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
favor—if this weren’t true, the casino would fail—so 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 game—in
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 simple—it’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 hour—enough 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
mind—there’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 money—which 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 in—they convert a lot of money into chips—because 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. You can even do this when on the go, in small
chunks, with their mobile app, or learn something new every day with their daily challenges,
or dive deep into something completely different with any one of their many dozens of super
high-quality classes. By high-quality I don’t mean that they look
good or work smoothly—even though they definitely do—but rather that their academics are designed
in a way that makes rather complicated subjects easy to learn. They teach you like the best teacher you’ve
ever had—by breaking up big concepts into smaller, digestible, intuitive chunks. So, if you want to dive deep on useful STEM
subjects, including learning more about the mathematics of gambling, make sure to be one
of the first 200 to head over to Brilliant.org/Wendover to get 20% off.
Felt kinda meh to me, mostly stuff about card counting that's pretty widely known. The logistics/flight stuff always has a lot more info that it feels like nobody else is really covering and feels much more interesting.
Plus he's way off with that $200bn figure. Blackjack has a 0.5% theoretical house edge but the real edge is usually more than 10% because most players don't play optimally even without card counting. Per dollar staked, it's a more efficient money-maker for the house than slots (if you ignore things like paying a dealer) which only makes about 8%. And I doubt MGM makes close to $1bn on blackjack, unless the game's much bigger in Asia than in the US. If you combined every casino in Nevada and take all their earnings for the past 20 years, I don't think there's been $200bn staked on blackjack.
There was that plus a few wrong numbers on screen where he read out a different number to what appeared, combined with the lack of interesting new stuff it felt like one of Sam's weakest to me.
The scene where the dealer flipped over a 20 then proceeded to sweep up the cards before taking the losing bets ruined the whole video for me.
Genuinely enjoyed this one. Only downside is that now I want to go out and play Blackjack
Overall, a nice overview, but it did feel dry; instead of calling it "How to beat the Casino...", this video should have been titled "How the Casino beats you...".
I was unhappy that the high card advantage was glossed over, since that's a huge basis for providing player-advantage, as higher cards lead to more blackjacks which are paid out to the player and not the casino. I don't think that's too "complex" to explain, and it's the namesake of the game! Final point, if you're teaching how to beat the casino, a bit more on the bank size would have been important to focus more time on as well. I think that's interesting math that few people ever focus on. Love your videos though, keep 'em up!