To accept, support, or commit to an idea, plan, or decision, often after initial skepticism.
From poker terminology where players 'buy in' to a game by paying the entry fee (1940s). Extended to business in the 1970s-80s, maintaining the sense of making a commitment or investment, though psychological rather than financial.
The gambling origin is perfect for business - both require you to put something at stake (money vs. reputation) to participate fully. Without genuine buy-in, team members are just spectators, not players in the game of organizational success.
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