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One Quick Try

Estimation Game

A crowd of dots appears for a moment, too many to count. How many were there?

Type
Perception
Takes
about 1-2 min
Result in
percent off

Estimation

~1-2 min

  1. A crowd of dots appears for 1.5 seconds: too many to count.
  2. Type how many you think there were, and press Enter.
  3. 10 crowds, from about 20 to 150 dots. Your score is how far off you are on average.

Don't count. Take in the whole crowd at once.

Your result: — % off

How it's measured

Try another challenge

How does the estimation game work?

A crowd of dots appears in a circle for 1.5 seconds and then disappears. That is far too short to count them, so you have to estimate: type how many you think there were and press Enter. The true number is shown with the dots again, faded, before the next crowd. There are 10 crowds, between 20 and 150 dots each, and every run includes small and large ones.

How is your result calculated?

Each guess is compared with the true count, and the miss is turned into a percentage of that count: saying 90 when there were 100 is 10% off, and so is saying 22 when there were 20. Your result is the average of those misses. You also see your closest guess, how many guesses landed within 10%, and your tendency: whether you usually guessed too many or too few.

Percentages are used because estimates naturally spread out as numbers grow. Being off by 10 is a big miss on 20 dots and a small one on 150, so counting the miss in dots would make the large crowds dominate your score.

How do people estimate numbers without counting?

Up to about four dots, most people see the number at a glance, without counting. Beyond that, the brain produces a rough sense of quantity instead, and that sense gets less precise as the number grows: the typical error is a roughly fixed fraction of the true number. Psychologists call this the approximate number sense.

That sense can be off in a consistent direction. In studies of quick dot estimates, guesses for large crowds are often too low, and showing people the true count even once shifts their later guesses, a calibration effect reported by Véronique Izard and Stanislas Dehaene in 2008. That is why this game shows you the answer after every crowd: your later guesses get the benefit of the earlier ones.

How to win a guess-how-many game

  • Count a small part, then multiply. In a jar or a crowd, count the items in one small patch, judge how many such patches fill the whole, and multiply. Here the dots vanish fast, so glance at one quarter of the circle and multiply by four.
  • Learn from the feedback. If you keep guessing too few, nudge your next guesses up. The tendency in your result tells you which way you lean.
  • Don't start counting. Counting the first few dots wastes the moment you have to take in the whole crowd.

What this game does not measure

It measures how close your quick estimates came over 10 crowds, on your device, in one sitting. It isn't a maths test or an assessment of anything. To see how many dots you can take in at a glance, try the Dot Counting Test; to judge size by eye instead of number, the Line Length Test.

Questions

Why can't I count the dots?
They are only on screen for 1.5 seconds, too short to count 20 or more. That is the point: the game measures estimation, not counting.
Why is my score a percentage?
Because a miss of 10 dots means much more on a small crowd than a large one. As a percentage of the true count, every crowd weighs the same.
Do people usually guess too high or too low?
For large crowds seen briefly, studies often find guesses that are too low, and a single look at a true count changes later guesses. Your own tendency is shown in your result.
Why is the average of many people's guesses so accurate?
Individual errors partly cancel out. In 1907 Francis Galton reported that the middle guess of about 800 people at a fair, estimating an ox's weight, was within 1% of the true weight. It works when the guesses are made independently.
What is a good estimation score?
No published average exists for this exact game, so read yours this way: 10% means your guesses were off by a tenth of the true count, on average. With 1.5 seconds per picture nobody can count, so everyone relies on a sense of quantity that gets less precise as numbers grow. Compare runs, and watch whether you lean high or low.