The expected number of rounds until the first time to be in possession of >=\ n dollars if at each round you lose one dollar with prob., 1/4, and win 2 dollars with prob., 3/4, for n=1 to n=, N0 1/2 1/2 2 21 8 21 [- 2/5 + -------, - 28/5 + -------, 2.9284844477173760422, 5 5 3.4148469569224961607, 4.4630244919019526114, 5.0666446244556823190, 6.0220376270552407937, 6.6990770325151053408, 7.5963742566933744062, 8.3193841456077752435] and in Maple notation [-2/5+2/5*21^(1/2), -28/5+8/5*21^(1/2), 2.9284844477173760422, 3.41484695692249\ 61607, 4.4630244919019526114, 5.0666446244556823190, 6.0220376270552407937, 6.6\ 990770325151053408, 7.5963742566933744062, 8.3193841456077752435]