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This is fun but you need to put "click the line" higher on the page. It took me a while to figure out what I was looking at.
this is fun and helping me get grounded :). adding a timer would be a good idea, I think.
0.11% by luck, because I actually got lucky the target number was too close to zero, out of a big scale.
Love it!

It would be great to have a 'training' mode, where you get to repeat ones you miss. This would increase the learning speed.

Easy training- repeat the one you just borked Medium training- cycles through say 5 examples until you get all five within your target range (1%, 0.1%, whatever)

I love these kind ones! Really engaging also yes as someone commented, the training mode would be an awesome idea.

Also, I tried this on laptop as well as my phone, I liked it more on my phone (I know the whole point is about precision though)

800

0 out of 1,600

I still missed. Even when there was centered text.

Maybe the human is the weakest link

10 round avg 4.5%.

A time limit would make sense imho. For extra challenge, add diagonal or curved lines.

10 perfect hits in a row!

...

handleClick({clientX: els.bar.getBoundingClientRect().left + els.bar.getBoundingClientRect().width / state.n * state.target })

Cool idea, love how simple it is. Minimal and clean.
my avg was around 2% not able to do more than that lol
Definitely need an iOS version! An angle version on a circle would be nice too.
What does native give you that this doesn't?
Great idea! Have you considered storing triplets <range, correct number, selected number> for each try and making image plots of these (x/y coordinates are correct/selected numbers, color of each pixel represents frequency) for multiple users for each range? I think the image might reveal interesting properties of human eyeballing, like near-perfect accuracy around 50%, but with less obvious correlations.
A modern take on Matthias Wandel's classic [0], which has you guess a variety of geometric attributes (e.g. angle bisection, centroid locating, shape regularization), not just simple partitioning of a line.

[0] https://woodgears.ca/eyeball/index.html

Oh, this is actually fun! How about if you change the target every few seconds to add a bit of pressure.
Simple premise, oddly hard to put down.
The fact that the numbers are in a brighter color than the end marks, and that the numbers go inwards, makes it slightly more difficult than it would otherwise be, because the eye is biased by the more prominent space between the numbers being different from the line between the marks.
Nice! Would be nice to see your progress over time (if you got better, also as a function of speed...)