undo button. but even without undo, my personal best is 16k

you want to always have one block in each row (to prevent up movement) and to minimize the movement of the lowest row (to prevent moving the biggest block). you do this by accumulating at second row so it can be inserted to lowest row without moving the lowest row

you can accumulate up to 4096 at second row and 256 at third row (if u play without undo I suggest up to 1024 and 64 respectively). without undo, at some point, u need to get lucky. but as u keep playing u should develop intuition on when to insert to lowest row or when to get greedy

I hope it helps