The Mathematics of Casino Games: Complete House Edge Reference\n\n## Introduction\n\nThe vibrant lights, the thrilling sounds, and the promise of a life-changing win—casino games have an undeniable allure. From the spin of the roulette wheel to the flip of a card, players are drawn to the excitement and the possibility of beating the house. However, beneath the surface of every game lies a fundamental mathematical principle that ensures the casino always has an advantage: the house edge.\n\nThis article delves into the mathematics of casino games, providing a comprehensive reference to the house edge across a wide variety of popular games. Understanding this concept is the first and most crucial step for any aspiring gambler looking to make informed decisions and manage their bankroll effectively. While you may not be able to overcome the house edge, knowing how it works can help you choose the right games and strategies to maximize your chances of winning in the short term.\n\n## What is the House Edge?\n\nThe house edge is a term used to describe the mathematical advantage that a casino has over a player in a particular game. It is most commonly expressed as a percentage of the player's original bet. For example, if a game has a house edge of 2%, it means that for every $100 wagered, the casino expects to make a profit of $2 in the long run. It's important to understand that this is a theoretical, long-term calculation. In the short term, anything can happen, and players can and do win.\n\nAs the Wizard of Odds explains, "The house edge is defined as the ratio of the average loss to the initial bet." [1] This is a crucial distinction, as some games allow players to increase their wagers during play. In such cases, the house edge is still calculated based on the initial bet, not the total amount wagered.\n\nIt is also important not to confuse the house edge with the hold percentage. The hold percentage is the ratio of chips the casino keeps to the total chips sold at a table during a specific period, like a shift. This figure is influenced by how long players stay at the table and the circulation of money, whereas the house edge is a purely mathematical calculation based on the rules of the game.\n\n## Why the House Always Wins (in the Long Run)\n\nThe persistence of the house edge over millions of bets is the reason why casinos are profitable businesses. While individual players can walk away with winnings, the law of large numbers ensures that the casino will eventually realize its statistical advantage.\n\nMany players misunderstand the true impact of the house edge on their bankroll. They might think that a 5% house edge on a $100 bankroll means they'll only lose $5. However, the house edge applies to the total amount wagered. As Investopedia illustrates, if a player makes $5 bets on a roulette wheel that spins 50 times an hour, they are wagering $250 per hour. Over four hours, that's $1,000 in total wagers. With a 5.26% house edge in American Roulette, the player's expected loss is not $5, but $52.60. [2]\n\nCasinos employ various tactics to encourage longer play, such as offering complimentary drinks and creating an environment devoid of clocks and windows. The longer a player stays and gambles, the more likely their results are to align with the house edge, resulting in a loss for the player and a profit for the casino.\n\n## House Edge Reference by Game\n\nThe house edge can vary dramatically from one game to another, and even between different bets within the same game. The following tables provide a comprehensive reference for the house edge of many popular casino games, based on data from the Wizard of Odds. [1]\n\n### Table Games\n\n| Game | Bet/Rules | House Edge (%) |\n| :--- | :--- | :--- |\n| Baccarat | Banker | 1.06% |\n| | Player | 1.24% |\n| | Tie | 14.36% |\n| Blackjack | Liberal Vegas Rules | 0.28% |\n| Craps | Pass/Come | 1.41% |\n| | Don't Pass/Don't Come | 1.36% |\n| | Place 6, 8 | 1.52% |\n| | Place 5, 9 | 4.00% |\n| | Place 4, 10 | 6.67% |\n| | Hard 4, 10 | 11.11% |\n| | Any Seven | 16.67% |\n| Roulette | Single Zero (European) | 2.70% |\n| | Double Zero (American) | 5.26% |\n| Pai Gow Poker | | 1.46% |\n| Three Card Poker | Ante & Play | 3.37% |\n| | Pairplus | 7.28% |\n| Caribbean Stud Poker | | 5.22% |\n| Let It Ride | | 3.51% |\n| Casino War | Go to war on ties | 2.88% |\n\n### Other Games\n\n| Game | Bet/Rules | House Edge (%) |\n| :--- | :--- | :--- |\n| Keno | | 25% - 29% |\n| Sic-Bo | | 2.78% - 33.33% |\n| Slot Machines | | 2% - 15% |\n| Video Poker | Jacks or Better (Full Pay) | 0.46% |\n\n## Games with the Lowest House Edge\n\nFor the savvy gambler, choosing games with a low house edge is paramount. These games offer the best chances of winning and can significantly stretch a player's bankroll.\n\nBlackjack stands out as one of the best games for players, with a house edge that can be as low as 0.28% with liberal rules and optimal strategy. The low house edge is due to the element of skill involved. Players who learn and apply basic strategy—a mathematically proven set of decisions for every possible hand—can dramatically reduce the casino's advantage. For those serious about their game, a Bankroll Tracker [blocked] can be an invaluable tool for managing funds and tracking performance.\n\nBaccarat is another excellent choice, with the "Banker" bet having a house edge of just 1.06%. The game is simple to play and requires no complex strategy, making it a favorite among high rollers and casual players alike.\n\nVideo Poker, specifically the "Jacks or Better" full-pay variant, offers a remarkably low house edge of 0.46% when played with perfect strategy. An Odds Calculator [blocked] can help players understand the probabilities of making different hands.\n\n## Games with the Highest House Edge\n\nOn the other end of the spectrum are games with a high house edge, which should generally be avoided by serious gamblers. These games are designed to be highly profitable for the casino.\n\nKeno is notorious for its high house edge, which can range from 25% to 29%. The odds of hitting a large number of spots are astronomically low, making it a game of pure chance with very poor returns for the player.\n\nSlot Machines are another category of games with a wide and often opaque house edge, typically ranging from 2% to 15%. While they are incredibly popular due to their simplicity and potential for large jackpots, the odds are heavily stacked in the casino's favor.\n\nSic-Bo offers a variety of bets, some with a reasonable house edge, but many with an extremely high one, reaching up to 33.33% for specific triple bets.\n\n## Conclusion\n\nThe house edge is the mathematical foundation upon which the entire casino industry is built. While it guarantees the casino's long-term profitability, it does not preclude players from winning in the short term. By understanding the concept of the house edge and knowing which games offer the best odds, players can make more informed decisions, manage their expectations, and ultimately have a more enjoyable and potentially profitable gambling experience.\n\nRemember that gambling should always be a form of entertainment, not a way to make money. Always gamble responsibly, set limits, and never bet more than you can afford to lose.\n\n## References\n\n[1] Shackleford, Michael. "House Edge of Casino Games Compared." Wizard of Odds, 19 Dec. 2024, wizardofodds.com/gambling/house-edge/.\n\n[2] Maverick, J.B. "How Casinos Ensure Profit: Understanding the House Edge." Investopedia, 15 Oct. 2025, www.investopedia.com/articles/personal-finance/110415/why-does-house-always-win-look-casino-profitability.asp.\n