It isn't complex at all. There's a checkbox on the multiply BTC page to randomise the client seed on every roll or if you are playing manually you can simply reload the page.
What I don't get is why they need to change the server seed for each new bet! Given the reputation of freebitcoin.in, am sure there is a good reason for this.
You are spot on with the point that we don't know if you are going to bet hi or lo. We also don't know if you are going to change the client seed or not. Both of those things mean that if we tried to anticipate then someone would work out when we would do it and they'd be guaranteed to win.
Some small sites use a static server seed but you're right that it would be impossible on a site this large. The "computing resources" more specifically disk space required would be astronomical and make the site financially unviable. Most people won't even know what it is and will never reveal their server seed at all meaning would have to store all their rolls for eternity. With over 135 billion rolls so far that would be infeasible.
It's also completely pointless. Both systems perform the function of being provable fair meaning that every player has the opportunity to prove if we cheated or not to themselves. Changing the system just because a handful of customers have a preference isn't a good idea.
The server knows the result as soon as it receives your client seed and bet details. On most sites, there's some sort of animation going on to keep you amused while you wait for that information to come back over the internet to you.