MySQL: update a field only if condition is met

Yes!

Here you have another example:

UPDATE prices
SET final_price= CASE
   WHEN currency=1 THEN 0.81*final_price
   ELSE final_price
END

This works because MySQL doesn’t update the row, if there is no change, as mentioned in docs:

If you set a column to the value it currently has, MySQL notices this
and does not update it.

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