# What are betting odds?

In the context of gambling, an odd is a number that that indicates the potential reward of betting in favor of certain event happening. Different formats of odds exist, but the most intuitive one is the decimal format. An odd in the decimal format is equal or higher to 1, and it is the factor by which the original wager must be multiplied to obtain the final total quantity of money the player will obtain if he wins. A brief example will illustrate this:

Suppose there is an event x, and the odds offered are:

x: 1.25, -x: 4

If the player gambles ¤ 100 to x, then, if x happens, he shall obtain the ¤100 of his original wager, plus ¤25, for a grand total of ¤125, because ¤100 · 1.25 = ¤125. If he instead bets ¤100 for -x, then, if x does not happen, he shall get his initial ¤100, plus ¤300, for a grand total of ¤400, for ¤100 · 4 = ¤400.

The odds being x: 1.25, -x: 4 is not something arbitrary. Those two numbers, are the reciprocals of some percentages:

1 / 1.25 = .8 = 80%

1 / 4 = .25 = 25%

Individually, each odd implies a probability. If the odd of x is 1.25, it implies a probability of 80% for x happening, as the reward it pays is the even return for such probability. This means that if x truly had a chance of 80%, and a player gambled always on x, in the long term he would end up with the same ¤1, not losing nor earning anything. However, this is only true if the odds offered were actually “fair odds” (or “even odds”), and they truly corresponded to the actual probabilities of an event, but that never happens in sports betting, firstly because it is very difficult, and perhaps impossible, to determine with high precision what are the true probabilities of an event, and secondly, because the bookmakers always add a margin to the odds, from which they obtain their profits.

The odds of the example in the percentage format add up to 105% (80% + 25% = 105%), which is 5 percentage points higher than the sum of 100 percentage points that should result if the odds truly were equivalent to the probabilities. Were they equivalent, if the player wagered proportionally to both x and -x, his return would be exactly his original bet; yet, as that is not the case, if he wagers to both, he will lose money:

Initial money: ¤1050

Wager: ¤800 for x at 1.25, and ¤250 for -x at 4

Final money if x happens: ¤800 · 1.25 = ¤1000

Final money if -x happens: ¤250 · 4 = ¤1000

Loss in either case: ¤50

The extra percentage points are the source of the profits of the bookmaker.

Nevertheless, this does not mean that the odds are completely independent of the actual probabilities. If the offered odds are markedly lower than what potential players believe are the even odds, the players will not bet; and on the other hand, if they are drastically higher than the even odds, the bookmaker risks losing money.

Suppose that x has a chance of 50%, the even odds would be:

x: 2, -x: 2

Then suppose that the bookmaker is offering the same odds as before:

x: 1.25, -x: 4

Such sharp difference treats x as the favorite outcome. Yet, it might not be difficult for many potential players to notice that such estimation is mistaken, even if they do not know the exact probability of 50%, as long as they can intuit that the true chances of x must be closer to 50% than to 80%. Hence, very few players will want to risk betting for x, and plenty of players will bet for -x, seeing that reward is dramatically higher than the risk.

The prize of the winners is usually funded with the bets of the losers. In this case, as there would be very few wagers for x, they would not be enough to fund the payment of prizes if x does not happen, and the bookmaker will have to pay from its own reserves. Not only could it lose plenty of money, but this would lead it into bankruptcy in the long term.

Of course, the bookmaker could simply overestimate both outcomes and pay little to both, for example offering these odds:

x: 1.66 (≈60%), -x: 1.66 (≈60%)

With this very large margin of 20%, it is very unlikely that players will gamble on this event, and even if they very much want to bet, they will prefer to search for another bookmaker that offer better odds.

For all these risks, the bookmaker has strong reasons to attempt to reflect the true probabilities in its odds. But bookmakers are not perfect, they may not reflect adequately the probabilities of an event, and if a player can constantly identify discrepancies between the odds offered and the actual chances, he can profit in the long term. Bookmakers know this, and that is why they take plenty of care when setting the odds.

When the bookmakers make an initial offer of odds, they produce them based on an informed estimation of the probabilities of an event. They consult experts in sports who are well informed about the teams, their players, and the little particularities of the matches and the competitions. They make statistical analysis of the recent performance of the teams and the players, observing how many points each one scored, what are their positions in their leagues, which games they won and which ones they lost against whom, etc. And they analyze their inside knowledge of their market share, such as the preferences and the trends among their clients. They combine all this information to come out with an estimation of the probabilities of the possible outcomes of a match.

After the initial offer, the players will start to input their wagers, and the bookmakers will frequently adjust their offered odds depending on the demand for either option, the bets that their best gamblers make, the odds offered by the competition, and the analysis of any new information about the match.

The odds offered right before the start of the match are called the “closing odds”, and are often considered to be the most accurate prediction of the probabilities of the match, as they are the product of the constant application of the aforementioned analyses, up to the very last moment possible.

When a game starts, the odds offered, if any, are called “live odds”, and they are updated constantly depending on the gambling that happen during the match, the performance and the scoring of the teams during the match, and the live odds of the competition. Live odds can vary drastically during the whole match, and often culminate some seconds before the ending, with extreme estimations, like 1.001 (≈99.9%) for the leading team, and 100 (1%) for the trailing one, as it is definitely close to 100% the probability that a team that is winning a minute before the end of the match, win the match.