There are two types of online betting sites - bookmakers and exchanges. A bookmaker allows you to place bet on the outcome of some event, and will often reward your risk taking (and long term gain for the bookmaker) by allowing you to make another bet for free. An exchange allows you to be the bookmaker or bet placer - letting you 'lay' the outcome of an event where another person you find on the exchange makes a bet with you as if you were a bookmaker.
With this system you can easily break even on bets you make with a book maker, which will end up in you getting a free bet that you can do the same thing with to end up with a profit overall. For example, in the UK Ladbrokes offers a free £50 bet if you sign up with them and place a £50 pound bet. Lets say that for a particular event Ladbrokes say they will offer odds of 2 for your bet. You then go to an exchange like betfair and find that you can make the opposite bet and the odds you'll have to offer are 2.05. Betfair will also take a 5% commission on all bets placed. You can then work out the optimal amount of money to bet in the opposite direction in order to only lose a little bit of money from the bet.
There are many odds calculators online but they really just apply a simple formula. Lets say you have placed the £50 bet with ladbrokes (with odds of 2) and you are going to let someone place £x against you (at 2.05).
If the bookmaker bet wins then the final profit will be:
If, instead, the bookmaker bet loses the profit will be:
To work out the optimal play safe strategy for this bet you need to employ a bit of linear programming.
This is a graph of P against x for the two lines. The play safe x will be the point where the lines cross and this is trivial to calculate. It is negative here because of the commission and difference in the odds on the two platforms. An arbitrage bet is where the optimal x gives a positive number and so in placing the bet you make profit. This is quite rare and bookmakers are generally opposed to this sort of betting which is where projects like peer plays will be excellent in stopping bookmakers stopping arbitrage bets.
To find the x where they intercept the value for P is the same for both lines so
and when x = 50
So you will have lost £2.50 but made a £50 free bet with Ladbrokes. You can then consider different profit equations for clamming the free bet, remembering that the stake is not returned with the bet. A quick search around the web will let you find betting sites in your area offering free bets, as well as odds matching to find the right events to bet on.
