I wonder how much better a less greedy algorithm would be-- e.g. one that considered many possible moves a few positions deep, and took one step towards the bes

I wonder how much better a less greedy algorithm would be-- e.g. one that considered many possible moves a few positions deep, and took one step towards the best... or one that after finishing unwrapped the beginning halfway and rewrapped it backwards from the middle, then unwrapped the end, and rewrapped it forwards from the middle, and repeated until convergence.