SPOOL RIDDLE - Which way will it roll?

It will wind up. This phenomenon is based on the KE that is only rotational, and there is not going to be any sliding, so the force that gets translated to torque is not going to be as much as the direct force on the string pulling it forward. It will only go backward if there is a translation of that torque to sliding, which we can see if we do this on a floor which can let the spool slide.