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Can I play the Gambler's Chest without the core game, and how do promo patterns and strain cards fit?

No, it needs the core game (the Phoenix, Butcher and Hand among other things), so it is an expansion rather than a standalone. Promo pattern cards with negative numbers can be used at your own risk because they weren't balanced for it, beta or promo insight patterns can be left out or drawn blind from the bottom, and strains remain part of Campaigns of Death and can still be used until you have those cards.

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