Inter-market Arbitrage in Sports Betting - National Centre for ...

, , 11 1 1 , 1 1 .
As already mentioned, Equation (2) is similar to Equation (1) besides the fact
that the commission fee is charged on the winning bet, whereas the bookmaker’s
margin is already included in the offered odds.
Alternatively, if a bettor goes short, he bets that the outcome will not occur.
The expected return on a short position bet with , is
1
, 1 1 , 1 1
1
, 1 1
1 .
, 1
As Equation (3) illustrates the opposite market position to Equation (2), the
expected return when going short also depends on the actual outcome probability
and the traded odd , inversely entering the equation. Thus, the
return on a short position bet, holding constant, decreases with ,. Next, we examine the composition of arbitrage opportunities in the betting
market. An arbitrage bet requires buying a contract at one price and contemporaneously
selling the same or equivalent contract at a higher price. The
stakes placed on each side have to be chosen such that the return of the combined
bet does not depend on the actual outcome of the game. We denote a
combined bet fulfilling this condition a hedged bet. An arbitrage opportunity
arises if the price difference exceeds the transaction costs involved. In order to
overcome these transaction costs, the arbitrageur must seek for favourable
selling conditions offered by other bookmakers (intra-market arbitrage) or by
the betting exchange market (inter-market arbitrage).
First, we consider intra-market arbitrage. Since, at the bookmaker market, a
bet can exclusively be placed on a given outcome to occur, to “sell” a bet re-
6
(2)
(3)