Probability question: names in hats

[Whateverist]

What I don't understand about this would fill a book. If the first branches of the tree (from the left) represent the four names the first person might draw, why is 1/4 written on the bottom most of these branches? Does that represent the case in which the first player draws his own name? If so a couple of questions come up for me. First, why track that possibility at all since it can't count toward a sequence that resolves the game either as a win or a loss? (By the way which are you counting as a win, last guy draws his own name -or- last guy does not draw his own name?) Second, if it isn't a sequence the game can actually include, why value at a probability of 1/4?

That, again, is only the tip of the ice berg regarding what I don't understand about either the problem or your solution.