byeong-uk yi (2009), on the other hand, argues that comparing the amount you would gain if you would gain by switching with the amount you would lose if you would lose by switching is a meaningless exercise from the outset. according to his analysis, all three implications (switch, indifferent, do not switch) are incorrect. he analyses smullyan's arguments in detail, showing that intermediate steps are being taken, and pinpointing exactly where an incorrect inference is made according to his formalization of counterfactual inference. an important difference with chase's analysis is that he does not take account of the part of the story where we are told that the envelope called envelope a is decided completely at random. thus, chase puts probability back into the problem description in order to conclude that arguments 1 and 3 are incorrect, argument 2 is correct, while yi keeps "two envelope problem without probability" completely free of probability, and comes to the conclusion that there are no reasons to prefer any action. this corresponds to the view of albers et al., that without probability ingredient, there is no way to argue that one action is better than another, anyway.