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According to the designer of Dominion, Donald X. Vaccarino:

Bridge makes all cards cheaper, not just ones in the supply. This was to prevent problems in weird situations. I am not sure the kind of thing you'd need to get those problems will ever happen, but I knew that this way of doing it meant I was safe. This also allows some unusual combos to work.

Which non-supply cards does he refer to? The only example I can think of is the Black Market.

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up vote 10 down vote accepted

All cards not in the supply could include:

  • Cards in your hand
  • Cards in your opponents hand
  • Cards in play (including opponents)
  • Cards in your deck
  • Cards in your opponents deck
  • Cards in your discard pile
  • Cards in your opponents pile.
  • Cards in other locations (ie Village Mat)
  • etc.

Example Play from Intrigue cards:

Play a two Mining Villages, play two Bridges, play a Swindler. Opponent turns over an Estate which is now valued at $0, replace opponent's Estate with a Curse.

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Also, the Prize pile, Madman pile, Mercenary pile, and Spoils pile are all not part of the supply. Of course, these aren't the cards that Bridge rule had in mind. – GendoIkari Oct 22 '12 at 14:15
As of the release of Adventures, there are also the Traveller upgrade lines, which have non-zero costs so they would be affected by cost reduction as well. (Events, since they're not cards, are not affected.) – ConMan Aug 6 '15 at 4:56

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