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A110617 The decimal expansion of 1/64532 (related to an optimal mixed strategy for Hofstadter's million dollar game). 1


%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 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 Laszlo Mero, Moral Calculations: Game Theory, Logic and Human Frailty, Springer-Verlag New York, Inc., 1998, pp. 15-21.

%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

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