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Dice Game (DP)

CalcMedium~20 min· Dynamic Programming
Problem

The Problem

You roll a fair six-sided die repeatedly. After each roll you may either stop and walk away with your accumulated total, or roll again. The catch: if you ever roll a 1, you lose everything and the game ends immediately.

Questions

  1. What is the optimal stopping rule?
  2. What is the expected payoff under optimal play?