Try creating a payoff matrix for a round of ner-rockscissors where you wager $1 per round. This will look like a table. Your choices are rock. paper. or scissors. So these will be the three rows. The future possible events are your opponent choosing rock, paper. or scissors. So these will be the three columns. The value to put in each cell '1' for winning. '-1' for losing. and '0' fora tie. Next do some calculations. Scenario 1: First assume that your opponent chooses their gesture at random lone in three}. What is expected value [EV] of you picking rock? What is the EV of picking paper? How about scissors? Hint: The EVwill be the probability of each possible future event multiplied by it's payoff. In other words. the answer for the first one is: EV = [{prob. of opponent selecting rock} 3: {payoff if opponent selects rock}] + [[prob. of opponent selecting paper} x {payoff if opponent selects paper}] + [{prob. of opponent selecting scissors} x {payoff if opponent selects scissors}] = .33 x D + .33 x -1 + .33 x 1 = -.33 + .33 = 0. You should nd that the EV of each alternative is the same. Scenario 2: Next assume that your opponent's behavior is non-random because when they win a round, they tend to repeat their winning gesture more often than would be expected at random (note: this is a real thing}. Let's say your opponentjust beat you with rock and so their probability of picking rock is .40. It is .30 for paper and .30 scissors. Now, what is E'v' ofyou picking rock? What is the EV of picking paper? How about scissors? Which option should you choose? Hint: Again. the EV will be the probability of each possible future event multiplied by it's payoff. In other words. the answer for the rst one is: EV = [{prob. of opponent selecting rock} 3: {payoff if opponent selects rock}] + [[prob. of opponent selecting paper} x {payoff if opponent selects paper}] + [{prob. of opponent selecting scissors} x {payoff if opponent selects scissors}] = .40 x D + .30 x -1 + .30 x 1 = -.30 + .30 = 0. Now should find that the EV of each alternative is not the same. One alternative should have a larger EV than the others. This is your optimal choice