Player A's score is determined by taking the highest of 3 dice.

Player B's is determined by taking second-highest of 8.

Who wins more games?

Player A's score is determined by taking the highest of 3 dice.— Ben Orlin (@benorlin) June 16, 2016

Player B's is determined by taking second-highest of 8.

Who wins more games?

The first is not hard to analyze. I get an expected value of 4.96. The 2nd was too hard to analyze for me. (Am I missing simpler ways of organizing the possibilities?) So I simulated it in Excel. (I wanted to use Python, but couldn't remember how to get started.) In Excel, I used Int(6*rand())+1, 8 columns across, for the dice roll. Then I used Large(a1:h1,2) to get the 2nd biggest. Then I copied down 1000 rows, and averaged. Copy-paste gets new random numbers. It was always between 5.1 and 5.2. So B wins more games.

ReplyDeleteIf the first one has an expected value of 4.96, could you just check the probability of player B getting a 5 or 6? I get a 96% chance of rolling at least one high die, so I would expect B to win more games.

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