Greetings - I'm visiting from my usual home on the BA forum

I'm booked on my first EK flight. Sadly it's LHR-DXB in Y (thanks to a cheap client) and I'm trying to figure out seats. As you might surmise, I like a window seat.

I have no status, so I'll have to stump up if I want to pick a seat. So - what are the chances that I'll be able to grab a window seat at checkin, if I don't pay? I appreciate no-one can give me exact information, but if there's a decent chance of a selection of window seats left at that time, I might just risk it.