For one, poque was actually brought to America by French settlers, including in areas of the Louisiana Territory where poker would first emerge in the early 1800s. Like the German game of poch, the name also resembles the name for poker, and many have speculated an Englished pronunciation of the word incorrectly emphasizing the second syllable provided a basis for the name.
Poque itself has a few precursors, among them glic (dating from the 15th century), brélan (first turning up around the 17th century), and bouillotte (from the 18th century). While glic is a lot more like the German game of poch and other similar games -- that was the three-phase game with the round board and nine cups -- both brélan and bouillotte are simpler, mainly just versions of the second “vying” phase of those other games.
Variations of brélan and bouillotte exist, including being played with differently-sized decks (increased sometimes to accommodate more players). For example, a game of bouillotte might have been played by four players with a 20-card deck, using just the aces, kings, queens, nines, and eights, and if there were a fifth player the jacks would be included, too, to make a 24-card deck. (Or if just three were playing, queens would be tossed and they’d use just 16 cards.) Chips (or some equivalent) were used as well for betting purposes.
Before the game began players drew cards to decide where to sit. I’ve seen some references to the game being played clockwise and others counter-clockwise -- I think the latter more likely.
Prior to the deal players would ante, then the player to the right of the dealer would have the option to raise the stakes by putting in an additional bet called a “carre” -- kind of a like a straddle, as no one has any cards yet. If that player does make a bet, the next player can fold, call, or raise and so on, meaning players can drop out of hands even before cards are dealt, if they wish.
Next comes the deal -- three cards to each player, plus one more card set face up in the middle. This last card, called the “retourné” essentially functions like a “community card” in that each player is making a four-card hand that includes the face-up card. Another round of betting follows that again somewhat resembles the betting in poker (there are some differences, but I’m glossing over them here). Once the betting is completed, players left in the hand show their cards.
When it comes to hand rankings in bouillotte, there are basically just three hand types:
After that, whoever has the most points in their hand wins, with aces worth 11 points, court cards 10, and nines and eights their numerical value. In the case of ties, suits come into play, with the suit of the retourné functioning like a trump suit and the player with the highest card in that suit winning.
brélan carré (highest) = four of a kind (including the retourné, of course) brélan = three of a kind, all in the player’s hand (i.e., not using the retourné) brélan favori = three of a kind, two in the player’s hand plus the retourné
That’s the game that would eventually become poque, as I understand it, although poque also existed as that three-phase game, too, apparently. Eventually only the middle “vying” game would be played, though, and bouillotte started getting called poque thanks to players using the verb “poque” to describe their betting action (“Je poque” = “I bet”).
In any case, this is the game that certainly most resembles the earliest “Old Poker” games that involved smaller deck, a single deal and round of betting, and no draw (yet).
Image: “Peasants Playing Cards” (1700s), Norbert van Bloemen, public domain