Various companies allow you to bet on outcomes of sports matches and other events. It turns out it was possible in the past to use differences between odds offered by different companies to conduct an arbitrage, though the particular opportunity studied here (Premier League, British betting companies) has mostly closed.
Right now, we can bet on the outcome of the soccer match between Wolverhampton Wanderers and FC Liverpool:
If we bet on Liverpool winning and they indeed do, we get back 146% of our wager, for 46% gain. In the following we will assume the odds are quoted in this (European) notation, though there are other notations.
The implied probability of any event happening is equal to one over the odds. It can be seen that the implied probability of the Wolwerhampton win, Liverpool win or the draw sums to more than one (1/6.25 + 1/1.46 + 1/4.75 = 1.055). This is how the betting company makes money.
However, there are multiple companies in the same business, so it is theoretically possible to pit them against each other and find instances where the implied probability of the event is lower than one. This would offer an arbitrage opportunity. (But carrying the risk of bet being cancelled by the company.)
This possibility was studied in the thesis Arbitrage in the European Soccer Betting Market where Schwartz found that using UK betting companies, it was possible to find arbitrage opportunities for bets on Premier League matches.
Using data from this website we calculated the number of arbitrage opportunities (considering all betting companies included in the data) for the past twelve seasons:
We are able to confirm the conclusion of the thesis - there were numerous arbitrage opportunities in 2015. However, we see that this particular opportunity (Premier League, selection of British brokers) essentially closed in 2018-2019 season.