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A Gambling Game

In a gambling game, there are n players, and \( n>1\). Every player is randomly assigned an integer between 1 and \(y\), where \(y\) is also an integer. Let \(l\) be the lowest number someone is assigned and let \(u\) be the highest number someone is assigned. The distribution of these integers is uniform. \(u\) will receive \((u-l)\) currency from \(l\). If there is more than one winner, or more than one person is assigned \(u\), \(l\) will pay out \( \dfrac{u-l}w\) to each winner, where \(w\) is the number of winners. If everyone rolls the same number, no gold is exchanged. If there is more than one loser, the losers pay equal portions to the winner(s).

What is the expected value for a person entering into this game? Would you recommend that someone enters into this game given his odds?

Note by Oli Hohman
1 year, 3 months ago

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