Any help would be appreciated. I am interested in determining the average expected aggregate sum wagered if I reach a goal before going bankrupt without a time constraint. (Not considering any amount wagered if I do go broke.)

In particular, I would like to calculate the aggregate amount in units I expect to wager if I succeed in reaching my goal, G, before going bankrupt (without consideration of amounts wagered if I go broke and without a time constraint) and consistent with Formula 3 from Ch. 8 of BJAIII: probability of reaching a goal (G) = e^[mu (G-B)/sigma^2] times [sinh(mu/sigma^2 * B) / sinh(mu/sigma^2 * G)]; where mu=per hand ev in units, B=initial bankroll in units, G= my goal > B in units, sigma^2=variance per hand in units.

Is it sufficient to simply sove the following equation for exptected total units wagered to answer the question: advantage = mu / 1 unit = (G-B) / exptected average total units wagered.

Thank you in advance.