Question of the day
2026-08-10
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?
Answer it out loud first — like you would in the room. Then check yourself:
Reveal the model answer
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 = (1/2)(average of 4,5,6) + (1/2)(3.5) = (1/2)(5) + (1/2)(3.5) = 2.5 + 1.75 = 4.25.
This is option value: the right (not obligation) to redraw lifts EV from 3.5 to 4.25. With two rerolls it rises further (to ~4.67).
Want 10 of these a day, scheduled so they stick?
A free account gets you Daily 10 — ten questions a day from the full 2,300+ bank, spaced-repetition scheduled. No credit card.
Tomorrow's question, in your inbox.
One real IB interview question every morning — free, one-click unsubscribe, nothing else ever.