I could have an idea too:
For some of the card giveaways, you can give a little "task". For example, the ones, who want to participate, must answer a question, or the people must write a joke, a history with fun, a recommendation for a game, or even posting an opening of an anime or a show... There are many possibilities, but the main idea is "doing a task".
For this idea, you can easily use your creativity.
If you find, that the task is done, you can choose one or two or five winners.
If there are too many winners (in your opinion), they can do another task to get another chance. But generally, this is only an idea...