose a completely different explanation of your example about giving someone 5 dollar.

Because 80% chance for 6.25, requires 1) trust that you are honest and fair in how you come to this 80% and 2) it costs effort.

Getting 5 dollars straight up, doesn't require any trust. You just give it to me. It also requires less effort. 5 dollars is simply of such low value, that people don't really care. And because people don't really care, they also don't want to put in the effort. The effort simply doesn't outweigh the gains.

But looking at thins from a statistic perspective, doesn't really make sense to begin with. Because no one is exactly the average human, nor does one play an infinite amount of times. Like that, everyone thinks, and wants to think, they will stop after they have won. They however don't see and feel the psychological effect of addiction kick in. So it's not a statistical problem, it's a psychological problem. Because doing things that make statistically no sense, can still make sense when you take other factors into account.

Why do I have a military intranet. Is that connected to the server at 217 George St. & If your being paid what is the transaction.

.0001 percent chance of winning 500k

This one dude has fifty channels, I get it, monetize monetize monetize but maybe you could be a little transparent when you have the same ad running on twenty different channels by the same voice. I get it, you dont like youtube's policy, going around it doesnt solve it

No, the odds are the same for every bet on the roulette wheel.

May the odds be ever in your favour.

If the 0 and 00 didn't exist and you came in with $100 and played infinite times, wouldn't you leave with $0?

I’ve made $100,000s playing roulette for 1 simple reason – the Casinos cheat & I know how. Every # on the TABLE has an electrode that measures how many chips are on each number for each spin. There is only ONE reason this – so that’s how you win at roulette – you’re welcome 😎

It's easy: the gambler is paying for the entertainment value. The chance of winning big is a lot more entertaining than the chance of winning $20.

The thing is, it counts as entertainment. If you're having fun gambling, that's where the extra money is going

the thing is that a "i win $5 100% of the time is only equal to "I win $20 25% of the time" if the $20 25% of the time is 4 times