I am currently playing an online game where you can bet against other players with pixel money.
The probability for win and loss is 50%. There is no (pixel money) fee or anything that would change the expected value to anything else than 0$ in the long run.
B-but I'd like to profit from it so I thought of a simple (!) strategy, but I am not proficient enough in math to know 'how' to check, if it is a winning, losing or neutral strategy.
I'd appreciate the thoughts of you!
The bankroll would be 100€.
I'd bet 1€.
If I lose my bankroll would become 99€ and I'd start a new bet with 1€.
If I'd win, I wouldn't add the won dollar to my bankroll, but bet 2€. (bankroll still at 99€, 1€ of original bet and the 1€ won)
If this 2nd bet is a loss, I'd start with an 1€ bet (and 99€ bankroll) again.
If the 2nd bet is a win (4€ now), I'd put 1€ into my bankroll (now 100€) and bet the other 3€.
If the 3rd bet is a loss, I'd start with 1$ again (bankroll 100€).
If the 3rd bet is a win (6€ now), I'd put 2€ into my bankroll (now 102€) and bet the other 4€.
If the 4th bet is a loss, I'd start with 1$ again (bankroll 102€).
If the 4th bet is a win (8€ now), I'd put 3€ into my bankroll (now 105€) and bet the other 5€.
If the 5th bet is a loss, I'd start with 1€ again (bankroll 105€).
If the 5th bet is a win (10€ now), I'd put 4€ into my bankroll (now 109€) and bet the other 6€.
and so on
I am not sure how I could explain my (simple) thought process better in english or math.
A win streak of 5 would make be enough to cover 9 losses.
But on the other side I'd need need at least 2 wins to get break even, 3 wins for profit. Everytime I only win once, I'd bleed money.
So I wonder what would be the expected value after 100 / 1000 tosses.
I'd appreciate any thoughts on this!
Have a nice day!