For this problem, consider a completely new game in which each of two players makes a single move. The actions available to each player are to either select the number $2,$ or to select a random action that assigns $($with equal probability$)$ either $1,2,$ or $3.$ The number the player gets is that player's score, and the goal is to have the higher score $($note that a player wins by having a higher score than the opponent $...$ the degree to which the score is higher is irrelevant$),$ and the second player knows the score of the first player before picking between the two available actions. Design a game tree for this game that takes the unusual rules into account, and fill the leaf nodes with $-1,0,$ and $1$ representing loss, tie, and win for player $1.$ Use these values to calculate the utility value at each node of the tree. Submit the drawing of your tree. For the game described in the previous problem, describe the optimal strategy of each player. Are there any extra issues that need to be taken into account to get optimal play when using such a tree? Is there any confusion as to the definition of optimal play for this game?