Fermi Estimation Game
Objective
Estimate the answer to Fermi questions as accurately as possible. You start with 500 points and earn or lose points based on how close your guess is on a logarithmic scale.
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:
- Hit (answer in range): base points × spread multiplier. Tighter intervals earn a bigger bonus (up to ×1.5), but very wide intervals (>10x) reduce your score (×0.8)
- Miss (answer outside range): you lose points, and tight misses are punished harder (overconfidence penalty). A wide miss is more forgiving
- Skip / timeout: −20 points
Base points (log₁₀ distance of geometric mean)
| Log₁₀ dist. | ≈ Ratio | Hit | Miss | Label |
|---|---|---|---|---|
| ≤ 0.05 | ~1.1x | +100 | −50 | Near perfect |
| ≤ 0.10 | ~1.3x | +80 | −40 | Excellent estimate |
| ≤ 0.20 | ~1.6x | +60 | −30 | Very close |
| ≤ 0.30 | ~2x | +40 | −20 | Good estimate |
| ≤ 0.50 | ~3x | +20 | −10 | In the ballpark |
| ≤ 1.00 | ~10x | +10 | −10 | Right order of magnitude |
| > 1.00 | > 10x | 0 | −10 | Too far off |
| — | — | — | −20 | No answer / Skipped |
Spread multiplier (interval width)
The spread multiplier depends on whether you hit or miss. Narrow intervals are high risk, high reward. On a miss, the overconfidence floor sets a minimum penalty based on how tight your interval was — even if your estimate was way off.
| Spread | ≈ Width | Hit mult. | Miss floor | Example |
|---|---|---|---|---|
| ≤ 0.30 | ≤ 2x | ×1.5 | −50 | 50 – 100 |
| ≤ 0.50 | ≤ 3x | ×1.2 | −30 | 40 – 120 |
| ≤ 1.00 | ≤ 10x | ×1.0 | −15 | 10 – 100 |
| > 1.00 | > 10x | ×0.8 | −10 | 1 – 1,000 |
The miss floor is the minimum penalty for that spread — you lose at least that much for missing, even if your estimate was way off. Being confident and wrong is always costly.
Strategy
This is a calibration game. Be narrow when you're confident, be wide when you're unsure. A tight hit (≤2x spread) can earn up to +150 pts, but a tight miss costs you dearly due to the overconfidence penalty. A very wide interval (>10x) is safer but reduces your score even on a hit (×0.8 multiplier). The optimal play is honest confidence — match your interval width to your actual uncertainty. Skipping costs −20, so always submit something.