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How sure are you?

A quick claim — 17 × 23 = 391, 1 mile is more than 1.5 km — and seven taps for how sure you are it is true. Scored so honesty pays.

  • Probability
  • Timed
  • Endless levels

How it plays

Tap how sure you are, from "surely false" through 50% to "surely true". You are not asked to work it out — to judge it, and to know how good your judgement is.

The score is the Brier rule: a sure answer that is wrong costs the most, and over many questions the best score goes to whoever says exactly how sure they are. Levels add kinds of claim and bigger numbers.

Keys

Space starts and skips ahead · 1–9 pick · Enter submits · Esc stops. On a phone, tap.

What it trains

This practises matching confidence to accuracy on claims like these. Calibration is a learnable skill; this page claims no more than practice at it.

Learn

How to get better at how sure are you?: the method, the techniques, what each new level asks of you, and the traps the wrong answers are made of.

Your approach to each question

  1. Read the claim and note its kind — a product, a prime, a comparison of products, a unit comparison, a divisibility, a percentage. Each kind has a starting guess before you check anything.
  2. Spend your seven seconds on one quick check from the tricks below, not on working it out in full. A check that fails is a near-certain “false”.
  3. Turn what you found into a tap: a check failed — surely false or 10%; a check passed but could not settle it — 75% or 90%; no idea — 50%. Keys 1 to 7 tap the seven answers.
  4. Read the working afterwards and ask whether your tap was too sure, not only whether it was on the right side. Over many claims, your 90% taps should be right about nine times in ten.

Techniques and tricks

  • Say what you believe

    The Brier score is built so your best average comes from tapping exactly how sure you are. A right “Surely true” scores 1, a right 90% 0.99 — but a wrong “Surely true” scores about 0.02, and a wrong 75% still about 0.44.

    e.g. Right 9 times in 10 at a feeling: tapping 90% averages 0.91, tapping “Surely true” 0.90

  • Last digit, then digit sums

    For “a × b = c”, the last digit of c must be the last digit of the two last digits’ product; that catches offsets of 1 or 2. An offset of 10 keeps the last digit, so also reduce a, b and c to one digit each by adding their digits: a’s digit × b’s digit, reduced the same way, must equal c’s.

    e.g. 17 × 23 = 401: last digit 1 passes; 8 × 5 = 40 → 4, but 401 → 5, so false

  • Know the seven conversions

    1 mile = 1.609 km, 1 inch = 2.54 cm, 1 kg = 2.205 lb, 1 litre = 1.057 US quarts, 1 foot = 30.48 cm, 100 km/h = 62.1 mph, 1 acre = 0.405 hectares. Each claim compares one of these with a rounded figure.

    e.g. “1 foot is more than 30 cm”: 30.48 > 30, true

  • Products near a middle

    To compare two products, write each as a square minus a square: a × b = m² − d², where m is halfway between a and b and d is half the gap. With similar sums, the pair closer together is bigger.

    e.g. 23 × 17 = 400 − 9 = 391; 19 × 21 = 400 − 1 = 399

  • Divisibility rules

    3 and 9: the digit sum divides. 4: the last two digits do. 6: even and divisible by 3. 11: the alternating sum of digits divides. 7: double the last digit and take it from the rest, and repeat.

    e.g. 434: 43 − 8 = 35, divisible by 7, so 434 is

  • Primes: test small factors

    Every number asked about is odd, so skip 2. Try 3 (digit sum), 5 (last digit), 7 and 11; up to 120, a number that survives those is prime. Past that, survivors are likely but not sure, so tap 75% or 90%.

    e.g. 91 survives 3 and 5 but is 7 × 13, so false

As the levels climb

  • Kinds of claim unlock in this order: products, primes, comparisons of two products, unit comparisons, divisibility, then percentages. A new kind every other level; the levels in between make the numbers bigger.
  • Starting guesses differ by kind. Products and percentages are true about half the time here, and so are the unit comparisons. A claim that a number divides by 7 is true only about one time in seven before you check.
  • Primes thin out as the numbers grow: at the first size about half the numbers shown are prime, and fewer at each size after. Lower your starting guess for “is prime” as the numbers get bigger.
  • Once every kind is open, the numbers keep growing without end. Bigger numbers make full working impossible in seven seconds, so the checks — and honest middle taps — matter more.

Traps to avoid

  • “Surely true” on a claim you checked only roughly. A sure answer that is wrong costs almost the whole point; 90% costs little when right and saves a lot when wrong.
  • An offset of 10 on a product slips past the last-digit check: 17 × 23 = 401 ends in the right digit. Run the digit-sum check too.
  • A percentage claim off by 5 or 10. Build it from 10%: 15% is 10% plus half of it, 25% is a quarter, 40% is four times 10%.
  • Hiding at 50%. It scores 0.75 however the claim turns out — fine when you truly cannot tell, but a check that passes is worth a 75% or 90% tap, which scores more when right.

How to practise

  • Leave Time pressure at Normal: the seven seconds are the point. Set it to Relaxed only while you are learning the checks themselves.
  • Set Feedback to review “At each judgement”, then count your 90% taps in the review and how many were right. Fewer than about nine in ten means tap lower; nearly all means you can tap higher.
  • Raise “Answers each judgement looks at” towards 30 or more. Calibration only shows over many claims, and a small window judges you on luck.
  • Learn the seven unit conversions and the divisibility rules by heart; they turn whole kinds of claim from guesses into checks.

Levels

Each question has a clock that comes from the work it asks for. There is no last level: at least one dial turns without end. Your level is judged on your last ten answers, every ten: 90% moves you up, below 80% moves you down, which holds most people near four in five right.

All of it is in the settings beside Start — how many answers a judgement looks at and how often it recalibrates, the thresholds, the time, which questions, how many options, and whether you see each verdict at once or review them together at the judgement. You can also jump to any level.

More probability

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