Initiative OrderInitiative order is determined by numerical values as normal. Ties are broken using the following lists ordered strongest to weakest:
For example, Gold has a max value of 13, and Red has a max value of 12, while Silver has a max value of 12, and Blue has a max value of 11 and so on.
For quick reference, the Deck List on page 12 of the Three-Dragon Ante rulebook has the different dragons and their values.
JokersBahamut, Tiamat, and the Dracolich act as Jokers. If any combination of these cards is dealt or drawn in the same round, Bahamut goes before Tiamat, which is followed by the Dracolich. Having three cards as Jokers works well considering the deck has 70 cards.
Emperor's Gambit Deck
JokersIo and Hatchling serve as Jokers for this deck with Io being higher than Hatchling.
Quick EdgeThe Quick Edge in Savage Worlds still applies perfectly well using the Three-Dragon Ante deck, so there's no change there.
Other Uses for CardsSavage Worlds has a lot of various situational or setting rules that use a standard poker deck to determine other results such as Chases in the core rules, random traps in Pulp GM's Toolkit, and Rituals and Signs & Portents in the Horror Companion. In those cases, it's best to just use a standard poker deck rather than reconfigure all of those tables.
Updated on 2016-02-24: The deck from the Emporer's Gambit expansion was added thanks to a comment by +Chris Woods which offered a defined initiative order for that deck.
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