Arbitrage in Online Gambling

From Cheap Talk:

Via kottke.org, an article in New Scientist on the mathematics of gambling. One bit concerns arbitrage in online sports wagering.

Let’s say, for example, you want to bet on one of the highlights of the British sporting calendar, the annual university boat race between old rivals Oxford and Cambridge. One bookie is offering 3 to 1 on Cambridge to win and 1 to 4 on Oxford. But a second bookie disagrees and has Cambridge evens (1 to 1) and Oxford at 1 to 2.

Each bookie has looked after his own back, ensuring that it is impossible for you to bet on both Oxford and Cambridge with him and make a profit regardless of the result. However, if you spread your bets between the two bookies, it is possible to guarantee success (see diagram, for details). Having done the calculations, you place £37.50 on Cambridge with bookie 1 and £100 on Oxford with bookie 2. Whatever the result you make a profit of £12.50.

I can verify that arbitrage opportunites abound. In my research with Toomas Hinnosaar on sorophilia, we investigated an explanation involving betting. In the process we discovered that the many online bookmakers often quote very different betting lines for basketball games....MORE