True -- or my personal favorite algorithm:
Secretly roll until you get two 1's. Then say there is at least one 1.

So the chance of double 1's is 100%.

The algorithm which matches 1/11 is:
Roll until you get at least one 1. Ask whether both dice are 1.

Which is… a weird way to do it. Hence why I don’t think folks intuition tends to lean this way.

Well, if the algorithm is:
Look under, pick a number you see, ask the chances the other die matches it.
Then I’d say that’s just 1/6. Since there’s a 1/6 chance the dice under match. What you say isn’t really revealing any useful info.

What would you have said if there were no 1’s?
(I get the sense this is where the counter intuitive nature of this lies. Your actions aren’t well defined, so we have to put assumptions in.)

Video description: square full of green dots and blue dots spread out evenly but still randomly. They begin to slowly collapse into a web structure, then into something like galaxies. Green dark matter forms halos around the more compact blue gas clouds.

The clues were all there...

It's this light that forms the Cosmic Microwave Background that we see today.

This ancient light tells a pretty cool story about its journey. To learn a bit more, the first part of our project is available here: testtubegames.com/cmbjourney.h...

Video description: Dull grey hydrogen atoms move around the screen, photons move in straight lines, not interacting with them.

And here we are at about 380,000 years after the Big Bang.

The universe has cooled enough that neutral atoms are common, and loose charges are rarer. Photons can finally travel in mostly straight lines.

Some of them traveled in mostly straight lines for billions and billions of years, in fact!

Video description: Again red positive charges and blue negative charges bounce around the screen, scattering the white wiggly photons that are moving through. There are some dull grey atoms now, though, too, which occasionally form from the charges.

As the universe expands, it cools. Some neutral atoms (grey) are able to form briefly -- and these don't scatter the photons as much. Still the photons get bounced around.

(This is at about ~360,000 years after the Big Bang.)

Video description: A few dozen red positive charges and blue clouds of negative charge are bouncing around the screen. There are white wiggles representing photons moving around as well, some of which have paths traced behind them. The photons bounce frequently.

Video description: two disks of blue particles nearby one another - they start uniform, then each collapse into spinning objects. The orbit around each other, though one is larger, and pulls a bit off the small one on the near-point of each orbit.

Video description: Large blue circular shape in the middle, surrounded by many dots swirling in a diffuse ring pattern. We zoom in and see the central 'planet' is made up of thousands of dots packed closely together.