Natasi have a regular sized Prince and it goes l-m-h, and remembers the last setting when turning on.
i would assume the mini follows the same pattern...
and the prince is a very solid light, i have the copper version and it looks amazing. it is on the heavy side though, and gets pretty warm when running on high. its 1050 lumens on high and incredibly bright though, so the heat trade off isnt the worst. i usually only need low/med as i mostly just use it around the house at night. the high setting damn near fills my entire house with light so its just not necessary most the time. good to have the option though!