There are two possible outcomes for a sporting event — Team A wins, or Team B wins. How can I calculate the maximum profit given the following arbitrage opportunity?
Sportsbook 1 (Outcome Team A wins) — Odds 2.17 (I plan to bet \$100 and they will refund \$50 as part of a promotion if it loses)
Sportsbook 2 (Outcome Team B wins) — Odds 1.70 (No promotion here, but how much do I bet here to ensure maximum gain regardless of the outcome of the event).
If I bet \$100 and Team A wins, I stand to win \$217 (for a total profit of $117). If they lose, I only lose \$50.
How much do I need to bet on the second sportsbook to ensure that I can take full advantage of the arbitrage opportunity regardless of which team wins. There is no promotion for the second sportsbook.