%I
%S 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,
%T 2,3,2,3,1,8,8,4,9,5,6,3,0,0,7,5,0,0,1,5,4,9,6,1,8,7,9,3,7,7,6,7,3,0,
%U 9,2,4,1,9,2,6,4,8,6,0,8,4,4,2,3,2,3,1,8,8,4,9,5,6,3,0,0,7,5,0,0,1,5,4,9,6
%N The decimal expansion of 1/64532 (related to an optimal mixed strategy for Hofstadter's million dollar game).
%C 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 64532sided 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 100000sided die the probability that no one enters is "about 37%" (Mero).). The game payout to the single randomlyselected 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 Laszlo Mero, Moral Calculations: Game Theory, Logic and Human Frailty, SpringerVerlag New York, Inc., 1998, pp. 1521.
%H G. C. Greubel, <a href="/A110617/b110617.txt">Table of n, a(n) for n = 0..10000</a>
%e .0000154961879377673092419264860844232318849563007500154961879377673092419...
%t Join[{0, 0, 0, 0}, RealDigits[1/64532, 10, 96][[1]]] (* _G. C. Greubel_, Sep 01 2017 *)
%K cons,nonn
%O 0,6
%A _Rick L. Shepherd_, Jul 31 2005
