In this video (37:27 - 42:21), it is proved that buying a Euro with a Dollar and buying a Dollar with a Euro can both have positive expected value without varying the probabilistic structure of the problem statement.
My initial reaction was that this might be structurally equivalent to the necktie paradox. However, I cannot figure out how to map one paradox to the other.
Is there something else going on here? If a gambler came across a wager with this probabilistic structure (more likely than a forex trader, since the probabilities of future trading success are never pinned down precisely), how could they identify that their positive expected value is somehow misleading?
My initial reaction was that this might be structurally equivalent to the necktie paradox. However, I cannot figure out how to map one paradox to the other.
Is there something else going on here? If a gambler came across a wager with this probabilistic structure (more likely than a forex trader, since the probabilities of future trading success are never pinned down precisely), how could they identify that their positive expected value is somehow misleading?