Do not play every chord in root position. Choose the inversion whose notes are nearest the chord you just played — most of them should not move at all.
The harmony is decided by which notes are in the chord; the SOUND of a progression is mostly decided by how far they travelled to get there. Playing C, F and G all in root position moves the hand around the keyboard and produces three separate events. Choosing inversions can play the same three chords with the common notes held and only one or two moving, which is what makes a progression sound joined up rather than announced. On a common four-chord loop the difference is a factor of two or three in total movement, for identical harmony.
Smoothness is not always what you want. A deliberate leap is an effect, a rising bass line is worth breaking the rule for, and pop and gospel playing often keep root position in the left hand on purpose so the bass is unambiguous. Minimum movement is a good default and a poor master.
Estimate with the rule, then check it against the calculator that models it properly.
Open Piano Chords →