Pay to play with a cap

You may roll a die up to twice, you must pay $1 per roll, and you collect (in dollars) the value of your final roll. Playing optimally, what is your expected net profit? Give a decimal to two places.

Show hints (2)+
  1. Each roll costs $1 - fold that into the decision.
  2. Re-roll on 1–3, keep on 4–6.

Answer

Reveal answer →

2.75 (± 0.05)

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