Understanding the Math of Casino Odds

It’s Impossible to Win at Casino Games. But it’s Possible to Understand Casino Odds Math and, in So Doing, Have a Good Chance of Winning. Let Me Give You Some Basic Mathematical Properties that Will Help You Understand the Risk Involved and Make Better Bets.

Probability and odds are the mathematical descriptions of what odds (favourable outcomes versus unfavourable outcomes) will happen over the long run in gambling games.


Probability, expressed as either a percentage or odds in fractional, decimal or American moneyline formats, is a mathematical concept used to compare your chances of winning or losing when playing any type of game. Astute gamblers will often perform a trigonometry-based calculation of probability in order to evaluate risk.

But if you understand casino odds and probability, it can certainly help determine which games you might want to play and be successful. Whether you are a novice player or potential pro – you will improve your gambling skills and prowess.

House edge runs the gamut; blackjack, video poker and baccarat have lower house edges than, say, roulette and keno (on which each spin is independent of the last).


Odds are an integral part of casino gambling. Odds represent the likelihood that an event will occur during the course of a game of chance at a casino. Odds can be phrased in many different ways. Understanding odds and how to correctly use them can help gamblers make smart betting decisions and potentially enjoy their gambling experience more.

For example, when you flip a coin, the probability of it landing head or tail is equal (50/50), although the house edge is 10%, meaning that the house can be expected to gain more money from playing than it hands out to players.

Casino games employ both fractional and decimal odds in the calculation of their odds. Fractional odds, ie, 6/1, are usually written as a fraction of a number while decimal odds, ie, 5/2, are also shown as a ratio of a number or as an implied probability percentage.

House edge

This is known as the ‘House Edge’, the percentage long-term built-in advantage enjoyed by gamblers over players and built into all casino games to make sure that the house always comes out ahead come hell or high water, win or lose over the long haul. The more you know about your house edge and where it lies with respect to the game or games you’ve chosen to play, the higher your odds of winning as a gambler.

And, the house edge varies across games. In general, the simplest games (slots, keno) have the highest house edges while the higher bet games (blackjack, poker, Roulette) have lower house edges. However, as a corollary, casino profits are not hurt by lower house edge games that give the player better odds. It simply encourages people to play more often. A player who is aware of his house edges can pick his games that give the most fun for his time while giving him the best possible odds.

Bonus rounds

Bonus rounds in casino games – those little sections added on to most types of games that supply some sort of added entertainment value for the player amid one course of gameplay – are a distinct part of game experience that offer an extra opportunity for the player to gain more prizes, each with it’s own twist on theme games (be it free spins, odds multipliers or multiplier prizes) that are only to enhance the odds of a big payout for the player.

Each round, skilled gamblers use mathematical properties – notions such as the probability, odds and expected value – to measure how much risk they take on. They use these indicators as a numerical way of assessing risk, and can more or less confidently conclude whether it is worth it to place a bet.

But beginners tend not to really grasp cognitive accounting (too, too small wins followed by too, too large losses); they don’t manage to factor in the large ratio between short-term standard deviation and expected loss, and they don’t keep a real-time ledger of frequent small wins that will be averaged out in due course by occasional larger-than-expected and, hence, devastating losses.

Game variations

Although most casino games appear to possess mysterious odds in favor of the house, the odds can be calculated mathematically. This article examines many casino games and sucker bets in regards to their odds, chances of winning or losing, and the expected winnings (EV) as an indicator as to how volatile the game is, technically called standard deviation.

EV of a bet is the probability of winning multiplied by how much you win in that event, plus your losses and your odds of going home with nothing; something that all gamblers are all too keen to ensure against by using the simplest of strategies, such as counting cards in Blackjack. To make that work, though, the players have to be able to spend a long time figuring out quite small decisions; something, I admit, that might be hard to do but, if done, will absolutely help them win over time.

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