One of the most popular and exciting card games in casinos around the world is Blackjack. If you’ve never played, here’s the gist of it: Two players are dealt cards, and the object is to be the first to reach a total of 21. If you can achieve a total closer to 21 without going over, you win! If you go over 21, you lose. It’s easy to learn, quick to play, and a ton of fun (hence why it’s a top game at most casinos). But while it’s simple enough as a game theory, things can get pretty complicated when you actually want to analyze the odds and calculate an expected value (EV) of the game.
Let’s dive into the mathematics of Blackjack, so you can understand the calculations behind the odds and decide if betting on this game is right for you.
The Mathematics of Blackjack
As we mentioned above, Blackjack is among the most popular card games in casinos, so it’s not really a suprise that there’s a lot of interest in understanding its mathematical aspects. If you’re looking for a fast and easy way to earn or win money at the casino, Blackjack is a great option. But if you want to know how the game works mathematically, then buckle up, because here comes the geeky stuff.
Blackjack Basics
If you’ve never played Blackjack, here’s a quick primer on how it works. Each player is dealt two cards, and the objective is to be the first to reach a total of 21 without going over. If you do go over 21, you lose, and the casino wins.
The dealer also deals a card to the player, and after all the cards are dealt, player and dealer each check their cards and see who has the higher total. The one with the higher total wins. Pretty straightforward, right? Not so fast!
Studying The House Edge
In most cases, when a casino offers Blackjack, they also offer other more complex games like Baccarat or Punto Banco. For the sake of simplicity, we’ll use Blackjack as our example. When playing at a casino, you’ll typically be dealt three cards, and the dealer’s upcard is usually considered to be part of the hand. With three cards, the house edge is 4.9 percent.
“The house edge is the amount by which the house wins due to random chance,” according to the official FAQ of the game. For the purpose of this article, we’ll assume that the casino is offering a fair, 50/50 game with which you’re unfamiliar. The one thing that differs between casinos is the house edge, which can be as high as 15 percent or as low as 1.5 percent. It all depends on the rules and regulations of the casino, the version of the game the gambler is playing, and the table they’re at. In some cases, the dealer’s upcard can also be used to give the player an advantage. Although rare, some casinos’ rules do allow for this. The following sections go over the different types of edges and methods for minimizing them.
Static House Edge
As mentioned above, the house edge is the percentage by which the house wins due to random chance, and it doesn’t change from one game to the next or from one session to the next. Assuming you play at a fair, 50/50 casino, the static house edge is 4.9 percent.
This means that if you bet $100 and the dealer wins, you’ll win $49. You’ll keep winning until you either run out of money or the dealer wins again. Once the dealer wins once, the house edge will increase to 6.4 percent, and so on. You’ll note that the house edge can never be below 0 percent (unless the casino is cheating you), and it can never be above 5 percent (unless the casino is making a lucky guess).
Negative House Edge
Some casinos will give you a bonus, sometimes called a complimentary hundred, if you sign up for a VIP club card. These bonuses are completely optional and depend on several factors, the most prominent of which being the amount of money you wager. If you qualify for a bonus but decide not to take it, your adjusted credit rating will be affected, and you’ll have to wait to receive another bonus. The following example describes how a negative house edge can be established:
You begin playing at $100 per hand, and the dealer wins. You get dealt another card, making the total so far $109. You have $1 left in your account. The dealer is still holding his card, so the total is now $110, which exceeds the previous $100, resulting in a $10 loss for you. However, since the dealer also lost $10, the overall loss is $20. This means that your adjusted credit rating will decrease by 20 points (from a possible 950 to a possible 530). You can bet that the next bonus you qualify for, you’ll take it.
Royal Flush Advantage
Some casinos will also give you an advantage if the dealer’s upcard is a full house, suit, high card, or a royal flush. The following example describes how a royal flush advantage can be established:
You begin playing at $100 per hand, and the dealer wins. You get dealt another card, making the total so far $109. You have $1 left in your account. The dealer is still holding his card, so the total is now $110, which exceeds the previous $100, resulting in a $10 loss for you. However, since the dealer also lost $10, the overall loss is $20. This means that your adjusted credit rating will decrease by 20 points (from a possible 950 to a possible 530). You can bet that the next bonus you qualify for, you’ll take it.
Additional Rules & Regulations
Besides the basic rules of Blackjack enumerated above, there are several more complex rules that can determine the outcome of a game. In some cases, some rules can work in your favor and in others, the opposite can be true. Here are the most important additional rules to know:
- Hard Ways To Win
- Royal Flush
- Blackjack (Baccarat isn’t considered a variant of Blackjack)
- Ace-King-Jack vs. King-Jack, King-Queen-Jack, Ace-Queen-Jack, Ace-Jack-King, King-Queen-Jack, King-Jack-Queen, etc.
- Stiffed
- Fold
- Draw
- Community Cards
- Three Coins, Three Keys, Three of Spades, Three of Clubs, Four of Diamonds, Four of Hearts, Four of Spades, etc.
- Birds Of A Feather
- Four Of A Kind, etc.
- Three Of A Kind, etc.
- Straight Flush
- Five Of A Kind, etc.
- Four Of A Kind, etc.
- Five Of A Kind, etc.
- Full House, etc.
- Flush, etc.
- Deuces Wild, etc.
- Joker (Usually Mean’s Joker)
- Aces And Eights, etc.
- Ten Of Hearts, Ten Of Spades, Ten Of Clubs, Ten Of Diamonds, Ten Of Clubs, Ten Of Spades, etc.
The preceding list describes all the different types of edges that you might encounter while playing Blackjack. Keep in mind that some of these can give you an advantage while others can decrease your winnings. The goal is to figure out what kind of advantage you can get and use that to your advantage. If you want to learn more, hit up the FAQ or review the rules of Blackjack.