People have been informally betting on sports just about as long as there have been sporting events. Organized sports betting took off in the United States at the horse racing tracks that sprang up in the 1800s. Betting really caught on in the early 1900s when the pastime became more accessible to the middle and lower classes. At first, an auction system was used. Bettors bid on a lot that represented one horse in a given race. In this system, the bettors themselves automatically set the odds. Each bettor was vying for the full pot, and whoever had the lot for the winning horse got it. Horses that were highly favored to win were auctioned off at much higher prices, since the holder of that lot had the best chance of winning the pot. Lower-rated horses allowed bettors to take a chance at the pot for a smaller bet with a reduced chance of winning.
The auction system was limited because you could only take bets for the number of horses in each race. While some bookies opened multiple auctions on a single race, they still missed out on a lot of handle. The solution was to offer odds on each horse. Longer odds (like 50-1) meant a higher payout but a lower chance of winning. Horses given better odds were more likely to win but paid out at a lower rate (5-1, for example).
A similar system was used in other sporting events, such as boxing and early football games. It was hard for oddsmakers to set the odds accurately, and when a long-shot team came up with an upset win, bookies lost a bundle. Around World War II, the point spread concept was developed [ref]. This made betting on sports even more popular. The broadcast of sports on TV kept the cycle going -- sports became more popular, which made betting more popular, which made some people enjoy sports more.
Next we'll learn about some of the betting scandals that have plagued sports.