How much is a $100 free bet worth?

by Burkard Polster and Marty Ross

The Age, 23 March 2009

It’s almost footy time again. And it’s time to make a little wager on our beloved Saints winning the premiership. So, we investigated the various sports websites. It turns out that a number of them offer a free bet as inducement to open an account with them. However, the value of their offer is surprisingly tricky.

Suppose you are offered a $100 free bet. This is definitely not the same as being given $100: you have to bet on something. But there are other differences as well.

For example, suppose you want to bet that the Saints will win the toss of the coin in their first match. With a normal bet, you would hand over $100. Then, ideally, a successful bet would return $200, the $100 you wagered plus the $100 you won. In reality, you’ll receive slightly less than fair odds. So you might win about $95. But let’s ignore that.

With the free bet, you don’t give over the $100 stake and then you usually don’t get it back either. So, a winning Free Bet would mean you receive only the winnings of $100.

Imagine now that you have two free bets with two different companies. You can then use one to bet that the Saints will win the toss and the other to bet that they will lose. Then, whatever happens, the two bets result in your receiving $100.

So, it seems each $100 free bet averages to a worth of about $50. What is amazing is that you can actually do better. This was pointed out to us by our sports journalist friend, Gary Watt. Gary, who has no degree in mathematics, calmly explained it all in the face of our smug scepticism.

Imagine that the 16 teams in the AFL have an equal chance of winning the premiership. Then a $100 free bet on the winning team would win about $1500. Now imagine you have sixteen free bets, and you use one on each team. Then, whoever wins you’ll get back about $1500. So each free bet averages to a worth of $1500/16 – about $94!

The amazing conclusion is that on average a free bet is worth more if it is less likely to win. This makes it perfect for a flutter on our beloved but beleaguered Saints.