(a) Let's play a variation on matching coins. Each of us will choose heads or tails, independently and secretly. I'll pay you S30 if I show tails and you show heads. I'll pay you SIO if I show heads and you show tails. Finally, to make it fair, you pay me S20 if we match (i.e., both show heads, or both show tails). Do you want to play? Why?

(b) What are the optimal strategies of the two players in an ordinary game of matching pennies? (Recall that in this game, one player gets the pennies if they match, the other gets them if they don't match.)

Would you still toss your penny in such a game, rather than secretly selecting a head or tail? Why?