tl;dr¶
Goblin’s caterpillar method of generating stats doesn’t actually reduce the probability that some players will roll really good stats, and others will roll really bad stats.
There is a better method. Follow Goblin’s method as indicated, but instead of one stat being the sum of the top of the caterpillar, set one stat to be equal to the sum of the bottom (or “belly”) of the caterpillar.
For example, to replicate the 4d6-drop-lowest:
Stat 1: Add up the front face
Stat 2: Add up the bottom face - this is the only change to Goblin’s method.
Stat 3: Add up the back face
Stat 4: Add up all exposed faces on the left-most cube
Stat 5: Add up all exposed faces on the right-most cube
Stat 6: Add up all exposed faces on the centre cube. If the front face is a 4, 5 or 6, then also add the bottom face.