Brain Teasers & Mental Math
You roll a fair die and may either keep the result or reroll once (you must keep the second roll). Playing optimally, what is your expected value?
Model answer
4.25.
Step 1: a forced reroll is worth the plain average, 3.5. Step 2: so keep any first roll beating 3.5 — i.e., keep 4, 5, or 6; reroll 1, 2, or 3.
EV = P(keep) × E(kept value) + P(reroll) × 3.5…
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