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., 1/3, and win 2 dollars with prob., 2/3, for n=1 to n=, N0 1/2 1/2 1/2 1/2 [3 , -3 + 3 3 , -12 + 9 3 , -39 + 25 3 , 5.5115057222525332534, 6.3576026305178084767, 7.4702675131095607537, 8.3877910948236157543, 9.4481680234352303095, 10.403969044086569421] and in Maple notation [3^(1/2), -3+3*3^(1/2), -12+9*3^(1/2), -39+25*3^(1/2), 5.5115057222525332534, 6\ .3576026305178084767, 7.4702675131095607537, 8.3877910948236157543, 9.448168023\ 4352303095, 10.403969044086569421]