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Simple Dice Game
Goldman Sachs
You have a 6 sided die, and you get paid whatever you roll. First explain the concept of fair price of any game and then find it for this one. Can you explain fair price of a game without reference to probability?
Answer
Fair price of a game is the amount of money you expect to earn from playing this game. If you were to play this game a large number of times, the average win per game is the game's fair price (expected value explained in non-probabilistic terms).
For this game, the expected value is simply the average of all possible outcomes (getting 1-6), since they are all equally likely. Thus, $EV = \frac{1+2+3+4+5+6}{6}=3.5$