So I'm curious if there is a decent gambling strategy for this site I play on.
Essentially it's a coin flip where you can have anywhere from 49% to 51% chance to win against the other player.
Assume you can choose to have 51% odds, and that your winnings will be equal to your bet (x2 on win).
Last time I played I started with 1 dollar and used the martingale system. It worked great for a while, as whenever I lost and bet 2 dollars I won. However, eventually as expected around the time I reached $11 I lost too many in a row and struck out.
The last time I played I didn't pay much attention to my odds, but I have the ability to grab ~51% every bet.
So assuming all this, should I stick with martingale? Or just bet the minimum ($1) every time, only taking 51% odds and hoping that the 1% edge averages out to a profit?
Is there any strategy I can implement at all?
P.S. Unlimited money is not assumed since I start with only a few bucks at most.
Best Answer
You should start as low as possible to reduce volatility given your situation.
Then you can gradually move up towards the Kelly strategy:
$$f^{*} = \frac{bp - q}{b}$$
where