Betting & Stochastic Processes

[RomRom]

Dear Community,

I am faced with a challenge. I can't quite grasp the implications of this.
I schould've listened better in statistics lectures!
I would really appreciate your help. :)

I have a not normal stochastic process P on which I can bet.
Obviously, I don't know the distribution of P. It is somehow what I want to find in order to profit from the betting strategy.

I can either bet on the fact that P will increase in the future or that P will fall. (It works a bit like the stock-market, I like the analogy. I.e. I can either buy P or sell P. The value of P fluctuates over time).

What I did is take P through a "step function", so that I can map P to a random walk.
At each step, P can either go up or by the step size or go down by the step size. The step size is a fixed percentage of P's current value.
In other words, I had P represented in the value/time plane and I now have it in the value/step plane.

Now it turns out that P is gaussian in the value/step plane!
At every step, the probability of P going up/down is 0.5.

I think I can't fully grasp the implications of this.
Has anyone any idea how it can help betting on P?
What would be a positive expectancy betting strategy?

Thanks,

Julia

 

[EnumaElish]

I don't know much about betting, but the probability of up/down = 0.5 could suggest any symmetric distribution (e.g. uniform), not just Gaussian.