Search: id:A110617
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%I A110617
%S A110617 0,0,0,0,1,5,4,9,6,1,8,7,9,3,7,7,6,7,3,0,9,2,4,1,9,2,6,4,8,6,0,8,4,4,2,
%T A110617 3,2,3,1,8,8,4,9,5,6,3,0,0,7,5,0,0,1,5,4,9,6,1,8,7,9,3,7,7,6,7,3,0,9,2,
%U A110617 4,1,9,2,6,4,8,6,0,8,4,4,2,3,2,3,1,8,8,4,9,5,6,3,0,0,7,5,0,0,1,5,4,9,6
%N A110617 The decimal expansion of 1/64532 (related to an optimal mixed strategy 
               for Hofstadter's million dollar game).
%C A110617 Constants such as this one and .64532 have importance with respect to 
               the efficient usage of resources of various types and the minimization 
               of opportunity costs: According to the Mero source, if 100000 players 
               are considering entering Hofstadter's/Scientific American's million 
               dollar game, an optimal mixed strategy for maximizing the magazine's 
               expected loss -- thus maximizing the expected gain for the common 
               good of all 100000 players -- is for each player to preselect an 
               integer from 1 through 64532 and roll a 64532-sided die. A player 
               should enter the game if and only if that player rolls his or her 
               preselected number, which, of course will occur with probability 
               1/64532. (With instead a 100000-sided die the probability that no 
               one enters is "about 37%" (Mero).). The game pay-out to the single 
               randomly-selected winner from the pool of entrants is defined to 
               be inversely proportional to the number of entrants: 1000000 if one 
               entry, 500000 if two entries, etc.
%D A110617 Laszlo Mero, Moral Calculations: Game Theory, Logic and Human Frailty, 
               Springer-Verlag New York, Inc., 1998, pp. 15-21.
%e A110617 .0000154961879377673092419264860844232318849563007500154961879377673092419...
%Y A110617 Sequence in context: A019776 A057763 A054508 this_sequence A102081 A068397 
               A022344
%Y A110617 Adjacent sequences: A110614 A110615 A110616 this_sequence A110618 A110619 
               A110620
%K A110617 cons,nonn
%O A110617 0,6
%A A110617 Rick L. Shepherd (rshepherd2(AT)hotmail.com), Jul 31 2005

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