Fermi Estimation Game
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Objective
Estimate the answer to Fermi questions as accurately as possible. You start from zero and every answered question can add up to 200 points to your total. Your score depends on how close the geometric midpoint of your interval is on a logarithmic scale and how wide the interval is.
How to play
Each question, you’ll see a Fermi estimation question with a unit of measurement shown above the answer inputs. Enter a low and high estimate to form a confidence interval. Scoring is based on the geometric mean of your interval. Overestimating and underestimating by the same factor are penalized equally.
Scoring
Your score depends on how close your estimate is and how wide your interval is:
- Every submitted estimate starts with a 50-point answer credit before any miss deduction
- Hit (answer in range): the credit plus base points × spread multiplier, up to 200 per question. Tighter intervals earn a bigger bonus (up to ×1.5); very wide intervals (>10x) reduce the bonus (×0.8)
- Miss (answer outside range): a width-based deduction comes off your answer credit, never below 0. Tight misses lose the full credit and earn nothing
- Skips and timeouts score 0: only submitted estimates earn points
Base points (log₁₀ distance of geometric mean)
| Log₁₀ dist. | ≈ Ratio | Base points | Label |
|---|---|---|---|
| ≤ 0.05 | ~1.1x | +100 | Near perfect |
| ≤ 0.10 | ~1.3x | +80 | Excellent estimate |
| ≤ 0.20 | ~1.6x | +60 | Very close |
| ≤ 0.30 | ~2x | +40 | Good estimate |
| ≤ 0.50 | ~3x | +20 | In the ballpark |
| ≤ 1.00 | ~10x | +10 | Right order of magnitude |
| > 1.00 | > 10x | 0 | Too far off |
Interval width
A hit receives the multiplier below: narrower captured intervals earn a larger bonus. When an interval misses, its width determines how much of the 50-point answer credit remains.
| Spread | ≈ Width | Hit mult. | Miss deduction | Miss score |
|---|---|---|---|---|
| ≤ 0.30 | ≤ 2x | ×1.5 | −50 | 0 |
| > 0.30 to ≤ 0.50 | 2–3.2x | ×1.2 | −30 | 20 |
| > 0.50 to ≤ 1.00 | 3.2–10x | ×1.0 | −15 | 35 |
| > 1.00 | > 10x | ×0.8 | −10 | 40 |
On a hit, your score is the 50-point credit plus base points × the hit multiplier. On a miss, the deduction comes off the credit. A question never scores below 0.
Strategy
Use a narrower interval when you have a strong estimate and widen it when you are less certain. A tight hit (≤2x spread) can earn up to 200 points, while a tight miss scores 0. Wider intervals preserve more of the 50-point credit when they miss, but receive a smaller bonus when they hit. Skipping scores 0, so only submitting an estimate gives you a chance to score.