Zig Zig Not Twice

Two plain rotations leave the accessed path essentially as long as it was, so the potential never drops. Zig-zig leaves the tree height balanced after every splay, and that standing invariant is what the amortized argument charges the work to.

Two plain rotations leave the accessed path essentially as long as it was, so the potential never drops. Zig-zig roughly halves the depth of everything on the path, and that drop is what the amortized argument charges the work to.

Two plain rotations leave the accessed path essentially as long as it was, so the potential never drops. Zig-zig repairs the BST invariant that the second single rotation would break, and that repair is what the amortized argument charges the work to.

Two plain rotations halve the accessed path exactly as zig-zig does, so the potential drops either way. Zig-zig saves a handful of pointer writes, and that constant factor is what the amortized argument charges the work to.