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DanielLC comments on Harry Potter and the Methods of Rationality discussion thread, February 2015, chapter 104 - Less Wrong Discussion
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Eliminating the snitch won't even solve the problem entirely. Sure, if there's an hour time limit, the game won't take forever, but they could still rack up points by alternately letting each other score 30 points. Come to think of it, why didn't they? They could have way more points by now.
No reason to trust the team that goes first to let the team that goes second score, and no rush. Just play normally without catching the Snitch until one of you can win by catching the Snitch, that team goes for it.