Casino Table Game Math Explained

The technical details of casino games such as craps, baccarat, blackjack, poker, and roulette include math. And knowing the math concepts relevant to these table games will help you set your expectations correctly. They give insight into how the house maintains its advantage and how every decision you make can affect the outcome of gameplay.

To help build you into a more grounded player, this article explains the math details you need to know about casino table games. We will also discuss why betting systems fail and how casinos manage risk. Let’s get started.

All Casino Table Game Math Concepts

Below are the casino table game math concepts you should know:

House Edge

House edge is the pre-determined mathematical advantage a casino game holds over the player in the long run. It can be expressed two equivalent ways: as the ratio of the player's expected loss to their original bet, or as 100% minus the game's Return to Player (RTP). For example, if a slot has a 95% RTP, its house edge is 5%.

Example: American roulette has a house edge of 5.26%. What this means for your wager is that if you bet $100, the house gets $5.26 on average in the long run.

However, the house edge of table games often varies by the type of wager placed. Baccarat, for example, has a 1.06% house edge on the banker's bet and 1.24% on the player's bet.

Knowing a table game's house edge is crucial for bankroll management. The table below shows the house edge of popular table games.

Table Game	House Edge	Note
Blackjack	0.5%	With basic strategy on a 3:2 payout table. Avoid 6:5 tables, they raise the edge to ~1.9%
Baccarat	1.06% and 1.24%	Your choice of wager determines which applies (player or banker’s bet)
European Roulette	2.70%	Single zero wheel
American Roulette	5.26%	Wheel with 0 and 00 pockets
Craps	0% to over 16%	From 0% on the Free Odds Bet to 16.67% on the Any Seven proposition

Variance

Variance, also called volatility, is a statistical measure that describes the frequency and size of wins you should expect from a specific wager. It captures how much the actual outcome of a bet can deviate from the expected average. It is one of the factors responsible for the unpredictable nature of table games.

Variance can be low, medium, or high. For example, even-money bets in roulette have low variance, which means they offer frequent but small wins. Conversely, a straight-up bet has high variance, meaning you will receive a large payout, but the frequency of winning is low. You might have to endure a long spell of losses before securing a payout when the variance is high.

House Edge vs Variance

House edge indicates the mathematical advantage the casino has over you in the long term. Variance, on the other hand, highlights the swings, i.e., deviations from expected outcomes, that can occur during gameplay. House edge impact is slow, usually over a long period of play. But variance can be immediate, a moment of huge win or a moment of huge loss.

Expected Value

Expected Value (EV) is a fundamental probability concept that applies to every casino wager. It is defined as the average outcome a player can expect per bet, assuming the bet is placed many times.

A positive EV indicates a long-term profit, while a negative EV signals a long-term loss. In the casino, virtually every standard bet has a negative EV, that's how the house edge works in practice. For example, a $10 even-money bet on red in European Roulette has an EV of -$0.27 per spin (reflecting the 2.70% house edge), meaning the average expected loss is 27 cents per $10 wagered.

Probability and Odds

While often used interchangeably, probability and odds have different meanings in casino table games. Probability is the number of favourable outcomes divided by the total number of possible outcomes, expressed as a percentage or decimal between 0 and 1. Odds express the ratio of unfavourable outcomes to favourable outcomes (this is called "odds against").

For example, the probability of having a royal flush is 0.000154%, while the odds are 649,739:1.

Why Poker is Different

Poker is a player-vs-player game where skill plays a crucial role. As a result, the concept of house edge does not apply, the casino has no built-in mathematical advantage over you. Instead, the casino charges a small fee called the "rake" (typically 2.5 - 10% of each pot, capped at a maximum amount) to facilitate the game. Variance, however, very much applies to poker, in fact, it is one of the most important concepts in serious poker play, which is why bankroll management is essential for poker players.

Furthermore, poker is a game of incomplete information. Probability and odds change as you progress through the stages of gameplay (flop, turn, and river).

Why Betting Systems Fail

Players often wager on table games such as roulette using betting systems such as Martingale, Fibonacci, D'Alembert, and flat betting. However, betting systems often fail because players try to use past outcomes to predict future results, which are independent events.

A quick example is betting on black in roulette, thinking it is due because the last five spin results were red. This is termed the Gambler's Fallacy. The outcome of a gameplay session in table games with an element of chance, e.g., roulette or craps, is independent each time the wheel is spun or the dice are rolled.

Additionally, betting systems can be affected by variance and table limits. Many casinos set a maximum and minimum wagering limit for their table games. So, using Martingale, which suggests doubling your bet each time you lose, will not help you recover all your losses before you hit the table limit.

The ultimate truth is, no betting system has been proven to work.

Risk Management from a Casino Perspective

Table games attract players of all kinds. While casinos love to host high rollers and whales, they also weigh their risk. A single win can disrupt their operations.

Casinos manage risk relying on the volatility of table games and the Law of Large Numbers. A high roller might win a few million on bets with high variance. However, casinos know that, over hundreds of thousands of total bets on that table, revenue will stabilize at the set house edge.

To manage risk under the Law of Large Numbers, casinos try to get as many players as possible to play table games. With a massive volume of bets, the impact of a single lucky player winning a large sum is mitigated by the thousands or millions of other players' lost wagers.

Another method casinos use to manage risk is by fixing minimum and maximum table wager limits.

However, this isn't to say that gambling establishments look forward to players losing. No, they want players to have fun while looking out for themselves, because running a casino is an expensive business.

Final Thoughts

As you set out to play casino table games, remember the math we have explained, from house edge to probability and odds. They will come in handy when you want to make some gameplay decisions, including which game to play and which wager to place. Good luck and play responsibly!

FAQ

What is the house edge in casino games?
The house edge is the percentage of each bet that the casino expects to keep over time. It represents the casino’s built-in advantage. For example, a 5% house edge means you will lose an average of $5 for every $100 wagered in the long run.

What is the difference between house edge and RTP?
House edge and RTP (Return to Player) are opposites. RTP shows how much money a game pays back to players, while house edge shows how much the casino keeps. For example, a game with 95% RTP has a 5% house edge.

What is variance in gambling?
Variance, or volatility, measures how often and how much you can expect to win. Low variance means frequent small wins, while high variance means rare but larger payouts. It explains why results can vary widely in the short term.

What is expected value (EV) in casino games?
Expected value (EV) is the average amount you can expect to win or lose per bet over time. In most casino games, EV is negative, meaning players are expected to lose money in the long run due to the house edge.

Can you beat the house edge?
No, the house edge cannot be beaten in the long run in most casino games. It guarantees the casino profits over time. The only exceptions are skill-based situations like blackjack with perfect strategy or poker, where players compete against each other.

Why do betting systems fail in casino games?
Betting systems fail because casino games are based on independent events. Past results do not influence future outcomes. Systems like Martingale also fail due to table limits and bankroll constraints, preventing players from recovering losses consistently.

What is the Gambler’s Fallacy?
The Gambler’s Fallacy is the belief that past outcomes affect future results. For example, thinking a roulette spin will land on black because red has appeared several times. In reality, each outcome is independent and has the same probability.

What casino game has the lowest house edge?
Blackjack typically has the lowest house edge, around 0.5%, when played with basic strategy. Baccarat banker bets and European roulette also have relatively low house edges compared to other casino table games.

Why is poker different from other casino games?
Poker is different because players compete against each other instead of the casino. The casino earns money through a rake, not a house edge. Skill, strategy, and decision-making play a major role in determining long-term results.

How do casinos manage risk?
Casinos manage risk using the Law of Large Numbers. While individual players can win big, a high volume of bets ensures consistent profits over time. They also set minimum and maximum betting limits to control exposure.