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 A322755 Numerator of expected payoff in the "Guessing Card Colors" game with a 2n-card deck, using an optimal strategy. 1
 3, 17, 41, 373, 823, 3565, 7625, 129293, 272171, 1139735, 2376047, 19743201, 40890483, 168947957, 348259369, 11464229693, 23547218611, 96587303059, 197831583443, 1618881562939, 3308327420393, 13508555185547, 27554570432479, 449278087454089 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS A 2n-card playing deck is shuffled and then revealed one-by-one to a player who guesses the color (red or black) of each card prior to its being revealed.  The player earns one dollar for each card whose color he guesses correctly; there is no penalty for being wrong. REFERENCES Thane Plambeck and others, Posting to Math Fun Mailing List, Dec 26 2018. LINKS Michael Andreoli (proposer), Guessing Card Colors, Problem #630, College Mathematics Journal Vol. 30, No. 3 (May, 1999), pp. 234-235. Solution by John Henry Steelman. FORMULA The optimal pay-off is n - 1/2 + 2^(2n-1)/binomial(2n,n). EXAMPLE 3/2, 17/6, 41/10, 373/70, 823/126, 3565/462, 7625/858, 129293/12870, 272171/24310, 1139735/92378, 2376047/176358, ... PROG (PARI) a(n) = numerator(n - 1/2 + 2^(2*n-1)/binomial(2*n, n)); \\ Michel Marcus, Dec 28 2018 CROSSREFS Cf. A322756. Sequence in context: A181981 A089637 A135471 * A226492 A092347 A215429 Adjacent sequences:  A322752 A322753 A322754 * A322756 A322757 A322758 KEYWORD nonn,frac AUTHOR N. J. A. Sloane, Dec 27 2018 STATUS approved

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Last modified August 10 07:54 EDT 2022. Contains 356030 sequences. (Running on oeis4.)