For implementation, basically, you add additional entries per player to a pool, and then choose from that pool randomly. So if you don't play events a lot, you may be three or four more times likely than people who do and get three or four more entries in the pool than that person's one. Of course this assumes a good PRNG.
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Hmm, but at the same time you don't want to punish players who are active and play events frequently. As it stands your opportunity to join events is proportional to your actual playing time. I don't think this system would be as fair since theoretically someone who played for 30 minutes a day would be able to join the same amount of events as someone who plays for 10 hours a day.
That being said, I have probably been in two minigames on Classic over the last three years, so I would say the system itself probably needs an overhaul. Perhaps it could be instantiated so that all of the players who join a queue are split into different independent events and each get an opportunity to play.
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It's not a punishment to people who play events frequently. It promotes the accessibility of events to a broader population. Some of us actually have jobs (like me), and some of the younger kids actually study for school.