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Implement an ELO (or similar) based system for running multiple tiers of events with a smaller number of participants (~16) at a time to derive higher-level rankings. e.g., if there are 20 participants, break them into two pools of 10 randomly-selected players, each. At the end of the first round, players are sorted by their scores, then placed into two 10-player pools, based on their first-round score. This continues, sorting players by their overall scores, for a predetermined number of rounds, to identify overall ranking.
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