Probability theory is the branch of mathematics concerned with probability. If asset prices are nothing more than a stochastic process, then the stock market, and specifically the options market, is nothing more than a game of probabilities. Play your cards right and you will be mathematically guaranteed to succeed as time reaches infinity.
In probability theory, the Gaussian distribution is a continuous probability distribution for a real valued random variable. The returns of an asset are random points derived from these curves. The shape is dependent on two parameters: stochastic drift and implied volatility. In the plot below, there are four curves. Each has a different implied volatility. Notice how the shape, which represents the structure of future returns, changes.