I will see odds on people winning elections as 5/1 etc, but have no idea how to figure out if that means they are likely to win or not, other than through context. I have looked it up but never quite ‘get’ it. Please explain to me how it works in a way so simply that a child would understand!
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Its a ratio. winnings/stake.
5/1 will get you $5 for every $1 you bet (plus your original bet back). 2/3 will get you $2 for every $3 you bet (plus your original bet back), which is called “odds on” or the short position
Generally, the “shorter” the odds mean the less you will win, but the more likely you will get a payout. “long odds” are less likely but pay more.
bear in mind, these are NOT the odds of a given event *happening*, just the betting payout when they do happen. They calculate these odds to make sure that no matter the outcome, they both have enough money to cover the winnings and some profit for themselves.
An odds ratio has two numbers, x and y. To get a sense of how likely each outcome is, suppose you put x blue balls and y red balls into a bag. The first outcome should happen about as often as you would draw a blue ball out of the bag. The second outcome corresponds to red balls.
So 5/1 odds means that there are 5 blue balls and 1 red ball. That means the first event is 5 times more likely than the second. This is an easy way to interpret any odds with a 1, which is the most common way people talk casually about odds. If the odds are “a million to 1” then the more likely outcome happens a million times for every unlikely outcome.
But this method also works for odds without a 1. 3/2 odds means that the first event will happen 3/5 of the time and the second event 2/5. Etc.
Odds are handy in betting because they can turn a situation with uneven outcomes into a fair bet. Suppose one team in a matchup is expected to win 2 times out of 3. It wouldn’t work to give even odds where people betting on the better team can win exactly as much as they bet. Everyone would prefer that side of the deal. Instead, the people who bet for the better team should have to stake $2 to win $1, and the people betting against get to stake $1 to win $2.
Betting odds are just an extension of statistics, and there are a couple ways of getting those statistics.
For something like Roulette or Craps, you can calculate the odds purely mathematically to determine the odds of success.
For some things where the math is really hard, you could just simulate it and run millions or billions of tests and look at the results.
But for things that you can’t calculate, and you don’t know enough to prerun, you try and collect as much data as you can. You can then statistically calculate odds with a certain amount of room for error.
That room for error is very important. While you can say the odds of a coin flipping heads is 50%, you would also say that the odds of someone winning an election is 51% +/- 4% (or something similar). That means if you repeated the same experiment over and over, you would expect to see values between 47% and 55% come back (and to have an error range that covers the 51% as well).
Betting odds are just taking these odds and giving the betting agency an extra edge. You won’t get 1:1 odds on a coin flip. You might get 9:10 odds, ensuring that the betting agency gets an amount on average.
Couple of other people have offered good explanation as to what odds are… but it’s also important to understand how odds are set.
In a lot of betting scenarios — betting odds to win a particular game, or for a person to win an election or an award — the organization taking the bets sets the odds by balancing the likelihood of an event happening with the way the betting public is likely to behave.
That organization is going to set odds to minimize their risk and maximize their potential revenue. They want a distribution of wagers such that whatever the outcome, they make a profit.
Sometimes the odds will change as an event gets closer. This is a reflection of what the betting public thinks will happen, as determined by the wagers they’re placing.
Horse racing (in the United States and Canada, at least) is different. Racing uses what’s called a parimutuel system, where the odds and payouts are set based on the amount of money in the betting pools. It’s annoyingly complicated, but long story short, the more people make a particular bet, the worse the payout will be if that bet wins.
Source: used to work in the gambling industry.
Hi!
There are two things here to understand.
The first is that betting odds speak to the payout if your bet wins. 5:1 odds in the betting world means that a $1 bet will pay $5 if your outcome happens (eg “your horse wins”)
The second is that these betting odds are made by bookies who use many data points to come up with their “odds / payout ratios”.
In the case of 5:1 odds above, the odds maker thinks that your event is likely to happen in less than 1 in 5 times if the contest were to play out. (remember the odds maker wants to make money, so they take a portion no matter who “wins”)
To the person who bet for the “sure thing” (the other side of the 5:1 longshot) gets way less of a payout.
Mathematically, this is linked together by Bayesian probability. In Bayesian probability, probability is subjective: what the person believe to be the probability something will happen. The subjective odd is the payout:stake ratio you accept to be fair (ie. neither is at an advantage). In other word, if you’re a rational self-interest person (who only want to gain money and not care about anything else when making the decision to make a bet), there is a critical ratio, in which if the payout:stake is higher you will accept, and if the payout:stake is higher you will reject. That critical ratio is the fair point.
The idea that these follows the usual rule of probability is done through the Dutch book argument: if your belief in fair bet is inconsistent with the rule of probability, someone can make money off you by tricking you into making bad bets.
In other word, if you think that a betting scheme with payout:stake is 1:1, then your (Bayesian) odd in believing it happen is also 1:1.
This is why betting behaviors of people can be a very useful metric to find their subjective judgment of how likely something is to happen. The aggregation of that behavior give you the community’s aggregate opinion on what is the winning probability.
Note that this is the *subject* judgment of probability. Under the right circumstances, community’s aggregated subjective judgment is very good.
If you’re doing sport betting though, your bookie won’t give you a fair odd, because they want to make money. The odd would be in such a way that they rake in money no matter what the outcome is.
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