Value of rolling until something other than a one

Question

You keep rolling a fair die until it shows anything except a $1$ , and you are paid in dollars the value of that final roll. What should you pay to play?

Short answer

$4. The stopping roll is equally likely to be $2,3,4,5$ or $6$ , with average $4$ .

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Lessons behind this question

Conditional Expectation and Variance Revisited
Counting and Combinatorics
Expectation, Mean, and Variance

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