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.