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@Discipulus_Didicit
I see it, but am inclined to disagree.
1. Forcing people to claim a game requires more research than forcing them to claim a player. Indeed, I see no reason to fake claim a player at all unless it is a player who only played in a few games. Grey claimed Danielle. Danielle was in a ton of games. There would simply be no reason to fake claim a player.
2. Yeah, they can hand pick a game that has a lot of roles, but this isn't a problem unique to this strategy. If you have a character like Danielle or me or Lunatic or someone else that was prolific, then you that necessarily comes with a ton of roles to choose from. Consider: In even the largest of Mafia games only had 20-30 people. However, players like me were in over a hundred mafia games over the years. Claiming me presents them with more role options than picking even a huge game.
3. Locking people into games first, then players increases the possibility of a CC since games are fewer than players and players are necessarily unique. The reverse makes it less likely since a given player will have more games than a game will have players and games aren't necessarily unique.