Question: 1. Each of two players hides either a nickel or a dime. If the two coins match, A gets both: if they don't match, B gets both. What are the optimal strategies? Is this game fair? What about games with coins of arbitrary but fixed denominations x and y?
2. Consider the variant of Morra in which each player can hide one, two, or three coins; for simplicity, assume that the players announce their guesses simultaneously. What are the optimal strategies?