Betting and gambling are activities that have been enjoyed for centuries, and while luck plays a major role, having a solid understanding of the math behind betting odds can significantly enhance your chances of success. Whether you’re placing a bet at a casino, wagering on sports, or trying your luck with the lottery, the odds determine your potential winnings or losses, as they reflect the probability of an event occurring.

Grasping the math behind odds allows bettors to evaluate whether a wager is worth taking. In this article, we will explain the different types of odds, how to convert them into implied probabilities, and how to use this knowledge to make smarter betting decisions.

1. Different Types of Betting Odds

There are three main formats used to express betting odds: fractional odds, decimal odds, and moneyline odds (also referred to as American odds). These formats are simply various ways to represent the same concept of probability and payout. Once you understand each type of odds, you’ll find that the underlying concept is quite straightforward.

Fractional Odds

Fractional odds, also known as traditional or British odds, are written as a fraction (e.g., 6/1 or 5/2). The numerator (first number) represents the amount you could win for every unit of currency you bet, while the denominator (second number) shows how much you need to stake in order to win that amount.

For example, with 6/1 odds, you stand to win $6 for every $1 wagered if your bet is successful. If you bet $10 at 6/1 odds, your profit would be $60, in addition to getting your $10 stake back.

Decimal Odds

Decimal odds are commonly used in Europe, Canada, and Australia. They show the total payout (including your initial stake) for every $1 bet. The payout is calculated by multiplying the stake by the decimal value.

For example, with 2.50 decimal odds, you would receive $2.50 for every $1 bet, meaning a $10 wager would give you a total payout of $25, including your original $10 stake.

Moneyline Odds

Moneyline odds are primarily used in the United States and are presented with a plus (+) or minus (-) sign. Positive odds indicate how much profit you would make on a $100 bet, while negative odds show how much you need to wager to earn a $100 profit.

For example, +200 moneyline odds mean that for every $100 you bet, you would win $200. On the other hand, -150 odds mean you need to bet $150 in order to win $100. If successful, a $150 bet at -150 odds would yield a $100 profit.

2. Converting Odds to Implied Probabilities

While odds are useful for determining potential payouts, converting them into implied probabilities is even more valuable. Implied probability shows the likelihood of an event happening, according to the odds. Knowing the implied probability helps you assess whether a bet offers good value.

Here’s how to convert the different types of odds into implied probabilities:

Fractional Odds

To convert fractional odds to implied probability, use this formula:

Implied Probability=DenominatorDenominator+Numerator×100\text{Implied Probability} = \frac{\text{Denominator}}{\text{Denominator} + \text{Numerator}} \times 100Implied Probability=Denominator+NumeratorDenominator​×100

For example, with 8/13 fractional odds (for Manchester City to win), the implied probability is:

Implied Probability=1313+8×100=61.5%\text{Implied Probability} = \frac{13}{13 + 8} \times 100 = 61.5\%Implied Probability=13+813​×100=61.5%

This means the bookmaker is assigning a 61.5% chance of Manchester City winning.

Decimal Odds

To convert decimal odds into implied probability, use this formula:

Implied Probability=1Decimal Odds×100\text{Implied Probability} = \frac{1}{\text{Decimal Odds}} \times 100Implied Probability=Decimal Odds1​×100

For example, if the decimal odds are 2.20 (for a candidate to win an election), the implied probability would be:

Implied Probability=12.20×100=45.45%\text{Implied Probability} = \frac{1}{2.20} \times 100 = 45.45\%Implied Probability=2.201​×100=45.45%

This means the bookmaker believes the candidate has a 45.45% chance of winning.

Moneyline Odds

For positive moneyline odds (e.g., +200), use this formula:

Implied Probability=100Moneyline Odds+100×100\text{Implied Probability} = \frac{100}{\text{Moneyline Odds} + 100} \times 100Implied Probability=Moneyline Odds+100100​×100

For negative moneyline odds (e.g., -150), use this formula:

Implied Probability=−Moneyline OddsMoneyline Odds−100×100\text{Implied Probability} = \frac{-\text{Moneyline Odds}}{\text{Moneyline Odds} – 100} \times 100Implied Probability=Moneyline Odds−100−Moneyline Odds​×100

For example, with -250 moneyline odds for Australia to win the ICC Cricket World Cup:

Implied Probability=250250+100×100=71.43%\text{Implied Probability} = \frac{250}{250 + 100} \times 100 = 71.43\%Implied Probability=250+100250​×100=71.43%

3. Why Bookmaker Odds Are Not “Fair”

It’s crucial to understand that the odds set by bookmakers don’t reflect the true probability of an event occurring. This is because bookmakers build a profit margin into the odds, ensuring they make money in the long run. This margin is known as the overround or vig (short for vigorish).

For example, suppose Australia’s odds to win the World Cup are -250, and New Zealand’s odds are +200. Using the formulas above, we can calculate the implied probabilities:

• Australia: 71.43%
• New Zealand: 33.33%

When we add these probabilities together, we get 104.76%, which is greater than 100%. This overage (4.76%) represents the bookmaker’s edge. In this case, if you were to bet on both teams, you would be risking $104.76 to potentially win $100.

The bookmaker’s edge ensures they make a profit no matter which outcome occurs. Understanding this overround helps bettors assess whether a bet is truly valuable.

4. Implied Probability and Its Role in Betting

Implied probability is a critical concept when evaluating betting opportunities. If the actual probability of an event occurring is greater than the implied probability suggested by the odds, the bet may be a good value.

For instance, if a bookmaker offers 6/1 odds (implied probability of 16.67%) for a soccer team to win, but you believe the team has a 20% chance of winning, you’ve found a value bet. The bookmaker is undervaluing the event, giving you a higher potential return on your investment.

However, it’s important to remember that bookmakers use advanced technology, data, and market expertise to set odds, so identifying value bets can be difficult. Experienced bettors often search for discrepancies between the bookmaker’s implied probability and their own evaluation of the odds.

5. House Edge in Gambling

The house edge is the built-in advantage that casinos have over players, ensuring the casino profits over time. The house edge varies between different games. For example, blackjack has one of the lowest house edges, typically ranging between 0.40% and 1%, depending on the rules and the player’s skill level. On the other hand, games like slots and Keno tend to have much higher house edges, sometimes exceeding 10%.

Casinos also use psychological tactics, such as lighting, music, and alcohol, to keep players gambling. Novice gamblers may not fully understand the house edge and can easily be influenced by these tactics.

6. The Difference Between Odds and Probability in Casino Games

While both odds and probability express the likelihood of an event, they are used differently in gambling. Probability is the percentage chance of an event occurring, while odds represent the ratio of the probability of an event happening to the probability of it not happening.

For example, in a coin toss, the probability of landing heads is 50%, and the odds are 1/1 (even money). In contrast, in a roulette game, the odds are much higher due to the lower probability of landing on a specific number.

7. Casino Games with the Best and Worst Odds

To improve your chances of winning, it’s important to choose games with favorable odds. As noted earlier, blackjack is one of the best games for players, provided they play strategically. Other games with relatively low house edges include baccarat, craps, and some forms of video poker.

However, games like Keno, slot machines, and the Big Six Wheel typically have the worst odds for players, meaning they offer much lower chances of winning. While these games can be entertaining, they generally provide worse odds compared to skill-based games like blackjack.

Conclusion

Betting and gambling are about managing risk and probability. While luck plays a role, understanding the math behind betting odds and implied probabilities is essential for making more informed decisions. Bookmakers always include a profit margin in their odds, so the actual probability of an event happening is often lower than what the odds suggest.

By mastering how to convert odds into probabilities, recognizing value bets, and understanding the house edge, you can make more educated betting decisions. However, it’s important to approach gambling responsibly, keeping in mind that it should be viewed as entertainment rather than a guaranteed way to make money.