Nice suggestion! How should that behave on mobile? Any idea on how to best tackle it?

I think you should lean into this problem and just call the game "clockwise"

Consistent across platforms, consistent "ideal" count, clever-ish game name

I would like to see either as you describe (which I think would be the most relaxing), or have the direction-changing buttons also count as a click each time they are pressed. I found it tempting to switch direction, turn a piece, then switch back, often using two clicks instead of the three it would take to turn it clockwise-only, but very inefficient since I switched back and forth many times. Making those count as clicks, though, does up the difficulty and would make hitting the target require you to use them only once, so perhaps removing them altogether is the solution.

If you did it as clockwise by default instead of listing the ideal turn count you could list the minimum number of “counter” turns. Then have a button to do the next turn as a counter turn.

I would have suggested having 2 zones per tile: one to rotate left, one to rotate right. But the tap zone is quite small already, so it's prone to errors.

One slower but more UX-friendly option would be to allow long-press on a tile, it would zoom in, and you can pick left or right with each button.

Double tap is also an option but you need to remove the ability to select the content of the page.

Maybe you could try swipe left/right or rotating gestures that snap to 90 degree increments.

That is, rotating with one finger by holding and dragging either in circle or straight line.

Better not the two finger rotation known from map apps.

Double tap

I think for mobile have two ideal click counts, one for a single direction and another with direction switches.

Or: pull down for rotate CCW, pull up for rotate CW. Just sum up event.movementY to calculate rotations.

Cons: A little slower than simply clicking, maybe, and makes it easier to overshoot. Need to count rotations instead of clicks.

Pros: Quite intuitive (that's how dials work in most DAWs for instance) and would work well on mobile, even if the tile size is small.

Not sure how easy it is to implement, but here is another idea: hold on the tile few seconds, then you have the choice to swipe left or right (has also some edge cases, when the elements are in the corner)

Short tap for CW, hold for CCW

Tap-and-hold a tile, move finger outside of it and then rotate by moving finger around tile's center (like using a handle that you just extended from the tile).

Click left half of square for ccw rotation, click right half of square for cw rotation.

Long press?

It's not uncommon for right-clicks to be blocked at the browser level.

A better option would be Ctrl-left-click for the other direction.

Who is blocking these? Paranoid corporates?

Or use scroll-up and scroll-down to rotate left/right?

I might just get rid of rotate all together

Right click is often blocked, but Shift+Click is not.

Blocked by whom?

By people who like browser's native context menus.

An alternative is to change the scoring system, and count consecutive clicks on the same tile as ‘one’

Alternatively, just count three consecutive clicks that are close in time as one.