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A110617
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The decimal expansion of 1/64532 (related to an optimal mixed strategy for Hofstadter's million dollar game).
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0
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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, 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, 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
(list; constant; graph; refs; listen; history; internal format)
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OFFSET
| 0,6
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COMMENTS
| 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.
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REFERENCES
| Laszlo Mero, Moral Calculations: Game Theory, Logic and Human Frailty, Springer-Verlag New York, Inc., 1998, pp. 15-21.
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EXAMPLE
| .0000154961879377673092419264860844232318849563007500154961879377673092419...
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CROSSREFS
| Sequence in context: A057763 A198609 A054508 * A102081 A068397 A022344
Adjacent sequences: A110614 A110615 A110616 * A110618 A110619 A110620
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KEYWORD
| cons,nonn
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AUTHOR
| Rick L. Shepherd (rshepherd2(AT)hotmail.com), Jul 31 2005
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