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} ((1)/(2)*(1)/(2)*2)-(1*(1)/(2)*(1)/(2)) \\ =((1)/(4)*2)-(1*(1)/(4)) \\ =((1)/(2))-((1)/(4)) \\ =(1)/(4) \end{gathered}`

The expected value of player B is:

`\begin{gathered} ((1)/(2)*(1)/(2)*2)-(1*(1)/(2)*(1)/(2)) \\ =((1)/(4)*2)-(1*(1)/(4)) \\ =((1)/(2))-((1)/(4)) \\ =(1)/(4) \end{gathered}`