Is this bet profitable?

Question

There's this !dice command in a discord server I'm in, and it has a $\frac{1}{6}$ chance of winning with a $5.4$ times payout. $5.4 \frac{1}{6} = 0.9$ times profit so I know in essence you can't profit over sheer time.

However me and some other people have made thousands without much effort simply by starting out with a bet of $\$5$ (fake money you earn by chatting) and increasing it by $\$5$ until we win, leaving us with a increase in profit around $\frac{9}{10}$ times (no math on the $\frac{9}{10}$, off the top of my head estimate).

The server owner says it's only luck but we've done it successfully every time. Is this actually a profitable method and if not is there one?

Answer 1

If you start out with a large amount of capital, you will indeed have a high probability of getting a small positive return, and a small probability of losing everything. On the average, since it is an unfair game, you lose money. But since it's only fake money, who cares?

Answer 2

The optional sampling theorem in martingale theory says that the optimal strategy for an unfair game in which you have only finite capital is never to play.