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Reroll Die

ProbabilityMedium
10 min
20 pts

Description

Roll a fair d6, option to reroll once and take second result. Find optimal expected value.

Game Rules

Roll a fair 6-sided die. You can either keep the result or reroll once and take the second result. What is the optimal strategy and expected value?

Examples

Keep if roll >= 4

Reroll if roll <= 3 because reroll EV is 3.5

Optimal EV = (3/6 x 3.5) + (3/6 x 5) = 4.25

Hints

  • Calculate expected value of rerolling

  • Compare with current roll value

Solution (Click to reveal)

Reroll if you get 1, 2, or 3. Keep if you get 4, 5, or 6. Expected value = 4.25.

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