# How the banker limits his risk?

In a game like Deal or no Deal, what is the formula the banker uses to give an offer to the contestant? The banker offers the contestant an amount of money to quit the game, the offer based roughly on the amounts remaining in play and the contestant's demeanor, the bank tries to 'buy' the contestant's case for a lower price than what's inside the case.

I am simply curious to understand how this work. Thanks!

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A fair offer would be the expected value of what's in the briefcase. That is you sum up the probability that they have some amount of money times that amount. If for example there are three cases left, $10, 5000, and 25000$, then the expected value of his case is
$$\left( 10 \cdot \frac{1}{3} \right) + \left( 5000 \cdot \frac{1}{3} \right) + \left( 25000 \cdot \frac{1}{3} \right) = 10003.33$$