byzantium

Byzantium is a card game for 1, 2, 3, or 4 players. It can thus play as a form of solitaire, or as a competitive game, depending upon how many wish to be involved. Players take turns in placing cards on the table forming an elaborate hierarchy that must obey a few strict rules. The aim is to place all of your cards, while preventing your opponents from doing so.

Byzantium is played with half a deck of playing cards: a red suit and a black suit. Begin by separating these suits out from a deck. Place an Ace in the centre of the table, and cross the other Ace over it. Then shuffle the remaining 24 cards.

How to proceed from here depends upon the number of players. Let's start with the solitaire version and learn the rules and strategy through a practice game. The multiplayer versions will then follow quickly from there.

Solitaire

When playing solitaire, each turn consists of drawing the top card from the deck and attempting to place it somewhere in the tableau. The challenge is in finding the right place for the card: somewhere that will help you place your cards on future turns. There are several rules which govern the positions in which cards can be placed, which we are easiest to learn through examples.

The first card from the deck turns out to be the Jack of Hearts. Let's place this to the East of the Aces, like so:

The Jack is now connected to the Ace of Hearts.

The next card is the 8 of Hearts, which we shall connect to the East of the Jack:

Next is the 5 of Hearts. Lets continue the sequence:

Then we draw the 4 of Hearts. We cannot connect it to the 5 as this would take is too far from the Aces. The furthest we are allowed to go from the Aces is three cards out, and this would be the fourth. Let's therefore connect it to the side of the 8.

The next card is the 10 of Spades: our first Spade. Cards can only be connected to cards of the same colour, so we have to connect this to the Ace of Spades (which is in the centre, partly hidden under the Ace of Hearts). We could connect it either to the North or the South. Let's choose the South (it doesn't matter much at this point):

We then draw the King of Hearts. As a red card, we must connect it to a red card. However, it cannot be connected anywhere on the East side of the Tableau since there is a rule which states that each hierarchy must either be descending or ascending. A hierarchy is a complete tree of cards that branches off from one of the four sides of the Aces. In our game, the hierarchy to the East is descending: each card was connected onto a card with a higher value. Since the King is higher than any card in that hierarchy, there is nowhere it could be legally placed within it. We can therefore start a new red hierarchy to the West:

We now draw the 4 of Spades. We could connect this to the 10 (in 3 different ways) or to the Ace. Let's use it to start the fourth hierarchy:

The next card is the 2 of Spades. This presents us with an interesting choice. We could connect it to either the 10 or the 4 of Spades. Since it is lower than the either, the hierarchy it is placed in will become a descending hierarchy. Currently both hierarchies are neutral: since they have only one card in them, they are compatible with being either descending or ascending. When a second card is placed there, their type becomes settled. The identity of the Eastern hierachy was settled when we connected the 8 of Hearts to the Jack, and we are about to settle one of these and need to choose which.

Recall that the object of the game is to place as many cards as possible. If both hierarchies were to become descending, then the King, Queen, and Jack of Spades would be unplaceable. If both were to become ascending, then the 3 of Spades would be unplaceable. If the Northern hierarchy were to become descending and the Southern one ascending, then the 5, 6, 7, 8, and 9 of Spades would be unplaceable. However, if we did it the other way around, then it would still be theoretically possible to place all the Spades. Let's try to achieve that by connecting the 2 to the 10.

There is a further choice here about which side to connect it to. Since this will become a descending hierarchy and the 2 is the lowest Spade, no more cards can connect onto it. It is therefore a bit of a liability. If we were to place it to the South of the 10, then the spot to the South of that would be unreachable. We shall therefore place it to the West of the 10:

We now draw the 3 of Hearts. We could connect this to the King, the Jack or the 8 of Hearts. We can't connect it to the 4 of Hearts since this would mean that the path from the 3 to the Ace would be four cards long, and we have already seen that the limit is three cards. Note that this means the play area is effectively a jagged diamond shape rather than a square.

Since both red hierarchies are (or will be) descending and the 3 is such a low card, it is easy to find valid spots for it. However, since it is so low, only one card (the 2) can connect to it. It is therefore important to block as little as possible with it. We can do this by connecting it to the 8:

The next card is the 3 of Spades. We have already noticed that making the Northern hierarchy descending would be a disaster, so we need to place it in the South. However, since there are no remaining cards lower than the 3, it is not very useful and may block off options. Lets therefore connect it to the East of the 10.

Then we draw the 6 of Spades. We could connect this to either the 4 or the 10 of Spades. The former is superior, since if it were in the South, the only card that could connect onto it is the 5. It would therefore block off a couple of spaces. We could connect it to the East, North, or West. The North is probably best since the 6 doesn't block many cards and will be useful for opening up the North.

The King of Spades. This one's easy. We can tuck it out of the way in the extreme North. Since it is at the distance limit, it won't block any other cards. This is the twelveth card, and so in some sense it marks the half way point. In terms of time and thought though, the game is well over half way through, since the first half involves the most strategic decisions about what options to leave open and this often determines your play towards the end.

The 5 of Spades. That's unfortunate. It can be connected to the 4 or the 10 of Spades. The latter is dreadful since that hierarchy is descending and there are no cards below the 5. This would mean three places being unfillable this game, and one can usually do better than that. The remaining choice is whether to connect it to the West or East of the 4. The East is probably better since there is one more legal card that could be connected to the King than to the Jack (the Queen of Hearts), and we are thus better off blocking the Jack than the King.

The 9 of Spades. Now this is a piece of good luck. The only remaining Spades below the 10 were the 7, 8, and 9, so to fill out the Southern hierarchy they will all be required. However, if we had drawn the 7 or 8 before the 9, we could have connected them to the 10, but they would have blocked one or two of these spots. Let's connect the 9 to the 10 and count our blessings.

The 7 of Hearts. The Eastern hierarchy is full, so it will have to be connected to the King. Let's connect it to the North of the King:

The 2 of Hearts. It is a good thing that we just got a higher heart last turn, as this would otherwise have completely blocked a branch of the Western hierarchy. The 2 will not allow anything to come after it, so we want to place it at distance three from the Aces. We could either place it to the West or the North of the 7. Let's place it to the West. This way we leave the area to the North of the 7 so that we could either play a black or a red card there later.

The Queen of Hearts. Finally. There is only one legal place to play it (next to the King). Just because there is only one spot to play something, it doesn't mean that you must play it. You are always allowed to set the card aside and count it as one of the cards you fail to place. It is unusual to do this when there are legal moves available, but it can be good play if placing the card is so bad that it would prevent more than one card being placed in the future. However the Queen is not such a card. On the contrary, it helps open up new places, so lets connect it to the King.

The Queen of Spades. We are now officially in the endgame, as only places of distance three are left. This means that the last few cards don't need to be very strategic. There is sometimes the possibility for a minor finesse, but typically they can be played out very quickly. The Queen could be placed to the West of the 6, though this would block the flexible red/black position mentioned earlier. It could also be connected to the East of the 6 or to the North of the 5. It doesn't make a difference which, so lets arbitrarily choose the latter.

The 6 of Hearts. Only one place to play it without blocking the other two remaining Hearts, so let's connect it to the 7.

The 10 of Hearts.

The 8 of Spades.

The 9 of Hearts.

The Jack of Spades. This doesn't fit in either of the remaining spaces, so we set it aside.

The 7 of Spades. This is the final card and connects to the 9. Our tableau contains 23 cards (plus the Aces), and only one card was set aside. That is not a victory, but is pretty respectable. It is certainly possible to have to leave two or three cards aside due to incautious play or very bad luck.

Now you have seen all the rules and some of the basic tactics and strategy. You are ready to play a solitaire game of Byzantium and very nearly ready for a multiplayer game.

Below is a concise summary of the rules (including 2, 3, and 4 player versions):

Setup

Use two suits from a deck of playing cards, one red, one black. Place an Ace in the centre of the table, and place the other Ace crossed over it. Shuffle the other 24 cards.

Connecting Cards

The main gameplay consists of connecting cards to form hierarchies. To connect a card in your hand to one in the tableau, the following conditions must be met:

1.
It must not overlap any of the cards in the tableau.

2.
It must not touch any card other than the one it is connecting to.

3.
Its short side must be placed flush against a side of the card in the tableau.

4.
The touching sides must touch in their centres.

5.
The two cards must be of the same colour.

6.
It must be at most three cards distant from the Aces. (It must connect to the Aces, or connect to a card that connects to the Aces, or connect to a card that connects to a card that connects to the Aces.)

7.
A single hierarchy (a tree of cards connected to the the Aces) cannot contain both ascending sequences of cards and descending sequences of cards.

Playing the Game (1 player)

Draw a card from the deck and either connect it to a card in the tableau or set it aside. Repeat this until all cards have been drawn. You win if you did not set any cards aside, and otherwise score a penalty point for each card set aside.

Playing the Game (3 or 4 players)

Deal out an equal number of cards to each player. Starting with the player to the left of the dealer and proceeding clockwise, each player either connects one of the cards in their hand to a card in the tableau or passes. The game ends when everyone passes consecutively. Players score a penalty point for each card left in their hand. As the earlier players have an advantage, the game is best played in sets of games equal to the number of players, with the dealer rotating.

Playing the Game (2 players)

The 2 player game proceeds as the 3 or 4 player game with the following exceptions. 4 randomly chosen cards are set aside face-down, and the game is played with the remaining 20. This is to avoid perfect knowledge of the opponent's hand. The four positions to the furthermost North, South, East and West may not have cards placed in them.

Notes

The 2, 3 and 4 player versions make for a nice, unusual, card game. Unlike the solitaire game, deliberate blocking becomes important. The fact that it is easier for the earlier players to get their cards out also makes for an interesting asymmetry. For instance, if the first player in a 2 player game blocks a single position, then it is more likely that it will be the other player who is left with an unplaceable card, so the first player has a mild preference for an odd number of blocked positions.

With 3 or 4 players, the game is more casual. Impromtu alliances sometimes arise between players whose hands go together well (for example who have mostly red cards and both try to block the black cards). Mostly, however, people just try to get their cards out and reserve some posiitions that only they can use. With so many players, the tableau can change considerably between turns and it is hard to control your opponents.

In contrast, in the 2 player game, one can exert considerable control. For example, if you wait for the opponent to open a new hierarchy, you can play the second card in it, choosing whether it is ascending or descending. Various properties of games like Chess and Go appear, such as tempo, parity, and the game dividing into subgames. If one wanted to make the game less casual and explore this to the fullest, one could decide not to set aside the 4 cards or block the 4 positions, and have it be a game of full information.

Finally, note that the second rule for how to connect cards prevents players from blocking an entire hierarchy by making two 'left turns' or 'right turns' from another hierarchy, like this: