If you planning to use 1 address i think you can track them by using sign message with his own bitcoin address..
This is one of the verification you should need in order to know if he is the owner of bitcoin that he pay.
But its still recommended to give them different addresses its not hard to generate new bitcoin address or if you are using a website with Json-RPC protocol you can generate bitcoin address in your website with correct command script ..
Whaaat
That makes no sense
What good is proving he owns a
BTC?
Doesn't mean he's going to send it
He needs to deposit the
BTC before the game starts.
this is not necessary to verify the address ,, because without it salat btc has been available all will run smoothly enough to send bitcoin for every game you want to play ,, and no need to bother yourself to verify ownership ,, which is basically it not useful for you to do