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  • This video was made possible by Brilliant.

  • Learn more about the math and science behind this video's topic for 20% off by being

  • one of the first 200 to go to Brilliant.org/Wendover.

  • Within the walls of the 51 licensed casinos of the Las Vegas Strip, there are 2,879 gaming

  • tables collectively bringing in $3.1 billion in revenue annually, or over a million dollars

  • each.

  • In addition, there are some 38,864 slot machines bringing in another $3.4 billion.

  • A single large Las Vegas casino, like the Bellagio, make more annually than some small

  • countries.

  • This is because the Casino business model is pretty much bulletproof.

  • Overall, the odds are always in the Casino's favorif this weren't true, the casino

  • would failso these floors just print money.

  • MGM International, for example, one of the world's largest multinational gaming companies,

  • has about 2.5 million square feet of Casino floor worldwide meaning it makes, on average,

  • $1,138 per square foot.

  • With the money their casinos bring in, they could line every inch of every foot of their

  • casino floor worldwide with a brand new iPad and still have money left over.

  • This is all to say, casinos make a lot of money, but to do so, they need a lot more

  • money coming through their doors.

  • You see, the casino business model all revolves around risk.

  • With every game they have, the odds are in their favor, but that's not to say the house

  • will always win.

  • Their advantage varies from game to gamein roulette, it's about 5.25%, in Poker, it's

  • about 3.35%, and in Blackjack, it's about 0.5%.

  • Of course, given how tight these margins are, there's a natural variability so casinos can

  • come out behind on a given table on a given night, but overall, with enough tables and

  • enough nights, they'll average out to these odds.

  • However, in order to do so, they need an immense amount of money running through their casinos.

  • Blackjack, for example, is one of the games with the lowest house edge, so if a casino

  • wants to earn $1 billion in a given year from the game, which would not be an unreasonable

  • estimate for a large gaming company like MGM International, they would need $200 billion

  • changing hands within their doors each year.

  • $200 billion is an enormous amount of money.

  • That's pretty much the entire GDP of New Zealand, passing through, in the case of MGM,

  • a physical structure barely larger than the Empire State Building.

  • When you have such a rapid throughput of money, very slight changes in the odds can make a

  • huge dent in the gaming company's earnings.

  • If, for example, the house edge in Blackjack changed from 0.5% to 0.4%, they would lose

  • $200 million, assuming $200 billion in annual play.

  • This is why making sure these odds stay in their favor is so important to casinos.

  • It can quite literally make or break them.

  • Despite what pop culture might portray, a casino's biggest problem is not robbers

  • or hackers or even technically cheaters, because each of those is relatively easy to prevent.

  • Rather, their biggest problem is people who are able to turn the odds in their favor without

  • robbing, hacking, or even cheating.

  • You see, in most common-law countries, such as the US, England, Ireland, or Australia,

  • cheating is legally defined as altering the outcome of the game, acquiring knowledge not

  • available to all players, or changing ones bet after learning of the outcome.

  • Cheating in a casino is generally illegal, however, it's possible for a player to consistently

  • win without cheating.

  • The best-known example of this is card counting—a type of advantage play used in the Blackjack

  • family of games which is not illegal and, in some cases, is even legally protected.

  • This advantage play technique essentially takes the basic principles of the game of

  • Blackjack and uses them against the casino, and these principles are fairly simple.

  • So start a game, each player bets an amount of money, then, six decks of cards are shuffled

  • together to form what's called the shoe.

  • Each player is dealt two cards, face-up, while the dealer gets one face-up and one face-down.

  • The goal for all participants is simpleit's to get their cards to total as close to 21

  • without going above 21.

  • The execution of that is much tougher.

  • Starting from the left, each player will either decide to stick with the total they have,

  • or to take another card to add to it.

  • Of course, the player doesn't know what the next card will be worth, it could be anything

  • from 1 to 11, so it's a gamble on whether it'll make the total go over 21—in which

  • case their bet is lost.

  • The higher the original total, the riskier it is to take another card, but there is,

  • in fact, a mathematically optimal choice for every scenario.

  • Once every player is done taking cards, or not, the dealer reveals the face-down card

  • and, automatically, if their total is below 17, they take additional cards until it isn't.

  • If it's 17 or higher, the leave it as is.

  • There are then three scenarios.

  • If the dealer goes above 21, all players' bets are doubled, as long as they didn't

  • go above 21 first.

  • If the player's total is higher than the dealer's, then the player's bet is doubled.

  • However, if the player's total is lower, they lose their bet.

  • Of course, this explanation skipped over plenty of smaller rules and unlikely edge-cases,

  • but it is these fundamental elements of game-play that tie into why card counting works.

  • Now, without getting too much into the math, on average, in Blackjack, higher-value cards

  • benefit the player, while lower cards benefit the dealer.

  • While the explanation for the higher-cards is more complex, lower cards benefit is based

  • on the fact that they are required to take additional cards when their total is less

  • than 17 and so a greater density of lower cards makes it less likely that they'll

  • total over 21—in which case each player's bet is doubled.

  • Therefore, if you know that a bunch of low cards are coming, you know that the odds are

  • against you and so you should reduce your bet or not play.

  • But, the question is, how do you know what's coming in a randomly shuffled deck?

  • Well, you perform process of elimination, or, even more simply, you count the cards

  • you see.

  • There are hundreds of different forms of card-counting that work in hundreds of different ways, but

  • all are more or less based on what's known as the Hi-Lo system.

  • With this, each card is assigned a value.

  • Two through six are assigned one, seven through nine are assigned zero, and ten, the face

  • cards, and the ace are assigned negative one.

  • This is based on the fact that, every time a high-value card is dealt, there are fewer

  • of them in the deck, which means the odds get worse for the player considering that

  • high-value cards are better for them, and vice versa.

  • So, card counting is quite simple.

  • With every card a player sees, they add up its assigned value.

  • So, if there are three players, and they are dealt these cards, the running count would

  • be one plus zero plus negative one plus one plus zero plus one plus zero, which would

  • equal a total of two.

  • That total of two indicates that the odds have shifted slightly in the player's favor,

  • while if it were negative two that would indicate the odds were in the dealer's favor.

  • As play goes on, and they get deeper into the deck, the running count will generally

  • increase in one direction or the other, giving the player more confidence on where their

  • odds stand and so if, for example, the running count equalled twenty, the player would know

  • that the odds were greatly in their favor and therefore that they should bet big on

  • the next round, as they have a greater than 50% chance of winning.

  • This is how people can reliably make money in Blackjack.

  • If a player changed their bet by a factor of fifteen depending on the odds, and the

  • dealer waited until they're through five of the six decks before shuffling, a player,

  • following perfect Blackjack strategy, could earn an advantage of about 1.182% over the

  • house.

  • That means that if, assuming a table completes a round of play every minute and the average

  • bet is around $200, a card counter could profit, on average, about $110 an hourenough that

  • some people can and do make a living by sitting at Blackjack tables, counting cards.

  • However, considering how simple and reliable this advantage play method is, casinos go

  • to great lengths to stop it, which is very, very difficult.

  • That's because the advantage is all in the mindthere's no good way to fully prove

  • someone's card counting.

  • Sometimes, people are just lucky, and it's quite a bad look for casinos to kick people

  • out just because they're winning.

  • That's why, instead of trying to prove it, most casinos implement rules to try and stop

  • card counting from working as well.

  • Remember that, generally, the running count will get further into the positive or negative

  • the further into the game one goes, because the card counter will have seen more cards

  • that are now in the discard pile, and therefore cannot be dealt.

  • While a few rounds in the running count might be in the single-digits positive or negative,

  • further on, it'll get into the double-digits which gives a counter great confidence on

  • whether they should bet big or not.

  • It's towards the end of the shoe, the collection of un-dealt cards, when card counters really

  • make their money, so to make it less profitable, casinos can just have their dealers shuffle

  • earlier on.

  • If they shuffle four decks deep into the six-deck shoe rather than five, that decreases the

  • player's advantage from 1.182% to just 0.568%.

  • However, shuffling earlier and more often also cuts into the casino's profits because,

  • anytime the dealer is shuffling, the non-advantage players aren't playing and losing moneywhich

  • is how the casino makes its money.

  • Another option for casinos is to increase the number of decks they shuffle together

  • to make the shoe.

  • Back before card-counting first became a widespread issue for casinos, they would play Blackjack

  • with just a single deck of cards, but if they did this today, it would only be a matter

  • of minutes before a card counter would have high confidence about the odds.

  • Therefore, they typically now play with six decks shuffled together, which increases the

  • time it takes to get to high confidence and, since time is money for a card counter, this

  • decreases their profits.

  • Some casinos take this a step further by using continuous shuffle machines.

  • With no discard pile, there is no increase or decrease in beneficial cards in the shoe,

  • so card counting is completely ineffective, however, these machines are not yet fully

  • widespread due to distrust by frequent players.

  • While these methods deal with stopping or reducing a player's ability to actually

  • know what the odds are at a given moment, the other method involves stopping a player's

  • ability to respond to this knowledge by changing the size of their bets.

  • Essentially, if a dealer or a pit-boss suspects someone might be card counting, they'll

  • change the rules on them and require flat-betting.

  • This is where a player is told to pick one bet size and then they are not allowed to

  • change that size from round to round.

  • Therefore, card counters might know that the odds are changing, but they will not be able

  • to respond to it with a larger or smaller bet, so the odds will stay in the house's

  • favor.

  • However, that poses the question, how do you spot a card counter?

  • Well, one of the most tell-tale signs is that they're wining.

  • Even if someone is card counting, the casino does not care as long they're losing, so

  • they don't really pay attention to people until they've made some real money.

  • Once they are, though, if a pit-boss notices that a player, for example, changes their

  • bet from $100 to $1,000 right before a series of wins or as the shoe is close to finished,

  • that's a good sign that they know what the odds are.

  • In addition, professional card-counters often start with a very large buy inthey convert

  • a lot of money into chipsbecause there is natural variance on whether or not they

  • win, even if they know the odds.

  • They can win infinite money, but they can only lose as much money as they have, and

  • even if they have an advantage, if they're unlucky and they lose all their money, there's

  • no way to win it back.

  • The math works out so that, if you want to win $170 an hour card counting, you need to

  • have $100,000 total in order to only have a 1% chance of running out of money.

  • In the end, casinos don't need to make it impossible to count cards.

  • Only a small minority of people will attempt it and those that do can only make so much

  • money per hour, so in a way, its a cost of doing business.

  • To avoid it making a big dent in their profits, all they need to do is make advantage play

  • at their tables just a little bit harder than those next door and, if this is the case,

  • the card counter will go next door.

  • There will always be an escalating arms race by both players and casinos to gain an advantage

  • and stop an advantage, respectively.

  • Mathematics, economics, and human nature combined mean that as long as Blackjack and other flawed

  • casino games stay popular, players will always find a way to tilt odds ever so slightly in

  • their favor.

  • Before I made this video, I took Brilliant's course on Casino Probability and, specifically,

  • the section on Blackjack to be sure that I understood most of the math behind what I

  • was talking about.

  • In fact, part of the reason why I wanted to make this video was because I found the mathematics

  • of gambling so interesting and so, if you did too, this course is a fantastic way to

  • dive deeper into the topic.

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How to Beat the Casino, and How They'll Stop You

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    joey joey に公開 2021 年 06 月 10 日
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