Cool idea but you need to figure the fees which are about 2 cents right now.
Since its all for fun, I wonder if you could just make transactions without a fee. Can you send out an unconfirmed bitcoin?
No, it has to be confirmed.
But to answer your question.
You don't need to make that many transactions.
Players send btc in the pool (1 tx each) which are then converted to game money and then when the round is done the winner converts his game money to btc and withdraw (1 tx each).
It's like casino games / gambling.