MySQL incrementing value

Question

Is there a way to make a value increment with every insert if having multiple inserts? (I dont speak of the primary key that autoincrements)

Lets say I have a struct

Answer 1

Purely to add to @Bohemians answer - I wanted the counter to reset every so often and this can be done like such:

SELECT *,(@position := IF (@position >= 15,1,@position + 1))

Where 15 is obviously the maximum number before reset.