Paid Rerolls
You roll a fair six-sided die. After seeing the result you may either stop and receive the face value in dollars, or pay $1 and roll again. You may pay to reroll as many times as you like, and each reroll replaces the previous result. There is no entry fee. Playing to maximize your expected net amount (payout minus all reroll fees), what is your expected net amount? Give an exact number of dollars.
Related problems & prerequisites
Worth solving first
- Optimal Dice Stopping 5.0/10
- Six Different Faces 4.0/10
- Ant on a Cube 4.0/10
Source: Standard optimal-stopping exercise in wide circulation; no traceable original source. Statement written for AxiomIQ.