A228246 - OEIS

A228246

a(1)=1; for n >= 2, a(n) = round(x), where x is the average length (not counting draws) of a first-to-n match between two chess players of equal strength.

1, 2, 4, 6, 8, 9, 11, 13, 15, 16, 18, 20, 22, 24, 26, 28, 29, 31, 33, 35, 37, 39, 41, 43, 44, 46, 48, 50, 52, 54, 56, 58, 60, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 105, 107, 109, 111, 113, 115, 117, 119

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

A first-to-n match between two chess players continues until either player reaches n wins. For example, in the 1978 and 1981 matches between A. Karpov and V. Korchnoi, n was 6; in the 1992 match between B. Fischer and B. Spassky, n was 10.

In chess, as in some other sports, e.g., football, a score k:m is called "big" if |k-m| >= 3. It is interesting that, e.g., a(6) = 9 corresponds to a big score, 6:3, and a(10) = 16 corresponds to a big score, 10:6. Thus a moderately big score in such matches is not a sufficient reason to revise a relative relation of strengths of the winner and the loser.

REFERENCES

V. S. Shevelev, Paradox of a big score, Preprint, VINITI, 1992 (in Russian).

LINKS

Peter J. C. Moses, Table of n, a(n) for n = 1..1000

FORMULA

a(n) = round(2*n*(1 - 4^(-n)*binomial(2*n,n)));

a(n) = 2*n*(1 - 1/sqrt(Pi*n)) + O(1/sqrt(n)).

MATHEMATICA

(Round[2 # (1- Binomial[2 #, #]/4^#)]&)/@Range[20] (* Peter J. C. Moses, Aug 19 2013 *)

CROSSREFS

Cf. A000984.

Sequence in context: A047294 A195173 A215000 * A184587 A345436 A225773