What are the odds of a bet?
Odds typically refer to the ratio between the probability of one event happening versus another where the two events are mutually exclusive and exhaust all possible outcomes. In simple games with dice it could be the odds of rolling a sum of five with two six-sided dice versus not rolling it. The odds of that happening versus not happening are one to nine. Alternatively, we have nine to one odds for not rolling a sum of five.
In the context of betting odds are directly linked to the implied probability of the outcome of interest. It could be the outcome of a sports game or match, a political race, or any number of things if expressed in terms of win/lose or win/lose/tie. There are different ways of giving odds in such a context and they are named mostly based on the geographical location where their use is most typical.
American odds
These are also known as 'moneyline' odds and span the range from minus infinity to -100, and from +100 to plus infinity. U.S. odds in the negative half of this range represent the amount one needs to stake to win $100 while odds in the positive half represent the amount one stands to win on every $100 staked. This means negative odds are given to the event which is considered more probable whereas positive odds are given to the event considered less probable. In the case of sports betting, negative odds are given to the favorite to win and positive odds are assigned to the underdog.
For a working example, consider an NFL game where team A is given odds of -120 and team B is given odds of 200. This means a bookmaker beliefs, typically based on data, that team A has much greater chance of winning compared to team B. That is expressed in the odds which result in that one would need to bet $120 to have the possibility to win $100 on team A whereas one need only bet $50 on team B to have the possibility to win the same $100 (200 / 100 * $100 = $50).
If you are reading this from the USA and are considering placing bets, then you need to consider your local legislation regarding gambling as it is still illegal in a number of US states as of 2024 (see reference [1] below for the current status of your state).
Fractional odds
In fractional form, odds of one out of five would be represented as the fraction "5/1", read "five to one". These are called "British" or U.K. odds and can be more intuitive than American or decimal odds since they tell you how much one stands to gain for a given amount bet.
For example, with 5/1 ("five to one") odds one stands to gain 5 dollars for each dollar staked, and the payout is for 10 dollars for each dollar staked. 12/5 ("twelve to five") odds mean one wins 12 dollars for every 5 dollars staked, and a payout is 12 + 5 = 17 dollars for every five dollars staked. Our odds calculator outputs the odds in all four types, as well as the payout and winnings.
Decimal odds
Known as "European" odds and "digital" odds, these are used across Europe, Canada, Australia and New Zealand. Their main advantage is that one can instantly spot who is the favorite and who is the underdog – the former will have the lowest odds and the latter – the highest. Typically written with a precision of three digits after the decimal point, decimal odds show the expected payout for every dollar wagered.
As an example, odds of 1.500 mean that one stands to get a payout of $1.5 for every $1 bet, for a win of $0.5 on every dollar. Odds of 2.000 would result in a payout of $2 for every $1 bet, or will double your bet in case of a favorable outcome.
Implied odds
Implied odds are odds transformed into a probability, expressed as a percentage, a.k.a. implied probability. It is possibly the most intuitive of all the types of odds when one is considering the risk and reward potential of a bet and is one of the outputs of our bet odds calculator.
For example, odds of +200 (American) equal 2/1 (Fractional) equal 3.000 (Decimal) and result in implied probability of 33.33(3)%, meaning that the odds setter thinks the probability of the event the odds apply to has 33.33% probability of occuring versus the 66.67% for the alternative.
How to use implied probability in betting
While we do not encourage or condone betting, if you've decided to engage in the practice, then it is best that you understand the concept of implied probability a.k.a. implied odds which are part of the output of this betting calculator. First, it is a probability that an event would happen expressed as a percentage. For example, a probability of 51% means there is slightly higher than coin-flip chance of the event happening. Second, it is 'implied', meaning that this is the probability implied by the odds given. In other words, this is the probability that you would be giving if you were setting the odds, but more commonly it is the probability the other party is implying through the odds they give you.
How can implied probability be used then? Ideally, before you enter into a wager of any kind you would want to assign a probability to the event being bet on, e.g. the outcome of a political election, of a sports game or match as in sports betting. This probability is often dubbed 'true odds' or 'your odds'. While arriving at your true odds can be very complicated, in any scenario you want the implied odds to be lower than the true odds. This positive difference between the true odds and the implied odds is your edge in a bet, and one should only take a bet if they have an edge. In other words, if they believe the other party's implied probability is underestimating the true probability of the event happening.
Odds calculations in science
Interestingly, some of the first works in odds and statistical probabilities which later became foundational for the discipline of statistics originated in games of chance and optimal betting problems by the likes of Girolamo Cardano, Luca Pacioli, Blaise Pascal, Pierre de Fermat, Christian Huygens, Jakob Bernoulli, and Pierre Simon de Laplace [2]. They often dealt with dice games, but also various others.
Nowadays odds are used in various ways in medicine and other sciences when presenting statistical results. For example, the often used 'Number Needed to Threat' (NNT) statistic is essentially a representation of the odds that a medical treatment will work on a given population. Likewise, odds ratios are often the statistic of choice when comparing the outcomes of an exposed group or treatment group versus a control group in an experiment. It is prevalent in epidemiology and environmental science.
People often have issues understanding different types of odds, so converting from a probability to decimal or fractianal odds and presenting all of them may be helpful in communicating findings. Likewise for sports betting it can be helpful to convert american odds to decimal odds for example.