Answer:
The key obstacle you face is that of this being defined as a lottery. Banks are generally prohibited from participating in lotteries. Opening the drawing to any entry is the way to avoid this problem.
A lottery is when you have three or more people who advance money, but know that one or more, but not all, will win. Advance money can be interpreted as them paying any fee to bank with you. This is not necessarily a direct payment as in for a ticket. As a national bank I look to 12 USC 25a which prohibits participation. You should consult your applicable federal law (which will be similar) and state law.
First published on BankersOnline.com 07/07/03