A passenger on a Mississippi riverboat was approached by a flashily dressed stranger (the gambler) who offered to play the following game: You take a red ace and a black deuce1 and Ill take a red deuce and a black trey2 ; we will simultaneously show one of the cards, if the colors dont match you pay me and if the colors match Ill pay you; moreover, if you play the red ace we will exchange the difference of the numbers on the cards; but if you play the black deuce we will exchange the sum of the numbers. Since you will pay me $2 or 4$if you lose and I will pay you $1 or $5, if I lose, the game is obviously fair. Set up and solve this matrix game by using the simplex method. Prove that the game is not fair; i.e., the value of the game is nonzero.