I think the OP should make it so there is a new address every time and that new address is given right when the round starts.
That way it's more fair to everyone.
If you do that, you ensure that someone that has a bot has an unfair advantage. A bot will be much faster at grabbing an address and building a transaction and sending it off. Additionally it could probably send dozens of transactions before a person could build the first one.
Right now there isn't any advantage of script over a person for the first transaction each makes unless you consider a script won't mind watching the clock. Now there could be an advantage on the second or third transaction, but if you are risking that much BTC, well that is a whole different discussion. Right now any person could be a script on that first transaction. You just have to time it right.