So, unfortunately, the answer to your excellent question is unknown. Tickling the palm and neck produced the least laughter. A statement at the end of your segment of Alan Alda's show seemed to state otherwise. The phenomenon of tickle and the laughter that it creates has been pondered for over two millennia by such illustrious thinkers as Plato, Bacon, Galileo, and Darwin. However, due to the scarcity of empirical work on this topic, tickle remains much of a mystery.
Most people think that surprise is an essential element.
Several writers have suggested that tickle responses are inherently interpersonal. Some have specifically claimed that one needs to believe that another person is performing the tickling in order to produce ticklish laughter and smiling. This last claim is what led me to do my machine tickle study. There are also a couple of hypotheses regarding the function of tickle. One possible function is that tickling may help facilitate the bond between parent and offspring.