Here's my contribution: ----------------- Approach 1: Absent new information, we cannot improve our outcomes. In the montey hall problem there is either obs

Here's my contribution: ----------------- Approach 1: Absent new information, we cannot improve our outcomes. In the montey hall problem there is either obscure new information, or a obscure change in the rules between firs choice and second choice. Montey hall collapses to an initial choice of the prize behind door A or the prizes behind both door B and C. When the true, collapsed, choice is revealed the common sense reasoning is correct. In this problem there is no new usable information. In the two envelopes problem the new information appears relevant but is actually not on it's own any more useful to reasoning about expected value than knowing that there is a red or green piece of paper in either envelope. ----------------- Approach 2: Keeping the quantities symbolic. There are two envelops with quantities x and y inside. We are told that 2x = y. After choosing it is revealed that our envelope has quantity z. It is not revealed if z=x or z=y. Let's consider the universe of possibilities. Possibility one (50% chance): z = y. Value of switching: -x Possibility two (50% chance): z = x. Value of switching: +x Therefore the value or switching is: .5 * -x + .5* +x = +/-0 The red herring here is that knowing value z feels like it is information about values x and y, but it isn't. The slight of hand is in trying to say that the other envelope is worth either .5z or 2z. This is false because there is an unknown but fixed universal constant variable x. We don't know from the available information if we are in universe z=x or universe z=y. In short: The two envelopes paradox mistakes an unknown constant for an unknown variable. Knowing that z = 20 doesn't change the universal constants x and y.