Deniz is playing a game of rock-paper-scissors with Phil. The loser of the game will pay the winner $\$100$. In the game of rock-paper-scissors, each player chooses either rock, paper, or scissors simultaneously. A winner is decided by the following rules: rock beats scissors, scissors beats paper, and paper beats rock. If both players make the same choice, then the game is a tie. Deniz is trying to decide whether to play rock or paper. Based on previous games, she knows that Phil will make his choice according to the probabilities in the table below. **What are Deniz's expected winnings if she chooses rock? Round your answer to the nearest dollar. $\$$[[☃ math-keypad 1]]** **What are Deniz's expected winnings if she chooses paper? Round your answer to the nearest dollar. $\$$[[☃ math-keypad 2]]** **If Deniz wants the best payoff in the long run, she should choose [[☃ dropdown 1]].** Phil’s choice |Probability :-: | :-: | Rock | $50\%$ Paper | $20\%$ Scissors | $30\%$