Probability of Casino Games
Understanding probability is an intricate part of becoming a better gambler; once you figure it out, you have a better idea of your winning odds of success. This can prove critical when playing games with multiple betting options.
Of course, this is not a one-size-fits-all kind of industry. Each game will have various levels of probability, and each version of those games adds tweaks and twists that adjust it. While it won’t be possible for us to cover every possible instance of casino probability for US players in all games, we can at least provide you with an overview. This is something we aim to do right here.
Casino Game Probability Explained
Before you explore the sheer depth of casino game probability, you have to ensure that you have created an account at the safe online casino. Gambling sites that offer games which are not RNG-certified are likely to cheat you; in this case, studying probability becomes essentially worthless.
Assuming you are playing at a safe casino, you can begin to study probability on casino sites in the USA, the UK, Europe, or wherever else you are living.
Probability is defined as the likelihood of one particular outcome coming true. In gambling terms, it is the odds of success when placing any given bet.
Probability is often expressed as a percentage. This shows how likely you are to land (or win) a bet that you place. The probability can change in each game, depending on the bet type you make.
For instance, your odds of landing any three-of-a-kind combo in a slot differ from landing a five-of-a-kind combo consisting solely of jackpot symbols. Similarly, the probability of landing a Pair of Jacks is much higher than landing a Royal Flush in poker.
How to Calculate the Probability
Calculating casino game probability requires you to know a few details about the game. For instance, you have to know how many possible winning combinations there are. How you go about it depends on the game you are playing. The formula is straightforward but applies differently based on the gambling title you selected. When discussing probability, we usually refer to one (your winning bet) divided by the number of possible outcomes.
For instance, there are a potential 2,598,960 hands in a conventional poker game. If you want to get a handle on the Royal Flush probability, you have to divide the total number of possible hands by the number of ways you can land a Royal Flush (there are four — one for each suit). Therefore, you can ascertain that your chance of success is 4 in 2,598,960, or 1 in 649,739. When calculated as a percentage, this gives you a probability rate of 0.000154%.
These are different ways you can show (or express, hence the name) the probability of something. They can be displayed as ratios, percentages, or as decimals. To better explain what we mean, we’ll show you the probability of rolling a six-sided dice and landing the number four.
It is important to note that despite each probability expression looking different, the actual odds of landing a Royal Flush remain the same, irrespective of how it is displayed. We’ll show you how to calculate each of these probability expressions later.
Probability of a Coin Toss
If you’re still struggling to grasp this point, let’s look at a coin. As you’re aware, there are two sides to a coin, usually heads or tails. You can call them A or B, X or Y; it doesn’t really matter. When you toss a coin, you have a fifty-fifty chance of success.
The probability of the coin landing on A, X, or heads is a firm 50%, or 1:2. Therefore, the other side, B, Y or Tails, has to be fifty percent; otherwise, the equation doesn’t balance. If there were a three-sided coin (an absurdity, we know), then the probability of landing A, B, or C would be 33.3%, and so on. Calculating probability in gambling games is similar, albeit a lot more complicated.
How to Calculate Return
While calculating probabilities at a casino is based on the number of possible outcomes in a bet, calculating returns is trickier. This is most easily done when placing sports bets. To calculate the return, you have to divide your net profit (win) by the total risk (stake) involved in your bet.
For instance, if you were to win $10 betting on sports at odds of 2.40, you’d win $24. However, that isn’t your return. Your return is the amount you’ve won/net profit ($24) minus the amount you’ve wagered/risked ($10), meaning that your return is $14. A successful sports bet sees your stake returned, so your total expected return is 140%.
You’ll need to use different calculations for alternative betting options. For instance, the methodology used to determine the ROI (return on investment) in blackjack is slightly different. Fortunately, there are plenty of ROI guides out there tailored to whatever specific game you wish to play.
Probability of Various Casino Games in Detail
The actual probability of casino games will vary, depending on what you choose to bet on. We’ll introduce you to the probability of landing wins in several popular online casino games.
Considering the house edge, a player has a 42.22% chance of winning (with any hand) in blackjack. The probability of landing a tie sits at around 8.48%. You have a 4.8% chance of landing a natural blackjack with your first two cards.
You have roughly a 2:9 chance of success with winning on your first roll in craps. Rolling a 7 is a 1:6 chance while rolling an 11 gives you a 1:18 chance. Together, this makes a 2:9 chance of success.
As we have mentioned before, your chances of landing a Royal Flush in poker are approximately 1 in 649,739 or 0.000154%. However, there is a 42% chance of landing a pair, and that may be enough to bag a win.
There are only three outcomes in baccarat. The banker’s hand will win 45.8% of the time versus 44.6% for the player’s hand. Ties only occur 9.6% of the time, so it is the least favorable bet, and thus, it pays the most, often at 11:1.
If you have tried your hand at online roulette, you will know a bit about your odds of success here. The true probability can vary, depending on the version you play. However, you have just a 2.7% chance of landing a Straight-Up bet at one end of the scale and a 48.6% chance of landing an even-money bet in European Roulette. In American Roulette, the odds of landing Straight Up and even-money bets rise to 2.6% and fall to 47.4%, respectively, because of the double zero sector.
Slot probability is the most difficult to calculate and varies from game to game. As there are thousands of slots, and even hundreds of those are amongst the best online slots, we can’t give you an exact success probability here. They can range from 1:5,000 to 1:34,000,000. It is down to the game you play and the winning combo you’re looking at.
Calculating keno probability depends on the number of balls in the game and the number drawn by the machine. In a typical game featuring eighty numbers, you have a 22.06% chance of landing at least one number and a 0.000072427678% chance of landing nine or more.
Odds of Winning at Casinos
There isn’t a surefire way to calculate casino probability overall. However, you can get some insight into how likely you are to win by studying a casino’s pay rates, its RTP rates, and house edges. For instance, when we talk about slot machines, the RTP rate determines how much of each bet a casino puts back into a pot for you to win. If a typical, run-of-the-mill slot has an RTP of 96%, it means that for every $1 you bet, 4¢ is going into the casino’s pocket as pure profit. The other 96¢ goes into a theoretical pot for all players to win. The higher the RTP rate, the fairer the game.
We should also touch on volatility. Slots can be low volatile, highly volatile, or somewhere in the middle. Low volatility slots pay regularly, albeit the wins are small. Highly volatile titles churn out the big bucks but do so much more infrequently. This, too, can impact how likely you are to win when playing casino games like slots.
What Is House Edge
As mentioned when we discussed casino probability above, the RTP rate is the bit of each bet the casino makes available for winning. The other bit, the pure profit, is known as house edge.
House edge is the slant towards the casino, the odds in its favor, or the house’s advantage if you will. In most slot machines, we’d expect this to hover around the 4 to 5% mark. In table games, though, the house edge is often much lower, at around 3% or less. Various versions will see you face different house edges. For instance, American Roulette has a house edge of 5.25%, which drops to 2.7% in European Roulette. However, if you opt to play French Roulette, the house edge is just 1.35% because of special rules, such as La Partage and En Prison.
Mathematical Models in Gambling
As touched on, to calculate probability, you need to divide the number of winning outcomes by the number of possible outcomes. Let’s go back to our six-sided dice example. To figure out the probability of this, you must divide the number of favorable outcomes (1) by the number of possible outcomes (6), like so:
1 / 6 = a one-in-six chance.
This initial calculation is expressed as a fraction, or ratio and shown as 1:6. If you wish to convert that into a decimal expression, you should divide the numerator (1) by the denominator (6), like so:
1 / 6 = 0.1666, rounded up to 0.167.
Finally, if you prefer a percentage-based probability expression, you can multiply that decimal by 100. You’ll then move the decimal point over to the right by two and add the percentage sign. For instance:
0.167 x 100 = 16.7%.
Remember, the exact probability of the event occurring (in this case, landing one number out of six on a die) remains the same regardless of the probability expression you prefer to use.
Why Betting Systems Do Not Work at Casinos
You may hear players speak of betting systems. These are designed to see you bet tactically, by raising or lowering your stakes based on whether you won or lost your previous bet. The idea is that when you win, you’ll win back all you’ve lost and make a small profit.
However, systems like Martingale require you to double your bet when you lose. If you go on a lengthy losing streak, you’d likely end up bankrupt before you win. Therefore, we do not recommend them. Instead, it is better to deploy genuine strategies, such as Basic Strategy. These charts give you a rough idea of what the best move to make is (in card games) based on what’s on the table.
They cannot guarantee success either, but they will help you become a better player and marginally increase your winning odds if you’re a newbie.
Examples of Customer Mistakes While Playing
Players make all sorts of mistakes when gambling, and that’s fine. However, the longer you spend betting, the more you want to hone your skills and improve your game. Doing so will see you increase your odds of success. Here are a few classic mistakes players make when gambling:
- Putting all their faith into erroneous betting systems like Martingale.
- Not understanding probability and their odds of success.
- Always betting on the option that offers the biggest prize without realizing that it offers the least chance of success.
- Choosing slots based on design instead of RTP.
- Not properly understanding volatility and how it impacts your winnings.
- Failing to explore options to lower the house edge in games.
- Not understanding the side bets that can have huge house edges and drastically lower your odds of success.