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</o:shapelayout></xml><![endif]--></head><body lang=EN-US link=blue vlink=purple><div class=WordSection1><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'>Earlier I wrote:<o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'>…</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>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. <span style='color:#1F497D'><o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>I don’t know the amount in that vault either<span style='color:#1F497D'>…</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>Name your bid and state your reasoning, if any.<span style='color:#1F497D'><o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>Is this identical to any ordinary trivial guessing game? State your reasoning if any.<span style='color:#1F497D'><o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='color:#888888'>spike<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'>It occurred to me that without some kind of indication of a range of possible amounts in the vault, this is any ordinary trivial guessing game. But if we assume the amount of money in the vault is somewhere between 0 and 6,283,185 dollars with each amount being equally probable, the problem becomes a calculation.<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'>Those who posted me offlist, now what say ye?<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'>It occurred to me it was in bad taste to put Dr. Gruber in the subject line, so we can go with a fictitious bad guy, such as Simon Bar Sinister or Mr. Potter the evil banker from the Jimmy Stewart classic. With that information on the max amount in the vault, you can do a calculation to suggest the optimal strategy. <o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'>If you post onlist, post your bid first before you explain your reasoning please. The vault opens Tuesday 5 pm US west coast time.<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'>spike<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'><o:p> </o:p></span></p><div><p class=MsoNormal><o:p> </o:p></p></div></div></body></html>