|
| |
|
|
A110617
|
|
The decimal expansion of 1/64532 (related to an optimal mixed strategy for Hofstadter's million dollar game).
|
|
1
|
|
|
|
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;
text;
internal format)
|
|
|
|
OFFSET
|
0,6
|
|
|
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.
|
|
|
REFERENCES
|
Laszlo Mero, Moral Calculations: Game Theory, Logic and Human Frailty, Springer-Verlag New York, Inc., 1998, pp. 15-21.
|
|
|
LINKS
|
G. C. Greubel, Table of n, a(n) for n = 0..10000
|
|
|
EXAMPLE
|
.0000154961879377673092419264860844232318849563007500154961879377673092419...
|
|
|
MATHEMATICA
|
Join[{0, 0, 0, 0}, RealDigits[1/64532, 10, 96][[1]]] (* G. C. Greubel, Sep 01 2017 *)
|
|
|
CROSSREFS
|
Sequence in context: A198609 A332794 A054508 * A234356 A338502 A102081
Adjacent sequences: A110614 A110615 A110616 * A110618 A110619 A110620
|
|
|
KEYWORD
|
cons,nonn
|
|
|
AUTHOR
|
Rick L. Shepherd, Jul 31 2005
|
|
|
STATUS
|
approved
|
| |
|
|
