How many distinct chess games are possible, and which is the longest?

Seven queens on a board is possible: Granted I've only spent a few minutes on this, but I don't think eight is possible. Very interesting discussions you all have on this thread. 

No matter how I attack this, at best I keep coming down to two free squares side by side after six queens are placed. Thus, wherever I place the seventh queen, both squares are taken. Alternatively, placing queens on "knight move" opposition allows you to maximize squares, but after b1 -- d2 /a3 queen satalites and f7root and e5/c6 satalites only h4 is a valid square.

Eight queens are possible.

You are correct LoekBergmen. Had I thought a little bit deeper on my knight/space queen idea, I'd have seen it quicker. The starting square is Qc1. 

Hi, I believe I have 33^49 as an upper bound which is approximately 2.6 x 10^74, which is considerably less than Shannon's number 10^120.  How does this compare to other upper bounds?  I'm not certain what the reigning (lowest) upper bound we have so far.

I just found a new upper bound.  (16^50‐1)/15 which is roughly 10^59.  What is the best upper bound known so far?

i plaayed 96moves game

If there is no limit on the number of moves, then the answer is aleph null, the lowest kind of infinity.

Perhaps most things that interest humans are lower than infinity.