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 A247064 Dynamic Betting Game D(n,5,4). 8
 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 64 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Players A and B bet in a k-round game. Player A has an initial amount of money n. In each round, player A can wager an integer between 0 and what he has. Player A then gains or loses an amount equal to his wager depending on whether player B lets him win or lose. Player B tries to minimize player A's money at the end. The number of rounds player A can lose is r. a(n) is the maximum amount of money player A can have at the end of the game for k = 5 and r = 4. LINKS Table of n, a(n) for n=1..62. Charles Jwo-Yue Lien, Dynamic Betting Game, Southeast Asian Bulletin of Mathematics, 2015, Vol. 39 Issue 6, pp. 799-814. FORMULA a(n) = floor(n*32/31). G.f.: t^31/((1-t)*(1-t^31)) + t/(1-t)^2. - Robert Israel, Sep 11 2014 EXAMPLE In the case of n=31: For the 1st round, player A bets 1. If A loses, A will end up with D(30,4,3)=32 per reference A247160. If A wins, he has 32 and will bet 0 for the remaining rounds. So he will end up 32. If A does not follow the proposed bet, he will have fewer than 32 at the end. So a(31) = 32. PROG (PARI) vector(100, n, floor(32*n/31)) \\ Derek Orr, Sep 11 2014 CROSSREFS Cf. A247060, A247061, A247062, A247063, A247160, A247161. Sequence in context: A273881 A048266 A123068 * A160547 A348520 A230034 Adjacent sequences: A247061 A247062 A247063 * A247065 A247066 A247067 KEYWORD nonn,easy AUTHOR Charles Jwo-Yue Lien, Sep 10 2014 STATUS approved

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Last modified August 4 01:40 EDT 2024. Contains 374905 sequences. (Running on oeis4.)