Running time question
The move-to-front heuristic is 4-competitive in the model where swapping adjacent elements costs one unit. This means that if the optimal strategy has cost $N$, then move-to-front has cost at most $4N$. In particular, if a swap list has cost $N$ on some searching sequence, then move-to-front will have cost at most $4N$.
See for example MIT OpenCourseWare or Princeton Slides.