Compare the following two games:
You have a fair coin. After one toss, you will get 1 dollar if you get a head, and 0 dollars if you get a tail. How much will you be willing to pay to play this game 1000 times?
You have a fair coin, after one toss, you will get 1,000 dollars if you get a head, and 0 dollar if you get a tail. How much will you be willing to pay to play this game once?
I know the distributions of the payoff are different. However, I cannot figure out how this affects (or does not affect) the amount of the money you wanted to pay to play either game. Could anyone help explain?
Other than distribution, are there any other differences between these two games?