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You play the following dice game with a fair six-sided die (with the standard numbering). You start with 0 points, and on each turn, you may choose to roll the die or stop playing. If you roll, you earn the the number that you roll in points. However, if your point total ever becomes 9 or greater, your point total is set to 0 and the game ends. (Totals 8 or less are safe, and you continue playing.) If you stop, you end the game with your current number of points. Answer the following questions by solving the associated Bellman equation. (a) What strategy maximizes the expected value of your final point total? (b) What is the expected value of that strategy?

user351037
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    What have you tried? – DifferentialPleiometry Mar 03 '22 at 20:11
  • DifferentialPleiometry, you will help me to solve this question – user351037 Mar 03 '22 at 20:13
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    Seven upvoted posts in the duplicate thread provide seven different forms of help. That ought to be enough to get started :-). – whuber Mar 03 '22 at 20:14
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    I downvoted this question. The reply to DifferentialPleiometry is very weird. He asks what you have tried. You respond by begging for help instead of going along with his question which is actually helpful if you just try to answer it. – Sextus Empiricus Mar 03 '22 at 21:17
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    Why did the question change completely from being about the random walk on a cube to the problem of rolling a dice? – Sextus Empiricus Mar 03 '22 at 21:21
  • Ordinarily we would request that a totally new question be posted in a new thread. However, because the new version is not suitable for the site, I have kept it closed but changed the close reason to be more pertinent. – whuber Mar 03 '22 at 23:50

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