Cumulative word Scrabble

This is a variant of Scrabble in which you get points for words as normal, and also for every valid word given by the 1st to nth letters of the word you put down, provided all the preceding sequences also make valid words.

For example, let us suppose an ‘A’ is on the board at the end of the word your opponent has played. You can put ‘H’ next to it to get points for the word ‘AH’ running orthogonally to your opponent’s word. If you put ‘HEMP’ down you would of course get the points for ‘AH’, but also for ‘HE’, ‘HEM, and ‘HEMP’, whereas under normal rules you would only get points for ‘AH’ and ‘HEMP’. Were you to put down ‘HEAPED’ however, you would only get points for ‘AH’, ‘HE’, and ‘HEAPED’. Thus, this rule promotes strategic play, and closer analysis of words hidden inside other words.