Consider the following three games. Which one would you be most likely to play? Which one would you be least likely to play? Explain your answer mathematically.
Game I: You toss a fair coin once. If a head appears you receive $3, but if a tail appears you have to pay $1.
Game II: You buy a single ticket for a raffle that has a total of 500 tickets. Two tickets are chosen without replacement from the 500. The holder of the first ticket selected receives $300, and the holder of the second ticket selected receives $150.
Game III: You toss a fair coin once. If a head appears you receive $1,000,002, but if a tail appears you have to pay $1,000,000.