We just had our 4th annual bingo night last Friday. This year, rather than stress out over predicting how many winners we'd have, we planned one bingo prize per child. Our ticket reservation (no charge, but limited capacity) asked for the number of kids and adults per family. We bought enough prizes for each child. We got a great discount, but at face value our prizes were about $2.50-3.50 each, not just junky carnival prizes (ex: painting kit).
Each child (including non-student siblings) could win one bingo prize. Our volunteers randomly handed out prizes as kids raised their hands. We stamped their hand to show they'd won. You can control how fast the kids win by clearing the cards and starting a new game as soon as the first winner(s) raise their hands, or continuing to pull numbers without clearing the card so even more kids win in that round. We found that kids started to lose interest once they had won their prize, so next year we might give out tickets for kids who win more than once and pull tickets for anothe prize at the end of the event. We need an incentive for the kids to stay in their seats.
We had a firm "no trading" policy on the prizes. Kids could swap amongst other kids, but they couldn't take their pick from our prize boxes. Amazingly, the worst offenders were parents! Some parents were even obviously disappointed that they couldn't win a prize! Dinner, 2 hours of bingo, a prize for your kid, and loads of fun for free - what more did they want?!
In the last few minutes of the evening, we had every child who hadn't won stand on their chairs and we gave them each a prize. We had 8-9 parent volunteers monitoring the games and handing out prizes (we had 470 people there). One more thought: our prize chair worked hard to buy a variety of prizes, some boy/girl, some young/old. She separated the categories into different boxes. Alot more work than just a generic prize, but the kids liked the variety.
Our event was free, also. We spent about $2k on the whole thing. Hot/pizza, chips, carrots, cookie, pop, popcorn (real healthy dinner!), prizes, rented bingo board (we already own the cards), an incidentals. We ran 6:30-8:30, dinner followed by bingo - we first game was at 7:15. In the end, I think we only cleared the cards 4 times since we continued playing after the first winner so more kids would win.
We didn't planned 1:1 prizes last year. We allowed kids to win up to 2 times. Some kids got 2, some got 0. Tears. Not good. It was more work this year, but well worth the effort to collect the # of kid reservations and buy enough prizes.
Hope this helps. Follow up if you have more questions. This is all very fresh at our end.