Of course you're calculating an expected value. If the expected value of an option isn't its price, what is it?
The no-arbitrage argument is another way of looking at it, but the two methods are equivalent. In particular, if the expected value of an option is higher than its price, you should buy the option - and if it's lower, you should sell it.
With just one transaction this would be statistical arbitrage rather than pure arbitrage, but if option prices regularly differed from the option's expected value, stat arb would be a fine strategy.
Sorry if my comment came across harshly, I didn't intend it to.
By expected value, I mean the price as you'd calculate it with a risk-neutral valuation based on some model of the underlying security.
For example, if you have a model that says an option is worth $4, and it's selling for $2, you should buy it if you're confident in your model. If you can do this repeatedly on a bunch of independent options you'll make money in the long run (assuming your model is correct and you're placing a large enough number of bets relative to the probability of making money on an individual option).
I learned this with a combination of practical experience, self-study, and coursework.