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.
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