Question

In a game, 2 players each flip a coin. If both land on heads, player A gets 2points and player B loses 1 points. If both land on tails, player B gets 2 points andplayer A loses 1 point. Find the expected value of the game for each player.

Answer 1

The expected value for player A is:

$\begin{gathered} (\frac{1}{2}\times\frac{1}{2}\times2)-(1\times\frac{1}{2}\times\frac{1}{2}) \\ =(\frac{1}{4}\times2)-(1\times\frac{1}{4}) \\ =(\frac{1}{2})-(\frac{1}{4}) \\ =\frac{1}{4} \end{gathered}$

The expected value of player B is:

$\begin{gathered} (\frac{1}{2}\times\frac{1}{2}\times2)-(1\times\frac{1}{2}\times\frac{1}{2}) \\ =(\frac{1}{4}\times2)-(1\times\frac{1}{4}) \\ =(\frac{1}{2})-(\frac{1}{4}) \\ =\frac{1}{4} \end{gathered}$