Expectation values

[Frustrated01]

The second question. I appreciate any help that anyone can provide.

Spin the dreidel is a gambling game which uses a 4-sided top, each side has an equal chance of being up when the top topples.

Side 1 The player wins the whole pot
Side 2 The player wins half the pot
Side 3 Nothing happens the next player gets the top
Side 4 The player puts a coin in the pot

Whenever the pot is emptied every player puts a coin in the pot.

Assume there are six players, who have each just put a coin in the pot.

Part A What is the expectation value for the player that spins first?

Part B What is the expectation value for the player that spins second?

The following doesn't format correctly when saved. f(x) is over 0.25, and x is over 6


f(x) x
Side 1 0.25 6
Side 2 0.25 3
Side 3 0.25 0
Side 4 0.25 -1

The following doesn't format correctly when saved. f(x) is over 0.25, and then over .0625, while x and x*f(x) are for the answers

f(x) f(x) x x*f(x)
Side 1 0.25 Side 1 0.0625
Side 2 0.0625
Side 3 0.0625
Side 4 0.0625
Side 2 0.25 Side 1 0.0625
Side 2 0.0625
Side 3 0.0625
Side 4 0.0625
Side 3 0.25 Side 1 0.0625
Side 2 0.0625
Side 3 0.0625
Side 4 0.0625
Side 4 0.25 Side 1 0.0625
Side 2 0.0625
Side 3 0.0625
Side 4 0.0625



E(X) 0