Two players, A and B.A goes first. They roll a dice that has random outputs between 1 and 30. The player who gets the higher number wins, and the loser pays the winner the amount that the winner gets on his dice.1. What is the expected winnings?2. Would you prefer being Player A or Player B? Why?
Question
Two players, A and B.A goes first. They roll a dice that has random outputs between 1 and 30. The player who gets the higher number wins, and the loser pays the winner the amount that the winner gets on his dice.1. What is the expected winnings?2. Would you prefer being Player A or Player B? Why?
Solution
- The expected winnings can be calculated by considering all possible outcomes. Since the dice has 30 sides, there are 30*30 = 900 possible outcomes. For each outcome, the winnings are the higher of the two numbers rolled. The expected winnings are the average of these winnings over all possible outcomes.
To calculate this, we can sum the winnings for each possible outcome and divide by the total number of outcomes. The winnings for each outcome are the higher of the two numbers rolled. Since the dice is fair, each outcome is equally likely, so we can simply average the winnings over all outcomes.
- There is no advantage to being Player A or Player B. Since the dice is fair, each player has an equal chance of rolling any number. Therefore, the expected winnings are the same for both players. The only difference is that Player A rolls first, but this does not affect the outcome.
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