“The Gittins index, then, provides a formal, rigorous justification for preferring the unknown, provided we have some opportunity to exploit the results of what we learn from exploring. The old adage tells us that “the grass is always greener on the other side of the fence,” but the math tells us why: the unknown has a chance of being better, even if we actually expect it to be no different, or if it’s just as likely to be worse. The”