Reminder to Self - Explore & Write about Probability Problems

Don't really expect anybody to read this. Just a reminder to myself to write about probability problems.... 1) http://en.wikipedia.org/wiki/Two_envelopes_problem 2) http://en.wikipedia.org/wiki/Saint_Petersburg_Paradox 3) http://en.wikipedia.org/wiki/Expected_utility_hypothesis 4) http://en.wikipedia.org/wiki/Monty_Hall_problem Crux of my point here is what I believe to be the crucial distinction between odds before an event happens vs. the odds after an event happens when you're not yet aware of the outcome. Maybe this is a semantic & meaningless distinction. Have to give it a lot more thought. But for economic and political policy reasons I currently think the distinction is important and woefully under-examined. Example: You and I want to bet on a fair coin-toss. If we bet before the coin is tossed then we can fairly reduce the variables down to the intuitively fair bet of 50/50. But if I toss the coin first and cover it before we bet then you can choose to implement heuristics and treat it as an identical situation. Consequently you think the odds are still 50/50. But the reality is the odds are 100/0 and you simply don't know which is which. I currently think this is a subtle but important point. Because I think it can nullify some of the counter-intuitive paradoxes (in the links above). In the two-envelopes problem it is obvious to everyone that switching for infinity can't actually increase your expected utility. I'm envisioning the permutation tree of possible outcomes for a given event. Standing at the point where it branches into two possible timelines is different from standing past that point and simply being blind to your position when you make a bet. My intuition is telling me that because the latter is a sucker bet for one side it is thus necessarily more game-able (cheat-able). Consequently, it requires greater protections/constraints on potential cheaters. This is related to the supposed geniuses who wrecked our economy by creating financial models that didn't appropriately track to the real world while nonetheless convincing investors otherwise.