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Casino Games Probability Explained

Every wager you place has a chance of winning or losing at the casino, making probability one of the most important parts of casino gaming. However, this is usually more complex than the 50/50 odds of a coin toss, due to something called the house edge. We’ll come to that later. For now, here’s a crib sheet of the casino games that offer the highest odds of winning:

• Craps - 49.29% (come or pass bet)
• Roulette - 46.37% (red or black, odd or even)
• Blackjack - 42.22% (beating the dealer)
• Slots - variableDon’t get too attached to these figures just yet. The way you play any game can dramatically alter your odds of success. A single number bet in roulette will win 2.70% of the time in the European game, for instance, while your chances of coming up trumps in a slot game are dependent on its Return to Player (RTP) rate.

Table of Content:

Check out our list of important terminology a little further down this page for more about RTP and other game mechanics.

Basics of Casino Games Probability

Understanding Probability in the Context of Casino Games

Probability is a major arm of mathematics (don’t panic), so there’s a wealth of information available about its inner workings. All you need to know for now is that while the odds are always calculable in casino games, the probability of a win or loss never changes.

Key Probability Terminology

• House edge - the advantage the casino has over the player in all casino games, inclusive of slots, blackjack, and roulette.
• Return to Player (RTP) - a figure, usually expressed as a percentage, that is the sum of money you can expect to have returned from each wager over a set number of plays (usually in the millions). As a guide, an RTP of 97% means that you can expect 0.97 back from each bet of 1.00.
• Volatility - describes how often, and how much, a slot machine will pay out based on a set number of example plays.

Random Number Generators (RNGs)

Role of RNGs in Casino Games

In online casino games, luck is guided by random number generators (RNGs). These are mathematical algorithms that decide the outcome of a dice roll, a drawn card, or the spin of a slot machine, among other things.

Ensuring Fairness and Randomness

The goal of an RNG application is to ensure unpredictability and, therefore, fairness when you play a casino game. This is usually achieved by collecting random information, “entropy”, to convert into a seed value, such as a computer’s heat signature or actions taken by the player.

Seed values, a sequence of numbers, can usually be retrieved after a game ends so that the fairness of its results can be checked. RNG systems are checked by testing agencies unaffiliated with the casino before use.

Slot Machines

Probability Mechanics in Slot Games

RTP, paylines, bonus features, and symbol types can all influence a player’s odds of winning in a modern slot machine. Like all casino games, the outcome of each spin is determined by RNG. This chooses the pictures that appear on each reel and, therefore, the number of winning combinations that pop up each turn.

Impact of Paylines on Probability

Paylines or winlines are invisible lines that crisscross the reels in slot games. When you get a win, you can guarantee that all of the symbols involved will be sat on one of these lines.

Only one to three paylines were used in the early days of slots, back when they gave out chewing gum as prizes. Paylines at this point were often set horizontally across the middle three positions. Today, there can be thousands upon thousands of paylines to win upon, as is the case in Megaways-branded games. Big Time Gaming’s iconic reel modifier adds 248,832 winlines.

Paylines do not affect volatility (definition above), but a greater number of paylines does increase hit frequency, i.e. how often you get a winning combination. There are simply more ways to win with more paylines.

Blackjack

Probability of Card Combinations

A raft of different outcomes can be calculated in blackjack, such as the card dealt to the player and the dealer, the chance of going bust, or reaching a total of 21, as well as the success rate of actions like hitting, standing, and splitting. As a starter, your chances of getting blackjack sit at 1 in 20 hands or 4.83%. Oddly enough, this figure changes by less than 1% even when a hundred decks are used to play the game. The standard is either one, four, or eight.

Strategic Decision Making Based on Probability

What makes blackjack special at the casino is the opportunity to use blackjack basic strategy to reduce the house edge down to 0.5%. That’s not to say that there’s a way of cheating the dealer. You’re only optimizing your chances within the rules set by the house. Let’s refer back to the actions we mentioned previously, namely, hitting, standing, and splitting.

Basic strategy charts offer directions for what to do in certain scenarios. For instance, you should always:

• Stand on any number greater than 17.
• Always split 8s and aces, but never split 10s.
• Double on 11s.Just to reiterate, there’s no way to predict or force certain card combinations in blackjack. Basic strategy is a bit like knowing when to pass or shoot in soccer and hockey. It’s the best idea at the time, but there’s no guarantee it’ll come off in your favour.

Roulette

Probability of Winning on Different Bets

As you can imagine, the likelihood of a win in roulette decreases with the number of potential outcomes. So, the single number bet has odds of just under 3% while positions that cover half the wheel, like red/black and odd/even, have a near-50% chance to produce a win. In practice, the house edge reduces this by a few percent, as we hinted at earlier on.

Understanding the Zero in Roulette Probability

The variant of roulette you play affects your chances of winning. The difference between European and American roulette wheels is just a single number (American roulette has one more, double-zero) but this reduces the success rate of a red/black, even/odd bet by 1.28%.

Betting on zero is a rare proposition in roulette, perhaps through superstition but more likely because it’s a single-number wager with a low chance of success.

House Edge

Definition and Significance

A running theme in this guide so far is that odds in casino gaming are influenced by the house edge. This reflects the money that the casino expects to receive from the game. The house edge is a certainty both online and offline but some games, like blackjack and roulette, offer the player a nearly even chance of winning with a well-rehearsed strategy.

Calculating House Advantage in Various Casino Games

The house edge differs from one game type to the next but is roughly consistent from casino to casino. It’s calculated by finding out the expected value of each possible outcome (like a bet on red) and then adding them all together. Once there, simply subtract that figure from 1 and turn it into a percentage.

Probability Strategies for Players

Bankroll Management

Care over your bankroll is one of the easiest ways to ensure that casino games remain a fulfilling experience. Many players create or borrow strategies to keep their bankroll in check. Everybody has their budgets for roulette, slots, and so forth, but the main thing to keep in mind is that you should always only bet within your means - and, as the saying goes, “when the fun stops, stop”.

Game Selection Based on Probability

The casino game that offers you the best odds will depend on several factors, including many we've already talked about such as the RTP, bet size, the variation of the roulette wheel, and your appreciation of basic strategy. In terms of pure odds, though, table games are usually friendlier to the player than slots, which can have highly variable probabilities.

Casino Gambling Probability FAQs

What casino games are based on probability?

All games that have action! In other words, slots, blackjack, poker, roulette, and plenty of other experiences are all at the mercy of probability.

What is the probability of winning in a casino?

This varies from game to game. Your chances of beating the dealer in blackjack are 42.22%, for instance.

What is statistically the best gambling game?

Craps, with a come or pass bet, provides an almost even chance of winning.

Does gambling involve probability?

Yes. Everything from a dice roll to the turn of a card involves probability.

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