From the option chain of a security, we can calculate the implied probability density at the maturity $T$ (assume the options are European. Now suppose we have our own view/prediction on the probability density of the underlying price at time $T$. What is the best way to trade this view?
For example, say the implied probability of the underlying will end above $150$ is $5\%$ and our own view of that is $10\%$. We would think that the upside calls are underpriced. However, if we express our view by simply buying an upside call, the chance for us to have profit is still very small even if our view is totally correct. Trading volatility does not seem to be quite relevant also since the view is about the terminal probability distribution.
To be more specific, in the situation described above, what are the good ways trading the view? Buying a 150 call only gives you a $10\%$ chance of winning even if our view is $100\%$ correct. Are there any other ways so that the winning probability is higher but still give us a positive expectation?