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Odds are simply a reflection of the chance or probability of a certain outcome in an event. In any event, every outcome has a chance of taking place. Odds are simply an interpretation of those chances. The bookies form odds or prices to reflect those chances.
In every game, there is a favorite and an underdog. In order to make the game even for you to bet on, bookmakers come up with a point spread, or line. The spread is a handicap, the amount of points you have to part with if you bet on the favorite, and the amount you will receive as an underdog. For example, if the Falcons are favored by 15 over the Patriots, (Atlanta -15 vs. New England ), and Atlanta wins 31 - 20, then those who bet on New England win, and those who backed Atlanta lose. Essentially, the game is looked at as a 35-31 New England win because of the spread. If Atlanta won 31 - 16, the game would be a push, and both parties would get their money back.
Most online oddmakers give you the option of which type of odds you want to bet on.
The money line is as odds bet. Instead of parting with points or receiving points to make the game even, you part with or receive extra money. For example, if the oddsmakers believe that it's twice as likely that Dallas will beat Arizona than the other way around, then the odds will look something like this: Dallas (-220) vs. Arizona (+180). Dallas -220 means that if you want to bet on Dallas, you have to risk $220 in order to win $100. Arizona +180 means that if you bet on Arizona, you risk $100 to win $180.
The reason why you lose $220 if you bet Dallas win just $180 if you bet Arizona, is that this disparity takes the place of the vig, i.e., the big is built into the odds here.