Beating a Loaded Die
You and a friend each roll a single die. Your die is a standard fair 6-sided die with faces $\{1, 2, 3, 4, 5, 6\}$, each equally likely. Your friend's die is non-standard: its six faces show the values $\{1, 1, 1, 6, 6, 6\}$, each face equally likely.
Both of you roll once. What is the probability that your roll is strictly higher than your friend's?
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