Dutch book two bookmakers
Asked at SIG
A tennis match has two possible outcomes. Bookmaker A offers decimal odds of on Player X winning. Bookmaker B offers decimal odds of on Player Y winning.
Can you lock in a riskless profit? How much do you stake at each book, what's the guaranteed return, and what's the general condition for such an arbitrage?
Show a hint
Add up the implied probabilities across the two books. What does it mean if they sum to less than one?
Your answer
This one is open-ended. Work it through, then check your reasoning against the full solution.