Can expected value be calculated in trading like one can calculate the (negative) expected value of casino games such as blackjack or roulette?
No. Casino games are technically Closed End Systems. Financial Markets are in theory, Open Ended Systems. Never the twain shall they (theoretically) meet. However, this does not preclude one from calculating the probability of 'price' being at a certain location (level) in the future - that is an entirely different question and a different mathematical model.
I use Density Probabilities for the Location of 'Price' at some future Time in my trading model and I do not consider 'price' to be a singular data point as most do. Just one of the things that gives me an edge in my trading. I consider real price to be somewhat smeared across Time and Space, giving me an ability to view price in way that is quite different than most other Traders and an ability to calculate the arrival of price at a specific location in the future, where Time is constant. You can't do that at Vegas!
This is one of the reasons why I chuckle when I hear someone say that Trading is Gambling. Those threads always crack me up a bit.