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., 1/6,  and win 2 dollars with prob., 5/6,

    for n=1 to n=, N0



  1/2               1/2
[5    - 1, -12 + 6 5   , 2.4984471899924290707, 2.8103432524556259423,

    3.7800201897400647617, 4.1878851884782432168, 5.0755948685913295890,

    5.5534682628476537253, 6.3813836346947062681, 6.9103274652115896638]



                             and in Maple notation



[5^(1/2)-1, -12+6*5^(1/2), 2.4984471899924290707, 2.8103432524556259423, 3.7800\
201897400647617, 4.1878851884782432168, 5.0755948685913295890, 5.55346826284765\
37253, 6.3813836346947062681, 6.9103274652115896638]