Question

Assume that you are playing a dice­rolling game. You will get paid by the number rolled out. What is the maximum entry fee you are willing to pay for one game (i.e. roll once)? Now assume that in each game you can roll at most 4 times and get paid by the last number rolled out when you decide to stop. What is the maximum entry fee you are willing to pay?

Answer 1

It will be better to pay the maximum entry fee equal to one dollar when you are allowed to roll just once.

This is because the dice is expected to show any number with equal probability, so the number 6 as well as number 1 have the same chance of occuring. So even if 1 comes up, you won't lose anything because you have just paid one dollar.

Next, when you are allowed to roll maximum upto 4 times, you have a good chance to stop the game at a big number, say 4 or 5. So in this case you should be willing to pay a maximum fee of 3 dollars.

Because you have a good chance of getting a 4 or a 5 or a 6.