  e-Valuate is a game on arithmetic expressions. The players have contrasting
roles of maximizing and minimizing the given expression. The maximizer proposes
values and the minimizer substitutes them for variables of his choice. When the
expression is fully instantiated, its value is compared with a certain minimax
value that would result if the players played to their optimal strategies. The
winner is declared based on this comparison.
  We use a game tree to represent the state of the game and show how the
minimax value can be computed efficiently using backward induction and
alpha-beta pruning. The efficacy of alpha-beta pruning depends on the order in
which the nodes are evaluated. Further improvements can be obtained by using
transposition tables to prevent reevaluation of the same nodes. We propose a
heuristic for node ordering. We show how the use of the heuristic and
transposition tables lead to improved performance by comparing the number of
nodes pruned by each method.
  We describe some domain-specific variants of this game. The first is a graph
theoretic formulation wherein two players share a set of elements of a graph by
coloring a related set with each player looking to maximize his share. The set
being shared could be either the set of vertices, edges or faces (for a planar
graph). An application of this is the sharing of regions enclosed by a planar
graph where each player's aim is to maximize the area of his share. Another
variant is a tiling game where the players alternately place dominoes on a $8
\times 8$ checkerboard to construct a maximal partial tiling. We show that the
size of the tiling $x$ satisfies $22 \le x \le 32$ by proving that any maximal
partial tiling requires at least $22$ dominoes.
