Consider the game below:

Player $1$ and player II each have two pennies. Each player holds $0,1,$ or $2$ pennies

in his left hand and the remainder of the pennies $(2,1,$ or $0$ respectively$)$ in his

right hand. Each player reveals both hands simultaneously. If the number of

coins in one of player I$\text{'}$s hands is greater than the number of coins in the

respective hand of player II$,$ player $1$ wins the difference in pennies; otherwise,

no money is exchanged.

a$.$ Which player is favored in the game? $($No work is required here!$)$

b$.$ Find the von Neumann value and the optimal strategy for each player in the