A366566 a(n) is the expected end time of a game with three gamblers, one of which starts with capital n, the others with capital 1 each. The end time, rounded to the nearest integer, is given for games in which one of the two poor players wins.
3, 6, 9, 13, 17, 22, 28, 34, 41, 49, 58, 67, 76, 87, 98, 109, 122, 135, 149, 163, 178, 194, 210, 227, 245, 263, 282, 302, 322, 343, 365, 387, 410, 434, 458, 483, 509, 535, 562, 590, 619, 648, 677, 708, 739, 770, 803, 836, 869, 904, 939, 974, 1011, 1048, 1085
Offset: 1
Keywords
Links
- Louis Bachelier, Calcul des probabilités. Tome I, Gauthier-Villars, Paris, 1912.
- Persi Diaconis and Stewart N. Ethier, Gambler’s Ruin and the ICM, Statist. Sci. 37 (3) 289 - 305, August 2022.
- Persi Diaconis, Gambler's ruin with k gamblers (slide 3), talk in the Rutgers Experimental Mathematics Seminar, Fall 2023 Semester, Oct. 12, 2023.
- Experimental Mathematics, GAMBLER’S RUIN WITH K GAMBLERS, recording of talk, Vimeo video (time after 11:55), Oct 22, 2023.
- Hugo Pfoertner, Example of the time history of a game with n=3, i.e., the "rich" player starts with 3 chips.
- Hugo Pfoertner, Distribution of the number of games won, n=3, plotted vs end time.
- Hugo Pfoertner, Distribution of the number of games won, n=5, plotted vs end time.
- Hugo Pfoertner, Distribution of the number of games won, n=6, plotted vs end time.
- Hugo Pfoertner, Distribution of the number of games won, n=10, plotted vs end time.
- Hugo Pfoertner, Distribution of the number of games won, n=20, plotted vs end time.
Formula
a(n) equals A366995(n)/A366996(n) rounded to the nearest integer. - Pontus von Brömssen, Oct 31 2023
Extensions
a(26)-a(55) from Pontus von Brömssen, Oct 31 2023
Comments