Imagine you have $\$50$ and every $2$ minutes you either gain or lose $33$ cents. How would you model the evolution of the hypothetical bankroll for the next hour?
My approach based on what i've read about about random walks:
$\sigma=.33\cdot(\frac{60}{2})^.5$
$\mu=50.$
Plug these into a normal distribution to find the probability of having $x$ amount of money after an hour.
Some sources say if $\frac{1}{2}$ then $\sigma$ would have to be divided by $2$. But others just use the square root.