# Thread: Fair Play Value calculation

1. ## Fair Play Value calculation

A coin is weighted so it comes up head 3/4 of the time and tails 1/4 of the time. You play a game where this coin is flipped. If it comes up heads, you must pay 1 dollar. If it comes up tails, you win 2 dollars. What is the Expected Value of your winnings in this game?

I solved this portion and had the answered verified : 3/4 x -$1 + 1/4 x$2 = -0.25

I need help with calculating the Fair Play value. The second part goes as follows:

Assume that you still have to pay $1 if the coin comes up heads. In order for the game to be fair (where Expected Value = 0), how much should you win if the coin comes up tails? Please provide the solution, not just the answer. I'll understand better that way. thanks 2. ## Re: Fair Play Value calculation$E[V] = -\dfrac 3 4 \cdot 1 + \dfrac 1 4 x = 0\dfrac 1 4 x = \dfrac 3 4x = 3$3. ## Re: Fair Play Value calculation Thank you for your response Romsek, however, I'm still not getting this, at all. Why is the 3/4 now negative? Why is the X = to 3? I've been out of school for 26 years so while this should be super simple to pick apart, it isn't. Any further break down would be really really helpful. 4. ## Re: Fair Play Value calculation Originally Posted by sweetconiferous Thank you for your response Romsek, however, I'm still not getting this, at all. Why is the 3/4 now negative? Why is the X = to 3? I've been out of school for 26 years so while this should be super simple to pick apart, it isn't. Any further break down would be really really helpful. Paying 1 dollar is represented by -1. With probability 3/4 you pay 1 dollar, that corresponds to the first term$-\dfrac 3 4 \cdot 1x$is the unknown value that we need to win upon flipping a Tail in order to make the overall expectation of winnings 0. With probability 1/4 we win$x$dollars. This corresponds to the second term$\dfrac 1 4 x$The sum of these two terms is the expectation of the value of winnings which we set to 0 and then solve for$x\$.

expected value, fair coin, fair game, fair play, probability 