Use binary search and you can get that shower dialed in three moves.

More than 3 moves if the 0%-100% control range is a very narrow sub-range of the input range. i.e. 90% of the handle movement doesn't do anything at all.

This is actually surprisingly common, often the full range of hot to cold happens between 5-15% of actuation or 85-95% of actuation.

Most European shower controls don't work this way anymore, they are thermostatic (i.e. you are just setting the desired water temperature, not directly adjusting the hot/cold balance). These are spreading to high-end US installs too.

This is one of the weirdest things about showers. You set your shower temperature on the heater itself and then you pull the temperature handle all the way to the hottest temperature.

There is no point in actually trying to dial in the temperature using the handle. Just don't.

Btw. I'm talking about tankless heaters.