To wager and win at casinos or bookmakers, it is not necessary to be a genius or mathematical whiz. Many who wager simply bet on hunches and trust their luck, often with excellent results. However, for anyone who wants to be successful at gambling by consistently winning, online or off, having a clear understanding of betting odds is of critical importance.

Odds are nothing more than numbers used to indicate the likelihood that an event will happen or not. For example, when a coin is flipped, it might come up either heads or tails. For someone who believes the result of the next toss will be tails, there is just one way to succeed (win) and one way to fail (lose). Winning or losing is equally likely so the odds are said to be 1-to-1. Other ways of saying this are “the odds are even,” “even odds” or simply “evens.”

There are many ways of expressing odds in writing. They can take the form of a fraction, a ratio, a percentage or a decimal. For the coin flip, there are two possible outcomes, tails being one of them. Tails should come up one out of every two tosses, or ½, or 1:2, or 50% or 0.5. All of these different modes of expression mean the same thing.

In much the same way, when a six-side die is thrown, it might land with any of its six sides appearing face up. For someone who believes the result of the next toss will be a six, for example, there is only one way to succeed (win), while there are five ways to fail (lose). This situation can be expressed as a probability of one out of six, or 1/6, or 1:6, or 16.7% or 0.167.

Whether the event is a coin flip or the roll of a die, the numbers will indicate exactly how likely it is that a given outcome will occur. These are often referred to as “true odds.” When betting, however, the odds that are offered are rarely true odds. That’s because the casino or bookmaker takes a small percentage of every winning wager as a commission or profit. This is known by many names, such as “house edge,” “vigorish” or “juice.”

In the game of European Roulette, the wheel contains 37 numbered slots: 18 coloured black, 18 coloured red and one coloured green—the zero. For someone who believes the result of the next spin will be Black, the casino will pay even money (1-to-1) every time a Black number comes up. However, the true odds are not really 1-to-1. Only 18 of the 37 numbers on the European Roulette wheel are Black. That means there are 18 ways to succeed (win) and 19 ways to fail (lose). The true odds are therefore 19-to-18 against Black—slightly worse than 1-to-1.

This difference between true odds and odds is the house edge. The player is always put at a slight disadvantage that ensures that the casino or bookmaker will earn a profit. In European Roulette, this edge is the result of having the green zero, which is one out of the 37 numbers, or 1/37 or 2.70%. In American Roulette, it is 1/38 or 5.26%.

Other games, such as Blackjack, also have a house edge built in. Depending on the specific house rules, the casino’s advantage at the Blackjack table will vary from 0.15% to 5.48%. By way of comparison, slot machines margins tend to range from 3% to 8%.

For horse races and sports betting, reading the odds can be a little more complicated. Nevertheless, the same principles are used. Bookmakers work with specialists known as “oddsmakers,” who calculate the probability of a runner or team succeeding. The odds that are offered to the public represent their calculations of what the outcome will be, based on true odds by adjusted slightly to include their vigorish.

Perhaps the most common types of odds seen in sports betting are called “fixed odds.” The prices are set before the event begins. They become final as soon as a wager is made, rather like a contract at an agreed amount. Fixed odds are usually expressed as fractions in the U.K., as decimals in continental Europe and as “money lines” in North America.

Fractional odds are the easiest to understand. U.K. bookmakers use them to show how much profit will be earned on a bet. For instance, odds of 3/5 on Arsenal mean the bettor will earn three units on every five units bet if the wager succeeds. A bet of £100 is the same as five units of £20. If the Gunners win, the payout would be three units of £20 or £60 in profit. That the same as receiving £160 in total, including the original stake.

Decimal odds used throughout Europe indicate how much a win will pay in total for each unit wagered. It doesn’t matter whether the unit is £1, £20, £100 or whatever. For example, if Arsenal are favoured to win at 1.60, then a £100 bet will return £160 in total. To calculate the potential of a £15 wager, multiply the bet by 1.60. The expected return is £24 in total.

U.S. money line odds are stated as either positive or negative numbers. Positive money lines refer to underdogs. They indicate how much profit can be won on a stake of 100 units. Negative money lines refer to favourites and show how much has to be wagered in order to win 100 units. In the Arsenal example, a negative money line of -167 would be offered, so a wager of £100, which is roughly equal to 167 units of 60p, would win 100 x 60p = £60.

Thinking back to the initial example of a coin flip, even money bets at true odds would be expressed in the three different systems as follows: fraction = 1/1 (“evens”); decimal = 2.00; and money line = +100. After the bookmaker figures in a commission, the actual odds offered might look like this: fraction = 9/10; decimal = 1.90; and money line = -110.