Being a huge Hangover fan, there is something that I have always wanted to do in my life and that is, gambling all night at a casino in Las Vegas for once. 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 in each table. In addition, there are some 38,864 slot machines bringing in another $3.4 billion dollars. A single large Las Vegas casino, like the Bellagio, makes more than some small countries, annually. 

This is because the casino business model is pretty much bulletproof. Overall, the odds are always in the casino’s favour. If this weren’t true, casinos 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, $1,038 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 favour, but doesn’t mean the house will always win. Their advantage varies from game to game - in Roulette, it is about 5.25%, in Poker, it is about 3.35%, and in Blackjack, it is about 0.5%. 

Of course, given how tight these margins are, there’s natural variability, so casinos can come out behind or lose money on a given table on a given night but overall, with enough tables and enough nights, they average out 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 the casino wants to earn $1 billion in a given year from the game, they would need $200 billion changing hands within their doors each year. That’s pretty much the entire GDP of New Zealand. When you have such a rapid throughput of money, very slight changes in the odds can make a huge variation in the gaming company’s earnings. If, for example, the house edge in the 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 favour is so important to the casinos. It could quite literally be the difference between millions of dollars in profit or filing for bankruptcy. 

Despite what the movie 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 and detect. Rather, their biggest problem is people who are able to turn the odds in their favour without robbing, hacking or even cheating. 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 play technique takes the basic principles of the game of Blackjack and uses them against the casino, and these principles are fairly simple. 

To start a game, each player bets an amount of money and 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 card. The goal for all the participants is simple, it’s to get their cards to total as close to 21 without going above 21. 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 in between one 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 sum, the riskier it is to take another card but there is in fact a mathematically optimal choice for every scenario called the 'basic strategy'. Once every player is done taking cards, the dealer reveals the face-down card and automatically if their total is below 17, they take additional cards until it isn’t over 17. If it's 17 or higher, they leave it as it is. There are then 3 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 less likely 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 the lower value cards benefit the dealers. While the explanation for the higher cards is more complex, lower card benefit is based on the fact that the dealer is 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 will go 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 the 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. Cards ranging from two to six are assigned 'one', cards from seven to nine are assigned 'zero', and card 10 and ace and all the face cards are assigned 'minus one'. This is based on the fact that every time a high-value card is dealt there are fewer of them left in the deck, which means the odds get worse for the player considering that high-value cards are better for them and vice versa. With every card a player sees, they add up its assigned value. So, if there are three players and they are dealt the cards in figure 1, the running count would be two.

As the 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 the odds stand. So, for example, if the running count equals 20, the player would know that the odds are greatly in their favour 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 changes their bet by a factor of 15 depending on the odds, and the dealer waits until they’re through five of the six decks before shuffling, a player, following a 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 an 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, 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 that a person is counting cards. Sometimes, people are just lucky and it is quite a bad look for casinos to kick people out just because they are 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 positive or negative the further into the game one goes because the card counter would 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 will get into the double digits which gives the counter great confidence whether they should bet big or not. It is towards the end of the Shoes, 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 4 decks deep into a six-deck show 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-advantaged 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 a show. 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 a continuous shuffling machine. With no discard piles, there is no increase or decrease in the beneficial cards in the shoe, so card counting is completely ineffective.

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 counting cards, they’ll change the rules on them and require flat betting which means making a player choose one bet size for all rounds and not allowing them to change the bet in future rounds when the count is in their favour. However, that poses the question, how do you spot a card counter? Well, one of the signs is if a player changes their bet from 100 to 1000 right before a series of wins or as the Shoe is close to finish, that’s a good sign that they know what the odds are.

At the end, the casinos aren’t much affected by card counters as they make a very small proportion of all the players and they consider it as a cost of running the business. Till this time these games continue to exist, players will always try to find new ways to shift the odds in their favour and this causes a never-ending cycle, but what we must know is that if we use basic math we can outwit some of these casinos.

If you want to learn more about Blackjack, click here.