The most powerful die
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In a dice game, two players each pick one of three dice and roll them. Whoever rolls the higher number wins (it doesn't matter how much higher). Here are the three dice.
A die is considered "more powerful" than another die if it wins more than it loses. For example, if A beats B 70% of the time, then we would say that die A is more powerful than die B. Which is the most powerful die?
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Solution Summary
An Excel spreadsheet with step-by-step calculations is provided. The Word file contains a summary of the results, and answers the question.
Solution Preview
Since there are only 2 players, we only need to consider scenarios where 2 dice are picked. An Excel spreadsheet was created to compute the probabilities of each of the possible scenarios:
A versus B
A versus C
B versus C
Note that each die has numbers that are repeated. Die A only has 3 unique numbers. Similarly with dice B and C. Since the numbers are repeated ...
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- MSc, California State Polytechnic University, Pomona
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- BSc, California State Polytechnic University, Pomona
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- "Hello, thank you for your answer for my probability question. However, I think you interpreted the second and third question differently than was meant, as the assumption still stands that a person still independently ranks the n options first. The probability I am after is the probability that this independently determined ranking then is equal to one of the p fixed rankings. Similarly for the third question, where the x people choose their ranking independently, and then I want the probability that for x people this is equal to one particular ranking. I was wondering if you could help me with this. "
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