The gambling game Bouillotte was widely played in France and elsewhere in the late eighteenth and through most of the nineteenth century. In the course of the late ninteenth and early twentieth century it was supplanted by the newly fashionable game of Poker.
Bouillotte was introduced at the time of the French Revolution as a regulated form of the popular game Brelan, which had been played since the seventeenth century. Brelan was a vying game in which from two to five players received three cards each from a pack of 24, 28, 32, or 36 cards, and the next card was turned from stock. As in Bouillotte, the best hand was a brelan carré, being four of a kind made with the aid of the turned card, followed by a simple brelan or three of a kind. When no one had three of a kind the winning hand was that with the highest card of the suit of which post points were in play.
The following description of Bouillotte is based on my understanding of the accounts in the following books: Friedrich Anton: Encyclopädie der Spiele (Leipzig, 1889), E. Lanes: Nouveau Manuel Complet des Jeux de Cartes (Paris, 1912), Jean Quinola: Nouvelle Académie des Jeux (Paris, 1893) and R.F Foster: Comprehensive Handbook to the Card Games (London, 1897).
The standard game is for four players, using a 20-card pack with the cards in each suit ranking from high to low A-K-Q-9-8.
It is possible for five people to play, adding the Jacks, which rank just below the Queens, to make a 24-card pack. Three can play using a 16-card pack without the Queens.
Each player starts with an equal supply of chips, known as the cave. Your bets are restricted by what you have left in your cave. Only when you have lost all your chips are you allowed to 'buy in', obtaining a new cave to continue playing. The monetary value of a chip and the number of chips in the cave (for example 100) are to be agreed before the game starts.
To choose seats, a card of each rank from the King down is taken from the pack. These cards are shuffled and each player draws one. The player who draws a King chooses a seat, and then the holders of the other cards take the other seats in counter-clockwise order around the table, in descending order of the cards they drew.
Deal and play are counter-clockwise.
Before the deal, the players must place an initial bet in the pot, equivalent to the ante in poker. Some authors specify an ante of 1 chip, placed by the dealer only. Others say that each player puts in 1 chip, and the dealer adds an extra chip (to make an initial pot of 5 chips in the four-player game).
The player to the dealer's right can now increase the size of the pot, by adding an amount equal to what it already contains. This is equivalent to a straddle or blind bet in poker. In French Bouillotte this blind bet was known as a carre. If the player to dealer's right straddles, the next player to the right can also straddle by doubling the pot again (contre-carre), and so on round to the dealer. If a player at his turn chooses not to straddle, or does not have enough chips to do so, this ends the straddling and the cards must be dealt.
The last straddler will have the advantage of being the last to act in the betting after the deal. This player thus has the advantage of waiting to see what the other players do, winning the pot if they all pass, and having the possibility of raising after finding out which of them are prepared to match his blind bet.
Some play that if the first and second players both straddle, the first player can buy back the right to bet last by doubling the pot again. Only if the first player does not want to buy back does the right to straddle pass to the third player, and if the third player then straddles the second player can buy back by doubling the pot.
After the straddling phase has finished, the dealer deals the cards one at a time, until each player has three cards, and turns the next card face up.
The players now bet on who has the best hand (see ranking of hands below). If no one straddled, the betting begins with the player to the right of dealer. If one or more players straddled, the player to the right of the final straddler is the first to bet. The first player can either pass, betting no money but reserving the right to enter the betting later, or open the betting. To open you must place at least enough chips in the pot so that your stake at least equals that of the player who has stakes most - this will be the final straddler or the dealer if no one straddled. So for example, if you play ther version where everyone places an initial bet or one chip before the deal and the dealer adds a second ship, the the player to dealer's right could open for one chip, making this player's stake up to 2, the same amount staked by the dealer. If the player to dealer's right straddled, by adding an extra 5 chips to the pot, then the next player would need to put in at least 5 chips to open. You can open for more than the minimum amount if you want to, placing anything up to your entire supply of chips, which is announced by saying 'va-tout'.
If the first player passes, the next player has the same options, and so on around the table. If there was no straddle and all four players pass, the cards are thrown in, the deal passes to the next player, the chips in the pot remain, and the dealer adds another chip. If three players pass after a straddle, the final straddler collects the pot, which includes the initial bets of the players, plus any previous straddles.
If a player opens, the subsequent players in turn, including any who passed before the opening, must now choose whether to call (tenir), by placing enough chips to bring their stake up to the same level as the player who openend, to raise (relancer) by staking a greater number of chips than are required to call, or to fold (filer), dropping out of the betting and abandoning whatever money they have already staked. After a straddle, if a player opens for the minimum amount and no one raises, the straddler can of course call without placing any further chips, but is allowed to raise instead. Once the betting hads been opened it is no longer possible to pass and reserve the right to bet later.
If the opening is raised, the betting continues around the table, omitting any players who have already folded, each player choosing whether to call, raise or fold. This continues until one of the following situations is reached:
It follows that a showdown between three or more players occurs only after the last bet (or opening) has been called by all the other players in turn, and then all these other players in turn have passed their opportunity to raise the stake again. At this point, the player who opened or most recently raised is not allowed to raise again. Instead there is a showdown between all the surviving players.
All the above is based on the assumption that everyone has an adequate supply of chips. A player who does not have enough chips left to meet the minimum required bet is not allowed to open or raise, but can call by placing all his remaining chips. At this point the pot is divided into two. The first part contains a number of chips from each player which is not more than the number of chips staked by the player who has all his chips in the pot. Any excess is placed in the second part. For example if the stakes of the four players are 2, 5, 8 and 16, and the 5 chips are all that the second player had, then the first pot will contain 17 chips (2 + 5 + 5 + 5) and the second pot will contain the remaining 14 chips (3 + 11). The player who has no chips left can only win the first pot; the other surviving players compete for the second pot.
The players look at their cards. In the standard game there are three possible types of hand.
The highest is the Brelan Carré: three cards of the same rank as the turned up card (for example, three Nines when a Nine is turned up).
Next highest is an ordinary Brelan - a hand of three cards of the same rank, different from the turned up card (for example three Kings when a Nine is turned up). If more than one player has a Brelan, the highest wins, the cards ranking in descending order A, K, Q, 9, 8.
If no one has a Brelan Carré or Brelan, the winning hand is determined as follows. The hands of the four players are exposed, and the total points showing in each suit are counted, using the values Ace=11, King=10, Queen=10, Nine=9, Eight=8. The winning suit is the suit with most points showing, and the winning hand is the hand containing the highest card of that suit belonging to any player who has not folded during the betting.
Some care is needed to resolve a case where two or more points show equally many points. Next, it must be determined to which player each of the tieing suits belongs. Considering only the players who have not folded, the owner of a suit is the surviving player who holds the highest card in it. The winning player will then be the first of the surviving players in counter-clockwise order, starting to dealer's right, who owns one of the suits that tied for most points.
Example: Player D is the dealer and the others in order are A, B, C. The turned card is 
A
A 
9 8 (folded)Q A 8K Q 
AK 8 Q (folded)Hearts and diamonds each have 39 points. If A had stayed in, diamonds would have won, but as things stand, with A having folded, B wins on position as the owner of the heart suit.
When there is a showdown, all players, including those who have dropped out of the betting, show their cards, and the winning hand (among those players who have not dropped out) is determined according to the ranking of hands. The winner collects the contents of the pot. In addition, anyone who had a Brelan Carré is paid two chips by each opponent, including those who dropped out of the betting, and anyone who has an ordinary Brelan is paid one chip by each opponent, including those who dropped out. If two players have ordinary Brelans, they do not have to pay each other (their payments cancel), but the higher ranked Brelan beats the lower for the purpose of deciding who wins the pot.
When the pot is split because a player ran out of chips during the betting, the first pot is settled first among all the players who have not dropped out, including the one who bet all his chips. The winning suit is determined by this first pot: when players who have contributed to the second pot compete for it, the winner (in the absence of Brelans) will be whichever of them holds the highest card of this winning suit.
The books mention many variations. For example, the amount of chips each player began within their cave and the amount staked before each deal varied.
Some recognised the Brelan de Mistigri consisting of the Queen of Clubs with two cards of the same rank and colour - for example Q-9-9. This ranked lower than an ordinary Brelan but higher than a hand winning on points. On the other hand some high stakes players did not recognise any Brelans at all, the best hand on points winning always.