Two players (1 and 2) take turns putting pennies inside a jar. Each player can place no less than one and no more than three pennies in the jar at each turn, that is, a player can put one penny, or two, or three, and then the other player takes her turn. Players stop when the number of pennies in the jar reaches 13. The jar is empty at the beginning of the game and player 1 starts first. The player that puts the 13-th penny in the jar wins and the other loses. Players only care about winning, that is, being the player that puts the 16-th penny in the jar, and are indifferent among all terminal histories that they win; or among all the terminal histories where they ose -) Required:
Let m, 0 <= m <=16, be the number of pennies in backwards the jar before player i takes her turn but without explicitly solving for an SPNE, determine for what values of m does the player whose turn is to move win?