Different Beliefs and Arbitrage:

You sit at a casinos roulette table with two others, Ron and Justin. You hear Ron whisper that he is certain that red only lands around 30% of the time. You hear Justin mumble something similar - that he is certain that red only lands 40% of the time. You know for a fact that the roulette wheel is fair (no 0s or 00s), and that the likelihood of red landing is 50%. The roulette payoffs are typical: you double your money when you guess the right color (black, red).

1. Suppose you could offer each a side bet based on their beliefs - they bet $X on red, you bet $100 on black, winner takes the pot. How much should Justin and Ron have to bet on red for the bet to be fair in their mind?

2. Would you offer these standalone bets? Explain your answer.

3. Suppose you reverse the bets - they bet $100 on black, you bet $X on red. Is this arbitrage?

4. Construct a riskless strategy using this fair bet with each player (where you bet on red) combined with a bet on the actual roulette table. What color should you bet on and how much?

5. Suppose you could get either party to take either side of their respective fair bets, and you cannot bet at the actual roulette table. Construct an arbitrage strategy using these two bets.