TicTacTix Game
This game tests the gamers’ ability to understand:

   1. Finding maxima and minima and saddle points
   2. Taking derivatives
   3. Solving equations
   4. Algebra
   5. Dexterity (might hit the wrong claim)



Claims:
min [x in X] max [y in Y] f(x,y) >= c

e.g.:
Claim Rel2Ex(c): min [x in [0,1]] max [y in [0,1]] (x*y + (1-x)(1-y^2)) >= c

Consider claims:
Rel2Ex(0.55)
Rel2Ex(0.60)
Rel2Ex(0.65)
Rel2Ex(1.00)

Rules of game:

   1. The game will provide the player 4 claims of which Player 1 will have to determine the one they should choose. [5 minutes]
   2. Once Player 1 chooses a claim, he/she has the opportunity to strengthen the claim further. [1 minute]
   3. After Player 1 is satisfied with the claim, they send the claim to their opponent, Player 2.
   4. Player 2 has the following options [5 minutes]:
         1. Strengthen claim
            Player 2 states that the claim is weak and adjusts c to a satisfiable level.
         2. Refute claim
            Player 2 states that the claim is incorrect and provides a value for x that asssures Player 1 is unable to find a corresponding y value for.
         3. Agree with claim
            Player 2 agrees the claim is optimal.
   5. Player 2 sends the decision to Player 1.
   6. Player 1 has the option that corresponds to the above choices: [2 minutes]
         1. Refute claim
         2. Find a corresponding y-value
   7. Round continues until either Player 1 or Player 2 has agreed with the claim. [2 minutes/action]
   8. Computer checks result 




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Claim Rel2Ex(c): [x in [0,1]] [y in [0,1]] (x+y) >= c

Consider claims:
Rel2Ex(1.00)
Rel2Ex(2.00)
Rel2Ex(3.00)
Rel2Ex(4.00)



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Strategy:

    * Pay - Building defenses
    * Calc - Building up attack