This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A286676 #30 May 01 2024 16:11:26 %S A286676 1,3,9,2,20,12,23,27,31,35,187,1461,485,105,64,69,67,18,11,41,87,23, %T A286676 97,828,251175,497650,1582733,480083,3070955,139927,1253,1301,160,83, %U A286676 172,89,184,181,187,193,199,205,211,217,223,229,235,241,247,253,259,265 %N A286676 Numerators of the Nash equilibrium of guesses for the number guessing game for n numbers. %C A286676 Consider two players: one player picks a number between 1 and n, and another player guesses numbers, receiving feedback "too high" or "too low". The number picker is trying to maximize the expected number of guesses, whereas the number guesser is trying to minimize the expected number of guesses. While a binary search would in expectation be the optimal strategy if the number were chosen randomly, it is not the case if the number is chosen adversarially. %H A286676 R. Fokkink and M. Stassen, <a href="https://doi.org/10.1007/978-3-642-25280-8_10">An Asymptotic Solution of Dresher's Guessing Game</a>, Decision and Game Theory for Security, 2011, 104-116. %H A286676 Robert Fokkink and Misha Stassen, <a href="https://www.gamesec-conf.org/2011/files/10_STASSEN_GameSec2011_11142011.pdf">Dresher's Guessing Game</a>, conference presentation, 2011. %H A286676 Michal Forisek, <a href="https://ipsc.ksp.sk/2011/real/solutions/booklet.pdf">Candy for each guess</a>, p. 15-19, IPSC 2011 booklet. %H A286676 Michal Forisek, <a href="https://ipsc.ksp.sk/2011/real/problems/c.html">Candy for each guess</a>. %e A286676 a(n)/A286677(n): 1, 3/2, 9/5, 2, 20/9, 12/5, 23/9, 27/10, 31/11, 35/12, 187/62, 1461/470, 485/152, 105/32, 64/19, 69/20, 67/19, 18/5, 11/3, 41/11, 87/23, ... %e A286676 For n=3, the Nash equilibrium of guesses is 9/5. This is attained when the number picker chooses 1 with 2/5 probability, 2 with 1/5 probability, and 3 with 2/5 probability. The number guesser guesses the numbers 0,2,1 in order with 1/5 probability, 2,0,1 in order with 1/5 probability, and 1,0,2 (i.e., binary search) with 3/5 probability. %Y A286676 For denominators see A286677. %K A286676 nonn,frac %O A286676 1,2 %A A286676 _Lewis Chen_, May 12 2017 %E A286676 More terms from _Lewis Chen_, Oct 29 2019