Most people are bad at knowing how much they know 💡. This app 📱 trains that one skill, and it does it
without a single multiple-choice question. Every answer here is a range: you drag ✋ two grips apart on
a logarithmic magnitude ruler to state the interval you think the true value falls inside, and pick
how confident you are — 50, 70 or 90 per cent. The width of that bracket is your answer and your
wager at the same time ⏱️. Squeeze it tight and a hit pays heavily while a miss costs just as much;
fling it wide and you are nearly safe and nearly worthless. Because the payout uses a real proper
scoring rule, neither hedging nor bluffing can beat simply being honest with yourself. Commit, and
the true value drops onto the same ruler as a marble pin: your bracket seals, or an ember span draws
from its nearest edge to the truth and reads your error ❌ in orders of magnitude.

Six round formats keep the skill from turning into a single habit. Bracket rounds are the core.
The Interval Ladder is proper Fermi estimation — break a big question into factors, bracket each
rung, and watch 👀 genuine interval arithmetic multiply them up the rail until you can see exactly
which rung wrecked the estimate. The Anchor Trap flashes a planted number 🔢, hides it, and then
measures your bracket against your own history ⏳ to show how far that number 🔢 actually pulled you.
Ratio Duels ask for the ratio between two quantities rather than either one. Magnitude Sprint is a
timed run up a power-of-ten ladder. Rung Repair hands you a plausible calculation with one factor
wrong ❌ by a hundredfold and asks you to find it.

Your record is the point. A real reliability diagram 📊 plots what you claimed against what actually
happened, with the honest diagonal drawn through it, so overconfidence shows up as a visible sag
rather than a scolding. There is a calibration score 🔢, a domain-by-domain breakdown 🧾 across twelve
subject areas, a full session ⏱️ log 📝 where every item keeps its bracket, the truth and the reason ❓
behind it, and an SM-2 spaced-review queue that brings back the quantities you missed. The Scoring
Room lets you drag ✋ a demo bracket and watch 👀 the expected-score 🔢 table 📋 prove that claiming what you
believe always wins. Everything is offline 📴, and the whole content bank — 324 sourced quantities,
60 decomposition ladders, anchor traps, ratio duels, broken chains, eight magnitude reference
tables and an 80-term glossary — was written from scratch for this app 📱.

For anyone who estimates for a living or for fun: engineers, forecasters, analysts, quiz ❓ players,
students, and anybody who has ever been confidently wrong ❌ by a factor of a thousand. There is also
an optional camera 📷 bench: photograph a real object beside a coin, measure 📐 it from the photo 📸, then
bet on its volume or mass *before* the geometry is computed.

Azure Star Solutions Group

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