As a limited-time promotion, if you gamble during your first week at this casino, and you suffer a net loss of money, the casino will give you half of your losses (up to a certain amount) as "free play", or cash only usable for more gambling.
It seems to me that for a simple game of slot machines, where the payback is mandated to be $95\%$ (avg) of what you bet, this tips the odds in your favor.
What is an optimal/very good strategy (highest % average return) using slot machines (or anything) for taking advantage of this scenario? Are the odds in your favor with this strategy?
Consider a machine with $95\%$ payout and a $50/50$ binary outcome (lose it all or not): It seems to me the simplest strategy, finding a machine that takes $1.00$ and has a $50\%$ chance of paying $1.90$ and $50\%$ chance of paying $0.00$, is in one's favor, since the half the time you would lose, you can get half of it back and bet $0.50$ for a $50/50$ payout of $0.95$ or $0$ (on a bet of $0.50$), for a total average outcome of $1.90\times0.5 + 0.95\times0.25 + 0\times0.25 = 1.1875$ on a $1.00$ bet, or a profit of $0.1875$.
I know one can solve the problem as a generalized binary (money or no money) two-action case (just like above) given a mandated payout of $95\%$ and some probability of winning (like $50\%$ above), and maximize the average outcome.
Losses incurred with "free play" are not $50\%$ redeemable like with the original funds.