The mechanism by which the amounts of the two envelopes are determined is crucial for the decision of the player to switch theirher envelope.<ref name="Tsikogiannopoulos"/><ref>{{citation |last1=Priest |first1=Graham |last2=Restall |first2= Greg |year=2007 |title=Envelopes and Indifference |url= http://consequently.org/papers/envelopes.pdf |journal= Dialogues, Logics and Other Strange Things |publisher=College Publications |pages=135–140}}</ref> Suppose that the amounts in the two envelopes A and B were not determined by first fixing the contents of two envelopes E1 and E2, and then naming them A and B at random (for instance, by the toss of a fair coin<ref name=":0">{{Cite journal|last1=Nickerson|first1=Raymond S.|last2=Falk|first2=Ruma|date=2006-05-01|title=The exchange paradox: Probabilistic and cognitive analysis of a psychological conundrum|url=https://doi.org/10.1080/13576500500200049|journal=Thinking & Reasoning|volume=12|issue=2|pages=181–213|doi=10.1080/13576500500200049|s2cid=143472998|issn=1354-6783}}</ref>). Instead, we start right at the beginning by putting some amount in envelope A and then fill B in a way which depends both on chance (the toss of a coin) and on what we put in A. Suppose that first of all the amount ''a'' in envelope A is fixed in some way or other, and then the amount in Envelope B is fixed, dependent on what is already in A, according to the outcome of a fair coin. If the coin fell Heads then 2''a'' is put in Envelope B, if the coin fell Tails then ''a''/2 is put in Envelope B. If the player was aware of this mechanism, and knows that theyshe holdholds Envelope A, but do not know the outcome of the coin toss, and do not know ''a'', then the switching argument is correct and theyshe areis recommended to switch envelopes. This version of the problem was introduced by Nalebuff (1988) and is often called the Ali-Baba problem. Notice that there is no need to look in envelope A in order to decide whether or not to switch.
Many more variants of the problem have been introduced. Nickerson and [[Ruma Falk|Falk]] systematically survey a total of 8.<ref name=":0" />
