th probabilities (x,y, 1-x-y). For further explanation of this strategy please refer to Display 3and/or Chapter 2 in the text. It is checked that Row’s and Column’s strategiesdo have a solution that equals 0. This is proven in Display 4. A 3x3 matrix is thekey to discovering an expectation - equalizing strategy. It is important to realizethat this method of equalizing expectations will fail if the solution to be 3x3 gameinvolves a 1x1 or 2x2 subgame. “In The End”Well there you have it. A ten page analysis of the day old game of Rocks,Paper, Scissors. My game varies slightly from the traditional but the scoresystem was essential towards discovering strategy. A matrix was reasonably theeasiest way to break the game down. The complexity of this game makes it goaround infinitely. There are no sure ways to win. No one strategy canguarantee a victory. No saddle points and no dominance makes this gameplayable forever. Both players are equal because the game matrix has no favortowards any certain player. My great grandparents have played this day oldgame, and will continue to solve everyday dilemmas like “who gets the extraslice” for many years to come. There is one rule, however, that mush never beforgotten. It is a game so have fun with it.Display 3Row’s Best Mixed StrategyRowRockx(0) + y(-2) + (1-x-y)(5)Row Paperx(2) + y(0) + (1-x-y)(-3)Row Scissorsx(-5) + y(3) + (1-x-y)(0)Column will be unable to take advantage of Row’s mixed strategy if theseexpectations are equal:x(0) + y(-2) + (1-x-y)(5) =x(2) + y(0) + (1-x-y)(-3) = x(-5) + y(3) + (1-x-y)(0)llllllllllllRow’s EV = (3/10, 5/10, 2/10)Thus Row’s expectation - equalizing mixed strategy is (3/10, 5/10, 2/10). By the symmetry of the matrix, this is also Column’s expectation - equalizingmixed strategy. The Value of the game is 0Display 2Legend:P= PaperS= ScissorsR= Rock...
