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</o:shapelayout></xml><![endif]--></head><body lang=EN-US link="#0563C1" vlink="#954F72"><div class=WordSection1><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>I thought of a fun game today to play with a group of analytical math-enabled types.<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>If you have exactly one sibling, you are likely familiar with the usual routine for dividing the last of the pie: one cuts, the other chooses which portion. This procedure results in two pie pieces so close to equal mass that a good micrometer would be required to distinguish between the two.<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>OK, now imagine a form of this game where you are dividing a whole into two portions, where your opponent or adversary gets to choose which portion, but with an evil twist: you do not know how big is the whole pie. You cut or select some portion, and your opponent (who knows how much is there but of course will not tell you) gets to take that portion if it is larger or the rest of it if that is larger.<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>For fun, imagine someone you don’t like to be your opponent in this game, ISIS or Jonathan Gruber for instance. A hypothetical weird rich person has set up a bank vault with an unknown amount of money, written down the amount and given the paper with the amount to a neutral third party, and locked the vault so it is a set amount. The crazy bastard won’t even tell you an order of magnitude, but you know this is one with plenty of orders of magnitude (imaginary dollars are easy to come by.) <o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>She offers you a deal that doesn’t even cost you anything: all you do is name an amount of money (N). If it is smaller than half of what is in that vault (V), you get that amount N, and Dr. Gruber gets the rest. If your bid is larger than half, Gruber gets the amount you named and you get the rest. If N is larger than V, he gets it all and you get nada, but worse than that: you must endure the insufferable Dr. Gruber (or Mohammad the antiquity-destroying terrorist) waving V in your face and taunting you for being a greedy and stupid voter (or infidel) oh the reprehensible ass.<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>Here’s the game, ExI-chatters: I place some number V of imaginary dollars in a vault. You name your bid, N virtual dollars. Imagine some unsavory character gets the larger of either N or V-N. <o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>I don’t know the amount in that vault either, but I know the formula and I will know Tuesday 24 November at 5pm PDT how many imaginary dollars I put in that imaginary vault. Then I will report the results. If you wish to bid anonymously you may post your bid offlist with a nickname.<o:p></o:p></p><p class=MsoNormal> <o:p></o:p></p><p class=MsoNormal>Name your bid and state your reasoning, if any.<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>Is this identical to any ordinary trivial guessing game? State your reasoning if any.<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>spike<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p></div></body></html>