I had some trouble understanding the question. I did not originally get the same numbers that you did.
Then I reread your comments, and it occurred to me that the $100 and $200 were �for� payoffs, and not �to� payoffs. That is, the player puts $30 into the �machine�. If he wins, the machine gives him $200 back, for a net win of $170. With this interpretation, I did get the $3.30 that you got.
Then I worked on the SD and Variance. I did get $71.50, but for the SD. When I first read your post, I thought you were saying that 71.50 was the Variance (or, more technically, the second moment). I get 5112 $^2 for the second moment, which is approximately the Variance.
The bankroll for a RoR of R is approximately - ln(r)/2 * (Var/EV) . For Var/2/EV I get 5112/2/3.3 = $774.
For a 5% RoR, -ln(5%) is about 3, so you would need 3(774) or about 2400$.
For a 2% RoR, -ln(2%) is about 4, so you would need about $3100.
I invite everyone to double-check the calculations.
I want to also comment on what No Name said
What you should do is post the detailed rules of the game you are playing.It is clear that you are beginer so there is a good chance you made a mistake estimating your edge.
If by any chance you do have 11% edge go borrow money, sell the furniture, pawn the wedding rings and play the game, you have a huge edge
I agree with the comments about him being a beginner, and agree with your suggestion that he should post the details.
However, as to how lucrative the game is, I would point out that we don�t anything about the game speed. If he can make 100 bets an hour, then this a $330 per our game with negligible variance. This is quite valuable!
However, if he can only make 1 bet an hour, then it is only worth 3.30 an hour. Not really enough, in my judgment, to pawn the wedding rings.