Here you'll find the rules of additional abstract games invented by Christian Freeling ordered on theme. Most of these can be played in the Pit, and free downloadable applets are provided to store the games offline.

Hexemergo and Chakra invented by Christian Freeling and Ed van Zon.
YvY invented by Christian Freeling and David J. Bush.
HanniBall invented by Christian Freeling and Arty Sandler.

All applets are by Ed van Zon.



Chess variants
The theme checkmate is existential to the core: the king must die. There exist hundreds, if not thousands, of chess variants because, unfortunately, it's very easy to make one that 'works'.



Shakti
Initial positionThis is without doubt the smallest chess game with a non trivial strategy.

In the initial position the board is covered with 45 tiles. During play this number is bound to be reduced due to the 'atlantis effect', a mechanism that lies at the core of this miniature, and without which no such reduction in material would ever be possible.
  • All play is on the tiles.
  • White begins. Players move, and must move (unless they cannot), in turn.

Initial position
  • The King, if not in check, may move to the first tile he sees in any of eight directions as shown in the diagram.

Initial position
  • If in check, the king is restricted to adjacent tiles. Anticipating on the warrior's move, the diagram on the right shows that pieces giving check from a distance therefore need no protection. It follows that the king can only capture an unprotected warrior on an adjacent tile.

Initial positionThe mutual check rule:
  • Kings may not see one another along the same rank, file or diagonal, with no tiles in between, so neither player may effectuate that situation.
    Thus a king may protect a piece against capture by it's counterpart. It follows that a king may protect a warrior it sees, as in the diagram, where the black king, in check, must move to the indicated tile.

Initial positionThe Warrior:
  • A warrior too may move to the first tile it sees in any of eight directions. If both are vacant, a warrior may also move to the second tile, removing the first. The removal is compulsory, but of course the player may not, in doing so, put his own king in check.
    The next diagram shows the warrior's options. If he chooses the second target-tile in any direction, the one jumped is removed. The black king is not in check because the vacancy-condition is not fulfilled.
    Warriors are strictly king oriented and cannot capture one another.

    Stalemate does not exist in Shakti: if a player cannot move, his opponent may move instead.

External links



Shakti © MindSports
Java applet © Ed van Zon



Caïssa
Initial positionCaïssa employs a different implementation of the 'atlantis effect'.
On top of that, Caïssa introduces another absolute novelty: 'capture by exchange', which is in fact no capture at all.

In the initial position the board is covered with 49 tiles.
  • All play is on the tiles.
  • Though tiles will be removed during play, the tile-complex must remain connected, that is, a tile or group of tiles must always remain orthogonally or diagonally connected to the rest.
  • White begins. Players move, and must move, in turn.

queenThe Queen
The king's role is played by the queen. The diagram on the left shows its options for movement and capture in a non-check situation.

queen in checkIf in check, it is restricted to adjacent squares, as shown in the diagram on the right. Thus pieces giving check from a distance, need no cover. The queen is the only piece with the power of capture in the usual sense.

The atlantis effect
If the queen moves, the tile it vacates is removed in the same turn. The removal is compulsory, but it may not violate the tile-connection rule.

The mutual check rule
Queens may not see one another along the same rank, file or diagonal, so neither player may effectuate that situation. Thus a Queen may protect a piece against capture by it's counterpart.

connection ruleThe pieces move as in Chess. Under the implicit condition of not putting its own queen in check and the explicit condition of not violating the connection rule, a piece can always move to any of its target-squares, whether or not it is tiled, and if it is, whether or not it is occupied, and if it is, regardless of the color of the occupying piece!
  • If the target-square has no tile, the piece takes its own tile with it. At the end of the move the tile-complex must still be connected. There is no 'during the move': the knight may legally move to the square marked A. Moving to B is illegal.
  • If the target-square has an empty tile, the piece may simply move there.
  • If the target-square is occupied by a friendly piece, the player must exchange the pieces.
  • If the target-square is occupied by an opponent's piece, the player must also exchange the pieces, but there is one exception: a switch between two pieces of the same type may not in the next turn be 'undone' by the opponent.

connection ruleAbout tile-surfing and the connection rule
This 'mate in 1' shows another application of tile-surfing and the connection rule. For clarity all other pieces have been omitted.

After d2c4, the queen cannot move because the tile on c1 would be disconnected. If black were able to exchange the knight on c4 immediately with any of his pieces, he could yet prevent the mate, but the queen would remain immobile until one of black's pieces would bring a tile to the rescue.

Applet
Sorry, you need a Java enabled browser to view the Caissa Player!
download applet play online a word on notation
You can download this MindSports applet, which is tailored to save games played in the Pit, offline.

External links


Caïssa © MindSports
Java applet © Ed van Zon



Chad
Initial positionThe diagram shows the Chad board with the pieces in the initial position. The areas covered by the pieces are called the castles Each castle has twelve adjacent squares that together constitute the wall.
  • White begins. Players move, and must move, in turn.
  • The king is confined to his 3x3 castle. He may go and capture using either the king's move or the knight's move.
It's customary to look at the king in terms of the squares it does not cover. In the center it covers the whole castle, on the side it does not cover the square on the opposite side, and in the corner it does not cover the other corner squares.

  • The rook moves like the rook in Chess, unhindered by castles and walls. If it ends its move inside the opponent's castle, it is promoted to queen.
    The queen moves as the queen in Chess, unhindered by castles and walls

  • The mutual right of capture exists, and only exists, between an attacking piece on the wall and a defending piece inside the castle.
    Apart from this situation pieces simply block one another.

This is a crucial rule! It is illustrated in the next diagram. Black's castle shows a rook on the wall facing a defender inside. In such a situation both have the right to capture. However, in this specific situation only white can capture because the black rook is pinned! This position shows one of the basics of attack.
Initial position If it were white's turn he could checkmate in two, so let's assume it's black's turn. Let's also disregard the other pieces for a moment and assume the postion around black's castle is part of an actual position. What can black do?
Interposing a piece on any of the squares between the black rook and either of the white rooks, would parry the immediate threat. If this isn't possible, black's only option is to move the defending rook towards the pinning one. But this leaves a white rook on the wall attacking three squares inside the castle - literally a thorn in white's side.
Needless to say that the white rooks illustrate a basic attacking pattern. It appears in a variety of forms in almost all attacking concepts.

A related basic concept is the promotion sacrifice. It derives from the fact that an attacker, once it is inside the castle (and thus automatically a queen), can only be captured by the king.
A king on the side leaves one square unprotected, and a king in the corner three. The sacrifice of a piece to force the king to the side or into the corner, to clear the way for a second piece to promote on an unprotected square, is very common.
A queen is worth the sacrifice of a piece anytime! Its strength is illustrated in the same diagram: if it were black's move, the lone queen could checkmate the white king in just two moves.

In positional respect, a rook on a square diagonally adjacent to the enemy castle covers two segments of the wall. Needless to say these spots are popular. Finally, every attack eventually draws from defending forces, so an attack to checkmate should drive home. If it fails, 3-fold is one's only hope!

Applet
Sorry, you need a Java enabled browser to view the Chad Player!
download applet play online a word on notation
You can download this MindSports applet, which is tailored to save games played in the Pit, offline.

Chad was first published in 'The Gamer' (may-june 1982).

External links


Chad © MindSports
Java applet © Ed van Zon



Rotary
Initial positionThe idea for Rotary came from Ploy, a proprietary game (3M) in the seventies.
In this game the number of directions a piece could choose from, also determined its maximum range. This had two major drawbacks: first of all the limited and different ranges of the pieces did put a strain on clarity. A simple look at the directions was not enough: one constantly had to check the different ranges. The second flaw was even worse. By increasing the range with the number of directions, the strong pieces became even stronger, the weak even weaker.
Moreover, three pieces of pathetic weakness - one step in one possible direction - were outnumbered by six very strong pieces, each able to go up to three steps in three possible directions.

Although the weak ones were compensated by their right to rotate in the same turn, I've seldom seen a better example of internal imbalance in a game. But I also saw the possibility of a complete and consistent set of long-range pieces, to provide for clarity, separated by very orthodox pawns, to bring at least some strategy to a system of capricious tactics.
Initial positionOnce the idea was there, implementation was simple.
  • The king may, at the cost of a turn, rotate on its place, provided this effectuates a change in orientation. It may also move one square in any of its four directions and rotate, but only after the move, as part of the same turn
The right to rotate stationary makes stalemate an impossibility. Another unique and implicit feature is that a king may give check, even deliver mate (as shown) to its counterpart.

The pieces follow a logical sequence. All are subject to the following rules:
  • A piece may, at the cost of a turn, rotate on its place, provided this effectuates a change in orientation.
  • A piece may move one square in any of its directions and rotate, but only after the move, as part of the same turn.
  • A piece may move any distance in any of its directions, but if it moves more than one square, it loses the right to rotate in the same turn. The only exception is the Scythe that has the right to rotate in the same turn regardless of the length of its move.

Initial position
  • The first piece is the Axe. It has a middle direction flanked by two directions making a 45 angle with it.
  • The second piece is the Rook. It has a middle direction flanked by two directions making a 90 angle with it.
  • The third piece is the Trident. It has a middle direction flanked by two directions making a 135 angle with it.
  • The fourth piece is the Scythe. It has a middle direction flanked by 'two' directions making a 180 angle with it. Here the variable directions melt into one. The Scythe's right to rotate after any move compensates for the actual loss of one direction.
  • Pawns are basically chess pawns, but do not have the option of an initial double step. They promote - optionally on moving to the seventh or eighth rank, compulsory on moving to the ninth - to Queen. A 'queen' is a rotaryrook with four instead of three directions. The player may choose its initial orientation.

Strategy
The strategic implications of the pawn structure differ little from Chess. Apart from this, it is difficult calculate deep in the game's rather capricious tactics, and in consequence also to make a specific overall plan.
The pieces are of roughly equal strength, but differ rather dramatically in timing. The forward oriented Axe, for instance, has no immediate possibility for retreat, so its encounter with an opponent's pawn structure should be avoided. The Axe usually becomes active in the later stages of the game when the number of pawns has reached saver levels.
The Rook, to a lesser degree, encounters the same problems. The best orientation is usually with its middle direction obliquely forward or even sideways, to ensure the possibility of a retreat.
The Trident can be brought into play in an earlier stage. Its directions are rather roundabout ensuring a greater flexibility.
The Scythe is the opening piece par excellence. Its greatest joy is penetrating behind the opponent's pawn structure and finding the pieces, from its opponent's point of view, in precisely the wrong orientation. The amount of havoc a Scythe can create in these circumstances is unbelievable!

External links


Rotary © MindSports
No applet



Loonybird
Initial positionPawns move and capture in different ways. One night I thought 'what if in a chess game ALL pieces except the king would move and capture in different ways' ? In what was very much the same moment I saw that the three basic pieces, rook, bishop and knight, gave rise to six combinations.
These consist of a top-piece called the hunter which constitutes the way the piece captures and a bottom-piece called the carrier, which constitutes the way the piece moves.
Of course only hunters can give check, therefore a piece is called after its hunter. I immediately decided for piece drops to avoid the possibility of a drawish system.
As an afterthought came the concept of Dragonfly which may be considered as 'normal Loonybird'. Thus I had two new games within a couple of minutes.

The diagram shows the board with the pieces in the initial position.
  • The nature of the pieces has been explained, but for the option to re-enter them.
    If a piece is captured, it becomes the captor's property, and he may drop it, at the cost of a turn, on any square. As in all systems that feature the re-entering of pieces, this is called a 'piece in hand'.
    The applet takes care of the switch.
  • Pawns are chess pawns, but do not have the initial double step. They promote on moving to the seventh rank to a piece the opponent has 'in hand'. This makes promotion exceptionally strong and, if all pieces are on the board, well worth even the worst exchange, say a rook for the bishop-knight, to force an opponent into a piece in hand.
    Pawns, if captured, are out of the game.
  • The king is the same as in Chess but there is no 'castling'.

Anonymous#1 - Anonymous#2
Sorry, you need a Java enabled browser to view the Loonybird Player!
download applet play online a word on notation
You can download this MindSports applet, which is tailored to save games played in the Pit, offline.

Note: Loonybird has been implemented on the Zillions game machine.

External links


Loonybird © MindSports
Java applet © Ed van Zon



Elimination
The theme elimination is existential: one must die lest two must suffer the insufferable draw. There's hardly a culture that has not implemented the basic idea of pitting two armies of uniform men against one another on a game board.

Well yet everyone know that cialis for sale cheap can be found with ease in the Internet. In exclusive on our website it is full of it. But you forget and constantly you ask.




Hexemergo
Hexemergo is a literal translation of Emergo to the hexboard, and has exactly the same rules.
Of course movement and capture are in six rather than four directions and there are 37 cells instead of 41 squares. But for the rest, things are pretty much the same. Or are they?

Applet
Sorry, you need a Java enabled browser to view this Hexemergo Game.
download applet play online a word on notation
You can download this MindSports applet, which is tailored to save games played in the Pit, offline.

A special case of 3-fold
To get a taste of what can happen on the hexboard, have a look at the above curious case of 3-fold, with no equivalent on the square board.
White's position is hopeless, of course, but ... see what happens.

Tactics generally tend to dress more capricious on the hexboard, but in Hexemergo they are over the top. In the above example white makes two moves, after which things run their own course. That happens quite often in Hexemergo - things running their own course. A perceivedly well calculated combination may go haywire by the slightest oversight, turning the board into a whirlpool of unforeseen captures, the outcome of which is in the hands of fate.
Nothing wrong yet, though. Capricious games where chances may turn several times have their own charm.

Initiative may be more prolongued than in Emergo too, especially with a strong piece, because of a property of the hexboard. If during leapfrogging the opponent's piece ends on the side, a player can more often than not draw it back into the field by a move parallel to the side. This way to keep the initiative is not possible in Emergo.
Sorry, you need a Java enabled browser to view this HexEmergo problem! 7- versus 4-cap, defender in opposition
Opposition in Hexemergo is always diagonal opposition.

Here the moves that draw black back into the field are white 3 and 8.
This type of move to continue a combination is impossible in Emergo.

Still nothing wrong yet, though. And in over the board play nothing is, because players just cannot calculate deep enough without losing track.
Hexemergo's flaw was spotted by Ed van Zon, in correspondence play. When playing white, he employed the usual Emergo strategy of trying to keep the game as flat as possible during the entering phase, always taking care not to lose the right on the first move after the entering phase.
Next he carefully sifted through the many possible feeding combinations to find a straight knock-out.
Hexemergo's flaw is that it is so rich in combinations that his quest invariably succeeded, i.e in correspondence play white has a winning strategy.
That's too bad because one can't 'change' or 'repair' or 'improve' a quintessential game.

But one can nevertheless enjoy its intricacies.
Sorry, you need a Java enabled browser to view this HexEmergo problem!
1e4f5! e6f7? leads to an even position after:
1ge7x
2fd7xe7f6!
3d75xdf6x
4e4g6xeg5x
5g64xg5f4!
6ge4xd54
7ec4xdb4x=
g76 gf7 is symmetrical.
2ef6ge6x Counterclockwise capture loses te same way.
3f5x Miniature magic!

A Hexemergo example game
Sorry, you need a Java enabled browser to view this Hexemergo Game. In this game between the inventors, white manages to keep the entering stage flat. Yet his initial efforts to create some muscle go astray and after some twenty moves each, black seems to call the shots with a solid 4 and a clear target: the four black prisoners under a single white man.
On move 23 however white finds a deep combination, involving two points where black has a choice of capture, that not only liberates a large stack, but rolls right into victory.

External links


Hexemergo © MindSports
Java applet © Ed van Zon



Crossfire
Crossfire is derived from Sid Sackson's game 'Focus'. It's predecessor features rather capricious tactics, involving the building of stacks of men, and Crossfire follows suit.
Yet, apart from the obvious difference of Focus being played on a square grid and Crossfire on a hexagonal one, there's one big difference: in Focus the 'capacity' of every square - the maximum stack it will hold - is five men. Any stack surpassing this number is reduced to five by taking the excess from underneath, whereby the opponent's men are captured, and friendly men are kept as 'reserves' that may be re-entered on the board.
In Crossfire the capacity of a cell equals the number of adjacent cells! Corners will hold at most a stack of two, sides at most three or five, and cells of the inner area at most six.
This gives rise to a strategy not possible in Focus: moving big stacks onto 'low-capacity' cells, corners in particular. This way considerable numbers of prisoners can be made and reserves created on fixed target cells. In Focus for instance one can never make prisoners, nor create reserves, by moving a stack onto a vacant square. In Crossfire, moving a stack of five onto a vacant corner renders three men. This fixed element makes Crossfire more of a strategy game than its predecessor.

Rules
Initial positionIf there's mention of men and pieces, a man is single, while a piece consists of a number of stacked men. If the difference doesn't matter, a man may also be referred to as a piece, for instance 'the number of pieces on the board'.

Object
  • If a player has no legal move he loses the game.
The diagram shows the board with the pieces in the initial position. The coordinates of a cell can be found by looking along the ranks and alternating files to obtain the letter and number.
  • There are two players, 'black' and 'white'.
  • Players move, and must move, in turn. White moves first.
  • A piece consists of one or more stacked men. It may be composed in any way. The top man determines its owner. Players move only their own pieces.
  • A move consists of either:
    • picking up the piece - or any number of top men of the piece - and moving it the number of cells equal to the number of men that are moved, in one of the six main directions.
      It does not matter whether, or by whom, the target cell is occupied.
    • entering a 'reserve' on any cell (except if excluded by the ko rule).
      It does not matter whether, or by whom, the target cell is occupied.
Move distancesThe diagram shows white's options for the piece of five - he may move ...
  • the top man onto any of the cells marked '1'.
  • the top two men onto any of the cells marked '2'.
  • the top three man onto any of the cells marked '3'.
  • the top four men onto any of the cells marked '4'.
  • the whole stack onto any of the cells marked '5'.

CapacityThe capacity of a cell
  • The maximum height of the stack it will hold equals the number of its adjacent cells. The diagram gives the capacity of every cell.
  • If a player's move results in a stack surpassing the capacity of the cell it occupies, then the player must remove the excess from underneath the stack.
    Friendly men thus obtained become part of the player's reserves.
    Opponent's men thus obtained become prisoners and are removed from play.

CapacityOvercapacity
  • If you consider once again white's movement options in this diagram, you'll see that moving the entire stack 5 cells horizontally to m3 leads to a stack of 5 on a two-capacity cell, and thus to an 'overcapacity' of three men.
    These three men - two prisoners and one reserve - are removed from under the stack in the same turn. The remainder, a stack of two white men, remains on m3.

CapacityThe 'ko-rule'
  • A player may not create the same position with the same move twice.
This example is not meant to illustrate any strategy, only the mechanics involved. Other pieces, prisoners and reserves have been left out for clarity. Let's assume that white has created a stack of six by moving a white-black-white stack onto a black-white-black one, and that black has next put a reserve on top of a white-black one and removed a reserve from underneath (diagram).
It is now white's turn. If he enters on g1, he immediately regains his reserve, which means that he effectively only reverses the colors of the stack. Now black cannot enter on g1 because he would, with the same move, recreate a position that already occured!

But black can enter on top of the six, also immediately regaining the reserve and effectively only reversing the colors of the stack. The difference is that white now still can enter on the six. Although he does recreate a position that already occured, he does so with a different move (since he first created the stack by moving a white-black-white stack onto a black-white-black one).
Black now of course cannot enter on either stack, though he may do so as soon the position as a whole, which isn't depicted here, has changed.

The ko-rule has been introduced for precisely the type of situation depicted here: even numbered maximum capacity stacks with alternating colors that, by nature, can be reversed while all else remains exactly the same.

Note: the ko-rule equally applies to odd-numbered alternating stacks, though not all remains the same there, because the moving player captures an opponent's man rather than a reserve. That's why no ko-rule is necessary in Focus: the situation sorts itself out by dwindling numbers. Situations involving alternating 5-stacks in Focus and, if on capacity, in Crossfire, may therefore have different tactical implications.

Example game
Sorry, you need a Java enabled browser to view this Crossfire Game.
download applet play online a word on notation
You can download this MindSports applet, which is tailored to save games played in the Pit, offline.

External links



Crossfire © MindSports
Java applet © Ed van Zon




Territory
The territorial theme is coexistential: both live, and whoever grabs the biggest piece of the cake is the winner. Go and Othello are the best known representatives. Here are several more, including the multi player game 'Phalanx'.



Medusa
atariI'll presume that the reader is familiar with the rules and some basic concepts of Go. In 1975 Mark Berger invented 'Rosette', a Go variant played on the intersections (triple contacts) of a hexagonal board.
His first idea was to simply apply the rules of Go and see how it worked out. As it turned out, regular concepts like 'ko' and 'seki' remained intact, but there was a big difference when a group was in 'atari', that is: when it had just one liberty left, like the white stone.
In Go a point has four liberties and extending from a group in atari may increase the number of its liberties by 2. In Rosette an extension increases that number at most by 1, and this one is consequently taken to keep the group in atari.

The attacker has the choice of direction and may lead the head of the 'escaping' group towards the edge or even around towards its own tail, to die.
Of course things were balanced by the fact that both players suffer or enjoy this to the same extent, but Mark concluded rightly that it gave rise to too much tactical involvement to leave much room for any long term strategy. So he invented a safety mechanism up and above the implicit safety mechanism of having two 'eyes', and called it a rosette.
A rosette is formed by six stones of one color, occupying a small hexagon. A group containing a rosette lives unconditionally. This turned out to be a great improvement and I made it a key idea in shaping Medusa and Lotus.

Thanx Mark, wherever you are!

Rules
board
  • The game starts on an empty board. Play is on the hexagons. Only the lighter colored cells are part of the board, thus a cell in the center has four neighbours, one on the edge has three and a corner has two.
  • Each player has enough bi-colored stones - black one side, white the other.
  • Off the board, players use a 19-point track marked in the center. Between evenly balanced players, the marker is placed 3 points towards the player who has white. This is the game's komi
Komi is a way of settling the first player's advantage. Many high level games would be needed to establish a reliable number. Nobody ever objected to three though.

Indicating komi is not the marker's primary function - it is there because refraining from putting a stone on the board at one's turn earns a point, indicated by moving the marker.
Although the track has 19 points, its unusual for it to move more than a few points either way.

Placement and movement options
  • Black moves first after which turns alternate. On his turn a player has two options:
    • He may place a stone on any vacant cell.
    • He may 'move' any or all of his groups.
  • He may use either or both. If he uses both, placing a stone must precede movement.
    If he drops the first option he may move the marker one point towards his side.

Movement
For movement purposes a group is defined as two or more connected stones of the same color.
  • Moving a group means taking one of its stones and moving it in a staight line over any number of friendly stones in an unbroken row, to land on the first vacant cell beyond.
  • No group may move more than once in a turn.
  • By movement groups may split or join.
  • If a group moves to contact a friendly group that has not yet moved itself, the latter therewith loses its right to move in that turn. Thus the order of moving groups may make a difference.

Life and death
  • A group lives unconditionally if it contains a 'rosette' - six stones around one of the board's 61 dark-colored cells.
  • For capturing purposes a single stone is, by definition, also a group. A group without a rosette lives as long as it has at least one 'liberty', that is: one adjacent vacant cell. A group that is down to one liberty, and thus under immediate threat of being captured, is said to be 'in atari'.
  • Assuming none of the groups involved is protected by a rosette, a group that loses its last liberty is captured and reversed immediately to show the opponent's color.
  • Capture may result from placement or movement or both. If a capture is the result of placement only, the stones are reversed before the movement phase. Thus the group resulting from the capture has the right to move in the same turn. Groups captured by movement contain at least one stone that has moved, and may not move in the same turn.
  • If placement results in one or more opponent's groups losing their last liberty, they are captured whether or not the stone placed has any liberties itself at the time of placement.
  • If placement results in losing one's own last liberty without killing any opponent's group, the placement is suicidal and the player's own stone or group is reversed before the movement phase.
    Suicide is legal.

Object and counting
  • The game ends by one player's resignation or if both pass completely on successive turns. In the latter case dead stones are reversed.
  • The winner is now the player with the most territory.
    Territory consists of a player's number of stones on the board plus the number of cells totally surrounded by his stones
    The player whose side it is on also adds the number of points indicated by the marker.
  • Seki may occur: empty points not totally surrounded by either player count for neither.

Examples
boardAt the top black is safe. A white placement at A is suicidal and gives black a rosette, making movement at B (qs15) useless. If white plays at B, black must answer by completing a rosette at A himself on the next turn.

At the bottom black threatens to connect by capturing the group on the bottom left side. It's white's turn however and the four black stones at the bottom are killed by a suicide placement at C, creating a five stone black group with two liberties, followed by two movements: ec1 and ec3.

boardThis is a seki
Neither player can occupy A or B without having his stones killed.


Strategy
In general sense Medusa strategy mirrors Go strategy, but there are differences.
Invasions in Medusa, including those unlikely to succeed, don't harm as long as the opponent must answer by placement. Failure only makes that the opponent gets some dead stones on cells that would have been part of his territory anyway, while the invader doesn't lose anything in trying. However, if the invading stone is so weak as to require no answer by placement, the invader loses a marker point.
The same holds for overdefensiveness: 'killing' already dead stones doesn't so much change the division of territory, but it gives the opponent the opportunity to refrain from placement and move the marker.

Medusa is highly efficient in that stones that lose their local importance in the course of a game, can often be moved to where they're needed more urgently.

Medusa and its support-act Lotus are featured in R. Wayne Schmittberger's 'New Rules for Classic Games' (John Wiley & Sons, Inc. New York; ISBN 0-471-53621-0).

External links


Medusa © MindSports
No applet



Lotus

Rules
atari
  • The game starts on an empty board. Play is on the intersections. A point in the center has four neighbours, one on the edge has three and an inward corner again has four.
  • Each player has enough bi-colored stones - black one side, white the other.
  • Off the board, players use a 15-point track marked in the center. Between evenly balanced players, the marker is placed 1-3 points towards the player who has white. This is the game's komi.

Komi is a way of settling the first player's advantage. Many games would be needed to establish a reliable number.

Indicating komi is not the marker's primary function - it is there because refraining from putting a stone on the board at one's turn earns a point, indicated by moving the marker.
  • Players move in turn. Black moves first. A move consists of placing a stone on a vacant point.
    Moving is not compulsory: a player may pass his turn without losing the right to move on his next turn.
  • If a player passes his turn, he moves the marker one point towards him. The player at whose side the marker is at the end of the game, receives the corresponding number of points in addition to the points he has on the board.
  • A group consists of a single stone or several connected stones of the same color. The liberties of a group are the stones that border on vacant points. The stones in a group share the group's liberties.
  • A group lives unconditionally if it contains a lotus - six stones around one of the boards seven hexagons. A group without a lotus lives as long as it has at least one liberty.

Capture
Assuming none of the groups involved is protected by a lotus, a move may result in:
capture
  • 1. One or more opponent's groups without a liberty. These are captured and reversed in the same turn. A captured group thus unites the groups responsible for its capture into one new group.
    This new group may itself have no liberties! In that case the original capture was in fact suicidal and a second reversal follows.
    An example is black capturing the white stone at the top of the diagram.
    A white move at that point is a regular capture.
  • 2. An own stone or group without a liberty. If, at the same time, the conditions under 1 are met, the procedure described there is followed. If not, the move is suicidal.
    Suicide is legal
  • 3. Neither 1 nor 2

Lotus and its ancestor Medusa are featured in R. Wayne Schmittberger's 'New Rules for Classic Games' (John Wiley & Sons, Inc. New York; ISBN 0-471-53621-0).

Lotus © MindSports
No applet



MacBeth
MacBeth is a hexagonal variant of Reversi and Othello. What's different? For one thing, it looks better!

Othello or Reversi mode
The diagram gives the initial position in Othello mode. In Reversi mode play starts on an empty board and the players first take turns to fill up the central hexagon. Disregarding rotations and reflections, there are three possible outcomes to start the actual game from. The rules from that point on are the same as in Othello mode.

Rules
board
  • Black starts. Players must move on their turn, unless they cannot legally move. In that case the turn goes back to the opponent. If neither can move legally, the game ends.
  • The players share 72 bi-colored stones - black one side, white the other.
  • A move must be a 'custodian capture': the stone played must trap at least one opponent's stone or unbroken row of stones, between itself and an already present stone of like color. It can do so in up to four directions simultaneously.
    Captured stones are reversed immediately.

Note a peculiar difference with Othello, where a move may capture in no less than eight directions. Because MacBeth is hexagonal, its directions of capture are along straight lines only - not along diagonals. On top of that one main direction is excluded for every cell by the nature of the board. This makes MacBeth somewhat easier to handle: colors do not switch quite that dramatically.
Object
  • The game ends by one player's resignation or if both must pass on successive turns.
    The winner is now the player with the most territory, that is: the highest number of stones on the board.

Strategy
The starting point of all reasoning is obviously the fact that there are six corners with the same feature that is makes them so popular in Othello: a man on it cannot be captured and becomes an anchor to capture along the edges. The fact that corners are strong makes the adjacent cells weak, so these should be avoided.
And so on: the basic reasoning is the same as in Othello, and 'minimal capture' - capturing as little as possible during the earlier stages, to reduce the opponent's options - also seems to apply.
The finer points of strategy are admittedly no less of a mystery to me than those of Othello.

Christian Freeling - Falco Freeling (The Pit 2008, 1-0)
Sorry, you need a Java enabled browser to view this MacBeth Game.
download applet play online a word on notation
You can download this MindSports applet, which is tailored to save games played in the Pit, offline.

External links


MacBeth © MindSports
Java applet © Ed van Zon



Square Off
Square Off is a territory game based on configurations of squares. It is played on a Chess board divided in four quadrants, as displayed in the diagrams. There are two players, Black and White. Both have 32 men in their color.
The game starts on a empty board, with a swap option for the second player: the first player puts a white man on the board after which the second player decides whether he accepts that move as his first, and thus plays white, or rejects it, in which case it is his turn and he plays black.

Rules
boardObject
  • The game ends by one player's resignation or when the board is full.
    The winner is now the player with the most territory, that is: the highest number of 'marked men' on the board

squaresPlay
  • After the swap, players move in turn to put one man on a vacant square.
  • If a man thus placed completes one or more 'squares' of 4 men of that color, either within one quadrant or with one man in each quadrant, then all unmarked men involved, including the one just placed, are 'marked'.

    The diagram shows a legal white and a legal black 'square', and a small white one on the brink of completion, where a man placed on the cell marked with the transparent man would complete the 'square'.


Swap
  • The swap rule is based on the fact that cells of a quadrant participate in different numbers of possible 'squares'. The first player can choose a '9-squares' cell, but then the second will certainly accept it as his first move, or he can choose a '4-squares' cell, in which case the second player might consider playing black and starting with a '9-squares' cell himself.


Square Off © MindSports
No applet



Dominions

  • six
  • five
  • four
  • four
  • four
  • three
  • three
  • three
  • three
  • two
  • two
  • two
  • one
Board and pieces
The Dominions board is a base 9 hexagon with 217 cells.

The pieces are two identical sets of 63 hexagons, black on one side, white on the other, displaying all the ways that 1 to 6 beams can radiate from the center.
A piece, if flipped along its horizontal axis, displays the same pattern in the opposite color.
Using the applet, you won't have to worry about that.

The 'blank'
  • blank
The blank features in the China Labyrinth as well as in the I Ching Connexion, but plays no role in the game of dominions (other than as move and score indicator in the applet).

The numbering of the pieces
Pieces are numbered following a simple binary code: the six 'ones' in the diagram are numbered as subsequential powers of two. All other numbers are obtained by simply adding the powers of two concerned.
If you move the cursor over a piece, its number will be displayed.

Applet
You can download this MindSports applet, which is tailored to save games played in the Pit, offline.
Sorry, you need a Java enabled browser to view the Dominions Player!
download applet play online a word on notation

Rules
The board is initially empty. Dominions' pieces have a fixed orientation. Pieces remain in that orientation throughout the game.

Groups - Liberties - Capture
  • A group consists of a single piece or several pieces of the same color that are connected by beams. Adjacent blank sides do not constitute a group connection.
  • The liberties of a group are the beams that border on vacant cells. The pieces of a group share the group's liberties. A group lives if it has at least one liberty.
  • If a piece, or the group that it is part of, loses its last liberty the piece or group is reversed, uniting its captors in a new group.

The Beam Structure - Sections - Placement
  • During the game pieces of both colors get connected by beams. In any position, all beams together (disregarding color) are called the beam structure.
  • Pieces may be placed without connecting to the existing beam structure. That way disconnected parts of the beam stucture are created. These parts are called called sections.
    Sections of course may merge by placement of pieces that connect them.
  • White starts by placing one piece on the board. Players next move in turn to place one piece. Moving is not compulsory: a player may pass his turn without losing the right to move on his next turn. The game ends if both players pass on successive turns.
    In consequence a player who trails in terms of territory cannot afford to pass, since his opponent would pass also and win the game.
  • A piece that is placed must always match adjacent pieces of either color in terms of beams and blanks.
  • The piece must be placed adjacent to at least one opponent's piece - this may be a beam-to-beam or a blank-to-blank contact.
    Exception
    A player may freely extend from his own piece or group if this piece or group makes up a complete section of the beam structure. To 'extend' means that the piece must add to this section.
  • A piece may not cause oscillation, that is, if it makes a capture, the resulting new group must at least have one liberty.
  • Suicide is legal: if a piece by placement takes all its own liberties - or creates a group with no liberties - it commits suicide and (the group) is reversed immediately. This constitutes the end of the turn.

Suicide has many tactical applications: it may be used to reduce the number of liberties of an opponent's group one aims to attack, while preventing extensions. It may also be used to create places to start a new section.
A piece starting a new section makes up a complete section of the beam structure and thus may be extended freely from by its owner! The nearest example is black commiting suicide on his first move: the resulting white group makes up a complete section and may be freely extended from by white.
suicideIn the example, white has started with the 'six' and black has put a 'five' on top.
White next has sacificed a 'one' by suicide to create space to start a new section.
Black follows up with his 'six' at the other end, and white starts up a new section with a 'five'. This piece demands black's immediate attention because it makes up a complete section of the beam structure and thus may be extended freely from by white!

A black suicide is no option: the resulting white group would still make up a complete section. So black is forced to engage in local conflict.


The Edge
The outward edges of border-cells are considered neutral blanks. Thus the maximum match for a cell on the side is an 'unbroken four', for a corner an 'unbroken three'.

Object
The game ends if one player resigns or if both pass on successive turns. In the latter case the winner is the player with the most territory. A players territory consists of the number of his pieces on the board minus the number of pieces he didn't place.
This implies that each player would like to end the game with as few pieces as possible 'in hand'. Pieces that in the end can only commit suicide do not affect the outcome: the moving player gains a point by getting rid of the piece, but so does the opponent because of the extra point of territory.

Eyes
Though strategy is largely unknown, creating groups that live unconditionally is a sure part of it. Tactics to achieve this are varied and subtle.
If a group has a liberty at a cell for which the opponent has no longer a matching piece, this cell is called an 'eye'.
A group with an eye lives unconditionally.
An eye of one player's group(s) is not necessarily at the same time an eye of the opponent's group(s) that may have liberties at it: one player may still have matching pieces for a cell, while the other doesn't.

General advise
Adding liberties to a group requires pieces with at least 3 liberties, so be economical with those. Taking liberties from an opponent's group while preventing extensions requires 'suicide pieces', usually 'one's' and 'two's', so be economical with those too. In short: be economical.
Special attention should be given to borderplay: towards the endgame opportunities for creating eyes and starting new live groups increase and the demand for pieces with fewer liberties rises with the possibilities to keep them alive.
Strength hides in the details!

Dominions © MindSports
Java applet © Ed van Zon



Connection
'Connection' is a well known sub-theme in a terrirory game like Go. We feature Havannah in the Arena. YvY is less known and less 'accessible', but very rewarding as a strategy game.



YvY
YvY was born out of dissatisfaction with Superstar that in turn was born out of dissatiafaction with Craige Schensted's Star. Where Star was too tedious and has been replaced by a better version, Superstar is too complex.

So when I suddenly caught a glimpse of a 'simpified Superstar' one night, I posted the rather immature rules in a couple of threads, the next morning, here and here. That was in October 2009.

However immature, the game turned out fine, eventually, because of suggestions made by David J Bush, a world class Twixt player, so he shares YvY's copyright with MindSports.

I'm very pleased with another strategy game, but at the same time I think it's time to call it a day. I missed YvY in the first approach, and even after David's suggestions, hunting it down to it's essence was rather tedious. I was surprised in fact when it suddenly came together in a very simple way. Read about it in A final whisper.

YvY base 4,5YvY is played on a special board. The image shows a 'base-9' one, with 9 sprouts - the green cells - along any two adjacent sides. MindSports will also provide a base-7 and a base-5 applet in the near future.
  • The game starts on an empty board. Players move in turn to place one stone on an empty cell. White moves first. The second player is entitled to a swap.

    The MindSports applet will shortly offer the swap under the 'choose' button. The result will be a switch of color of the stone on the board.

  • A player may pass his turn, without losing the right to move on the next one.

Groups & Loops
  • A 'group' consists of a number of connected like colored stones. A single stone is a group by definition.
    As in Go, calling a number of stones a 'group' is most of the time meant in a less formal way.
  • A 'loop' is a group that completely surrounds one or more cells. Whether or not such cells are occupied, or by whom, is irrelevant.

Object
  • The game ends in one of two ways:

    • By sudden death: if a player completes a loop he wins, regardless of the score.
    • After both players pass on successive turns: now the player with the highest score wins.

Life & Death
  • A group lives if at least one of its stones occupies a sprout, otherwise it is (as yet) dead.

Territory & Scores
  • If a game ends by the players passing on successive turns then dead groups are removed from the board before the counting starts.
  • After the removal of dead groups, any group fenced in by a group of like color, is considered part of that same group.
  • The score of each player is the number of sprouts he controls (that is: sprouts occupied or fenced in by his stones) minus twice the number of his groups.

If, for example, one player has followed a center oriented strategy, resulting in one group controlling 11 sprouts, his score would be 9. The other player controls the remaining 16 sprouts, so if he managed to do that with three groups, he has 10 points and wins, but if he needed four he has 8 points and loses. This is a game of 'divide and rule'!
Note: if one player's score is even, the other's will be odd, so the game cannot end in a draw.


Strategy & Tactics
In terms of tactics, YvY first and foremost requires reading the hexplane the same way as in games like for instance Hex and Y, but the presence of the loop as an absolute criterion to win makes its tactics much more Havannah like. In fact YvY might be considered a 'generalized Havannah' in which the concept of corners and sides has been replaced by by an odd number of evenly distributed sprouts and the goal is, roughly speaking, to connect as many of them as possible with as few groups as possible.

Not surprisingly, the strategic dilemma of Havannah - 'spider' versus 'snake' - is revisited here. The edge is important to get control of a sufficient number of sprouts, but the center is clearly the area where connections are made. One may sacrifice a couple of sprouts to connect one's own live groups, as in the example given in the rules: one group controlling eleven sprouts wins if the opponent has four groups or more, and loses if he has three groups or less. The resulting tension between moving near the edge or higher up is totally reminiscent of Havannah, as is the loop, that fulfills the same tactical role: a tool to cut and/or connect.

There are important differences nonetheless. In Havannah the fastest connection is usually very important, whether it be ring, bridge or fork. A frame doesn't mean much if the opponent has a faster one. In YvY the score is accumulative, and in terms of the absolute win, a loopframe will usually not face a faster threat (the only option being a faster loop). So basically framing is winning.
Another difference is that YvY will usually have a 'Go type' opening, with claims staked out along the edges, whereas Havannah can have many different types of opening. YvY definitely feels more Go like than Havannah.

Example game
Here is the first ever YvY game, played between Christian Freeling, white, and Ed van Zon. Both are seasoned Havannah players.
You can download the MindSports YvY applet, which is tailored to save games played in the ArenA, offline.


Christian Freeling - Ed van Zon (0-1)
Sorry, you need a Java enabled browser to view this YvY Game.
download applet play online a word on notation

YvY © MindSports and David J Bush
Java applet by Ed van Zon




Superstar
SuperStar was one of my last games, invented when I had already quit the games club "Fanatic" at Twente University, the Netherlands. The game grew out of dissatisfaction with Craige Schensted's game 'Star' which introduced a way to award pointvalue to a certain type of connection called a 'star' on a hexboard, and in particular a way to make connections between stars pay off. But in Star this is the only governing idea, which makes the game rather one-dimensional, with a strong suspicion of being a win for the first player.
The idea is implicitly present in SuperStar, but within a wider context. The game is played on a star-shaped board, with twelve sides that, in addition to stars, also allow the creation of superstars, connections with a much higher pointvalue, rendering a much higher reward for connecting them, and loops that allow for additional scores by surrounding territory or opponent's stones.
Its three sepatate goals are reminiscent of Havannah, Hexade and Rondo, while the pointvalues add a Go-like flavor.

Superstar, or rather dissatisfaction with it, eventually led to YvY and to the final chapter of the essay "How I invented games and why not".
boardThe ring of 60 cells surrounding the actual board is called the edge. It plays a role in defining a 'star'. The edge is not part of the playing area. In addition to defining a star, it is used for the coordinate system. For any cell, look left and right down the oblique lines to obtain its coordinates. Note that the 'D' and the '4' are shifted along the lines they define, to avoid having them end up on the same cell of the edge.

The board has twelve sides. A side is formed by 5 cells: an inward corner, an outward corner and the 3 cells in between. Thus the six inward corners each belong to two sides.

Rules
  • The game starts on an empty board. Players move in turn to place one stone on a vacant cell. White moves first. Moving is not compulsary. The game ends when both players pass on successive turns, after which the counting takes place.

Object
The object of the game is to score more points than the opponent. Points are awarded for creating 'stars', 'superstars' and 'rings'. All of these are unbroken chains of connected stones of one color.
  • A star is a chain touching at least 3 cells of the edge.
    The value of a star is two less than the number of cells of the edge it touches.
  • A superstar is a chain connecting at least 3 sides.
    The value of a superstar is 5*(S-2) where 'S' is the number of sides it connects.
  • A loop is a chain surrounding at least one cell.
    The value of a loop is one point for every vacant cell it surrounds and 5 points for every opponent's stone trapped in it.

A chain may be a star, superstar and ring at the same time. Of course seperate counts are made in each capacity.

From the first definition follows:
  • A single stone on an outward corner (touching 3 cells of the edge) is a 1-point star in itself.
  • A connection between two previously disconnected stars makes the new star worth 2 points more than the sum of its previous parts, thus making connections pay off.

From the second definition follows:
  • A single stone on an inward corner already 'connects' two sides, so that linking up with a third side will result in a 5 point superstar.
  • A connection between two previously disconnected superstars that don't share a side, makes the new superstar worth 10 points more than the sum of its previous parts. Thus these connections pay off even more.
From both definitions follows that a superstar usually will also be a star. An exception is a chain that connects two inward corners without occupying other cells of the sides: this constitutes a 10 point superstar without being a star. An example is the seven stones black chain in the diagram below.
boardThe white chains are a 2-point and a 1-point star respectively, but connecting at 'A' makes one star touching seven cells of the edge and thus worth 5 points, two more than the sum of the seperate parts.
A chain doesn't even have to be a star to add thus if connected: if the rightmost white stone were deleted, the other one is no longer a star, but connecting at 'A' will still bring two extra points.

The same can be seen at 'B', where a 10-point superstar is linked to a chain that is not a superstar itself because it touches only one side. The connection nevertheless brings 5 points.

A further connection at 'C', to a stone that touches two sides but again without point-value in itself, even creates a 25-point superstar.

Komi
The player moving second gets a number of points beforehand to compensate for the disadvantage of not moving first. Accurate komi have not yet been established.

Strategy and tactics
Superstars and connections between them obviously are prime strategic goals. Occupying two adjacent inward corners can hardly be wrong for starters. Loops are more dependent on a game's development and evolve later in the game when tactics come into play. Stars grow along the edge and are important in he endgame when the bigger issues have been settled. The center clearly is the area where the all important connections are made.

Ed van Zon - Christian Freeling (The Pit, 2008, 0-1)
Sorry, you need a Java enabled browser to view this Superstar Game.
download applet play online a word on notation
You can download this MindSports applet, which is tailored to save games played in the Pit, offline.

Superstar © MindSports
Java applet © Ed van Zon



Rondo
rondoRules
Like Havannah and Superstar, Rondo has a three-fold objective.
A player wins by:
  • connecting the inner and outer circle, or
  • forcing his opponent into a 'perpetual jump' on a circle, or
  • blocking his opponent completely.

Movement
Diagram 1 shows the initial position. There are two players, black and white, who alternate turns. On his turn a player must move one of his men. White starts.

If not obliged to 'jump', a player must move one of his men to an adjacent vacant cell.
For white the move must be:
  • clockwise or outward or clockwise-outward, as shown in diagram 2.

For black the move must be:
  • anticlockwise or inward or anticlockwise-inward, as shown in diagram 2.

Jumping
If the player to move is in a position to jump, he must do so. Jumping always takes place on one circle, clockwise for white, anticlockwise for black. The jumps are draughtslike, but no pieces are captured. A multiple jump must be completed. Majority jumps have no precedence.
Diagram 3 shows a white man that must make a double jump, and a black man that must make a single one. Neither may jump in the opposite direction. If a player gets trapped in a perpetual jump over six men, he has lost.

Connecting
If a move completes a connection between the inner- and outer circle, the player wins. The connection may have any number of men, but must follow the players' direction of play: clockwise-ouward or, which is the same, anticlockwise-inward, diagonals included.
Diagram 4 shows two identical 5-men connections, one white and one black. The black chain at the bottom is not a connection, because the two marked men are not connected: neither white nor black has a legal move from the one cell to the other.

Rondo © MindSports
No applet



Other themes
The greatest games are usually based on in one of the big four: checkmate, elimination, territory and connection. But there are interesting games on themes like breakthrough, race, configuration or 'bead collecting'.
Here's a couple of those.



HanniBall
HanniBall was invented the 6th, 7th and 8th of April 2009, without board or pieces, to show that an idea can 'explain itself' by listening carefully, the very point I try to make in this very essay. I didn't quite succeed. The main flaw turned out to be a dominant strategy for the player in possession of the ball, coined catenaccio. This was remedied with a rule against clustering, suggested by Arty Sandler of iGGameCenter.
Here's the story in a nutshell: A late arrival.

Rules
hannibalBoard
The board is a rectangle of 9x13 squares, with two additional goals of 1x3 squares. There are two 'goal areas' of 2x5 squares.
Both players, White and Black, have 11 pieces: 1 Keeper, 2 Lions, 4 Elephants and 4 Horses.
The diagram shows the board with the pieces in the initial position. The ball lies in the centersquare.

Object
The object of HanniBall is to shoot the ball into the opponent's goal. If a player shoots the ball into his own goal, he loses the game.

Moving and capturing
White begins and players move in turn. Each turn a player is allowed to make up to 4 moves, which must lead to at least one change in the position. However, white on his first turn may make no more than 2 moves.
A 'move' may be:
  1. Moving a piece that does not have the ball.
  2. Moving a piece that does have the ball, with or without it (the latter barring the Keeper).
  3. Shooting the ball.

Shooting the ball can only be done by a piece that has the ball in its possesion. The pieces move and shoot as follows:
  • The Horse moves as the knight in Chess, but may not jump to its target square if both the in between squares are occupied by pieces. A Horse shoots the ball 'king's move' wise. If a Horse shoots the ball, it lands on a straight or diagonally adjacent square.
    Note that a knight's move is always possible between a cornersquare of the goal and the backrow of the field on that side (for instance b2 and d1), because there are no two intermediate squares beween these squares.
  • The Elephant moves as the king in Chess. An Elephant shoots the ball 'knight's move' wise. If an Elephant shoots the ball, it lands on a square one knight's move away, no restrictions.
  • The Lion combines the options of Knight and Elephant, so it moves and shoots either way in any combination.
  • The Keeper moves as a Lion, but may not leave the goal area (except for the goal itself). A Keeper in possesion of the ball, may not let go of it other than by shooting it (that is, he may not move and leave the ball behind). A Keeper shoots the ball up to five squares away, queenwise. Direction and distance are the player's choice, but the ball must land outside the goal area.

Inside the goal the Keeper or a defender should not have the ball in its possession, because a ball inside the own goal immediately ends the game in a win for the opponent.

The Ball
The Ball may land on any square, whether or not occupied.
  • If a piece moves to a square where the ball is, it takes possession of the ball.
  • If the ball lands on a square occupied by a piece, other than a Keeper, the piece takes possesion of the ball.
  • If a player is in possesion of the ball, and it is his turn, and he has still one or more move options left, than he can do one or more of the following:
    1. Shoot the ball.
    2. Move the piece and take the ball along.
    3. Barring the Keeper: move the piece and leave the ball.
    4. Move another piece.
  • If a player is in possesion of the ball, and it is not his turn, then the piece holding the ball can be captured by the opponent. Capture is by replacement. The captured piece is taken off the board, and the capturing piece takes possession of the ball.

Please note that if a player shoots the ball to an opponent's piece, and he has still one or more move options left, he may, if he can, capture that piece!
Note also that the opponent's goal is a freezone with regard to such an action: a player would have to shoot the ball into his own goal to do so, and thus lose the game.

Shots at the goal or the Keeper
  • If a player shoots the ball into the opponent's goal, he wins the game. If he shoots it into his own goal he loses.
  • If the ball is shot to a square occupied by a Keeper of either side, the ball 'ricochets' off the Keeper, queenwise, up to five squares, but not into the goal (though it may land in the goal area). Direction and distance are determined by the shooting player, whether the shot is directed at a player's own Keeper or the opponent's Keeper.

Note that a Keeper can only take possession of the ball by picking it up in the goal area, or by capturing a piece there, that is in possesion of the ball. A Keeper in possesion of the ball risks capture like any other piece.

Obstruction
Obstruction is a 'red card' offense against the rules. It is permitted, but may and usually will be punished.
  • If a player on his turn finds a position in which he has at least one piece other than a Keeper, and not one of his pieces can reach the ball in any number of moves, then the opponent has committed obstruction and the player to move may (but is not obliged to) remove one of the opponent's pieces from the board as his first move. This may or may not be a blocking piece.
    If the obstruction is still in place at the beginning of the blocking player's next turn, he must to undo it himself, or risk having yet another piece removed.

Clustering is another 'obstructional' offence. It limits the size of 'groups' of like colored pieces.

Definition: A 'group' is a number of like colored pieces that are orthogonally connected. The ball, if it is not in a piece's possession, is a 'like colored piece' for both players and can be part of a black or a white group, or both. If the ball is in possession of a piece, only the piece is counted as part of a group.


Clustering
Clustering is a 'red card' offense against the rules. It is permitted, but may and usually will be punished.
  • If a player on his turn finds a position in which one or more of the opponent's groups occupy more than three squares then the opponent has committed clustering and the player to move may remove one of the opponent's pieces from the board as his first move. This may or may not be a 'clustering' piece.
    If the clustering is still in place at the beginning of the clustering player's next turn, he must undo it himself or risk having yet another piece removed.


HanniBall © MindSports and Arty Sandler
No applet

HanniBall has been implemented on the Zillions machine in June 2009.
HanniBall has been implemented at iGGameCenter in May 2010.
HanniBall's entry at BoardGameGeek.



Hexade
Hexade is Havannah's tactical support act. It does in fact somewhat hold the middle between this game and Gary Gabrel's Pente. It's very easy to learn, because its strategy is fairly straightforward. Tacticians will find it very rewarding.

Rules
  • The game starts on an empty board. Players move in turn to place one stone on an empty cell. White moves first.
  • Between white's first move and his second, there must be at least a two-cell distance. The diagram on the left shows a random first move with the forbidden area for white's second move. Black has no such restriction.

configurations
  • The game is won by the first player to complete a perfect six, which means creating:
    • six stones in a straight row, or
    • six stones in a compact triangle, or
    • six stones in a small hexagon,
    as shown in the right diagram, and well in such a way (here the 'perfect' comes in) that it outlasts the opponent's next move.
    If the opponent immediately destroys a six by capture, the game goes on.
  • Between white's first move and his second, there must be at least a two-cell distance. The diagram on the left shows a random first move with the forbidden area for white's second move. Black has no such restriction.

There are no restrictions to whatever stones are connected to a six. It doesn't matter for instance whether (or by whom) the cell inside a hexagon is occupied, or whether or not a straight six is an 'overline' of seven or more.

Capture
captureTwo adjacent stones of like color are called a 'pair'. If the placement of a stone results in one or more opponent's pairs being enclosed the custodian way (sandwiched between two enemy stones), these pairs are captured and removed from the board in the same turn.
Here a white play at 'A' captures two black pairs. A white play at 'B' makes the white pair save (for the moment), because pairs already enclosed cannot be captured. Of course white's capture of an enclosing stone may make his own pair vulnarable again.


Strategy
Strategy is obvious: you need a simultaneous threat at some point and see if you can force the six to perfect. That's the nice thing about tactical games: you're not in the dark about what's going on. To compensate for the lack in strategical depth, tactics are manifold, subtle and resourceful.

Falco Freeling - Christian Freeling (The Pit 2008, 0-1)
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Hexade is featured in R. Wayne Schmittberger's 'New Rules for Classic Games' (John Wiley & Sons, Inc. New York - ISBN 0-471-53621-0), but has since then undergone a minor change of rules, namely the introduction of the perfect six as object of the game.

A close relative
In 2009 a friend of mine, Benedikt Rosenau, drew my attention to an open letter addressed to me by one Steffer Mühlhäuser, posted on the web in december 2003, and concerning a game he'd invented called 'AVA'. It's a funny story because he basically invented Hexade anew. Then he heard of Havannah, but soon found it to be an altogether different game. So he wasn't troubled by it, till the Essen Gamefair of 2003:
"Als ich in Essen auf der „Spiel 03“ zum ersten Mal meine Spiele in der Öffentlichkeit vorstellte, kam es zu einem kleinen AVA- Nachspiel.
Irgendwann kam ein junger Mann mit einem dicken Ordner an unseren Stand. Nach einem prüfendem Blick auf SIX und AVA und einer kurzen Nachfrage sagte er mir auf den Kopf zu: „Das Spiel gibt es schon.“ Ich war nicht weiter beunruhigt, gleich würde er Havannah aus dem Hut ziehen, meine Verteidigungsrede konnte ich auswendig. Was kam war viel schlimmer.
Der junge Mann blätterte in seinem Ordner und hielt mir kurz darauf „Hexade“ unter die Nase. Christian Freeling (der Autor von Havannah) hatte es irgendwann einmal als Vorspiel zu Havannah entwickelt. Aber weder ihm, noch irgend einem Spieleverlag erschien es wohl interessant genug, um damit auf den Markt zu gehen (auch das noch!). Da waren sie: „meine“ drei Gewinnformationen Linie, Kreis und Dreieck. Freeling bezeichnete sie als „perfekte Sechser“ Das war nun wirklich ein Frust.
I must correct the story on minor points. I invented Hexade shortly after Havannah, not before - there wasn't much to 'invent' anyway: the game was very much there the same moment I got the idea of the three 'sixes'. And the shapes themselves are not called 'perfect'. The perfect comes in where a six can no longer be broken up by capture by the opponent on his next move.

Steffen has his own game company called Steffen Spiele and he was fair enough to recognize my authorship, so he eventually transformed the idea to a game called SIX, which deviates sufficiently from the original concept to be considered in its own right. You can play it online at Yucata.de

External links

Hexade © MindSports
Java applet © Ed van Zon



Minimancala
This is a Java implementation of Minimancala, the Noughts & Crosses of the mancala family. It's a board game for two players, and can be played against another person, the computer, or all by itself.

Applet

download applet

Rules
  • The board consists of two rows of two 'pits'. There are two players, north and south. Each player controls the two pits on his side. In the initial position each pit contains two beads.
  • Any player starts. Players move - and must move - in turn. On his turn a player selects one of his own pits, takes out all beads, and distributes them one by one in a counter-clockwise direction over the other three pits. If the pit contains more than three beads, the fourth (seventh) falls in the same pit as the first.
  • If a player on his turn finds both his pits empty, he has lost.

The Minimancala Tree
This is what you're playing against: the Minimancala Tree.
Backtrack coloring appears onmouseover.
Red moves lose, green moves win.
The pulsating draw represents best play for both sides.

MiniMancala Network

Note: MiniMancala has been implemented on the Zillions game machine.

MiniMancala © MindSports
Java applet © Ed van Zon



Swish & Squeeze
Swish & Squeeze are twin bead-capture games. The diagram shows one of countless initial set-ups for either. In both games each player has three 'hexagonal rooks' that move in the six main directions.

Object
There are 19 beads in the game. The first player to capture 10 of them wins.
initial positionInitial set-up
The initial set-up is totally up to one player. He puts three white and three black rooks on the edge of the board and up to 19 'beads' on cells of the inner area.

The bait
In case the player decides to place less than 19 beads, the remainder is placed next to the board and called the bait. The diagram shows a one-bead bait.

The pie
Who moves first is decided by the second player: after the first player has completed an initial set-up he may choose to either:
  • move first, in which case he may choose whether to play back or white, while the bait goes to his opponent, or
  • take the bait, in which case his opponent may choose color and move first.

Swish
This being settled, players move, and must move, in turn.
Each player must, on his turn, move one of his rooks. A rook must always end its move on a vacant cell. It may move:
  • Any number of vacant cells.
  • Any number of vacant cells followed by a bead or an unbroken row of beads, provided there's at least one vacant cell beyond to land on. Beads thus leaped over are captured and added to the player's store.
    If there are more vacant cells beyond the captured beads, the player is free to land on any of them.
  • Any number of vacant cells followed by an opposing rook or an unbroken row of opposing rooks, provided there's at least one vacant cell beyond to land on. Pieces thus leaped over are captured and removed from play. If there are more vacant cells beyond the captured rook(s), the player is free to land on any of them.
    Simultaneous capture of a piece and beads is not possible.
Squeeze
This being settled, players move, and must move, in turn.
Each player must, on his turn, move one of his rooks. A rook must always end its move on a vacant cell.
  • Rooks may neither pass over nor land on a cell occupied by a piece or a bead.
  • Beads are captured the 'custodian' fashion, that is: sandwiched between two of a player's rooks. The first piece must already be in place for the second to make a capture.
    With two rooks in place is possible to capture in two directions simultaneously with the third one.
  • Opponent's rooks may be captured the same way as beads. Squeeze allows the simultaneous capture of a piece and beads, but not as a 'mixed row': the captures must be in different directions.

Swish & Squeeze © MindSports
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Breakthrough

Breakthrough is a race game. Its object is to first get a man onto the opponent's back row. Apart from the opponent, the wall is the most important obstacle in this quest.
The diagram shows the board and the pieces in the initial position. Players move in turn. White moves first.

Object
The object of the game is to be the first player to get a man onto the opponent's back row. However, blocking the opponent completely also constitutes a win.

Movement
In turn, each player moves one of his pieces any number of squares diagonally, either forward or backward, with these restrictions:

initial position
  • A piece may not jump over another piece.
  • A piece may not move onto a square occupied by an opponent's piece.
  • When moving forward, a piece must stop if it reaches a square of the wall on the opponent's side of the board. Once on the far wall, a piece may not move forward from it except by explosion.
    A piece may move backward from or backward across the wall. The wall on a player's own side of the board does not affect the movement of his pieces.
  • A piece may move onto a square already occupied by one of his own pieces. Thus stacks may arise.
    Such a stack moves as a unit, following all rules and restrictions of single men, and 'explodes' if it's height surpasses the square's 'capacity'.
  • Moving is compulsory.

Capacity
  • Each square in the central three columns will hold at most two men.
  • Each square in the side columns will hold at most one man.

Explosions
If a move results in a square exceeding its capacity, the square explodes, which means that it shoots its men to the adjacent squares in forward and sideways directions.
  • For the central columns this means one man forward, one to the left and one to the right.
  • For the side columns it means one man forward and one sideways.
  • The remainder, if any, stays on the original square.

Men dispersed by an explosion ignore the second and third restriction listed above under movement. Thus an explosion may require a piece to be dispersed onto a square occupied by an opponent's piece. This piece, whether a single man or a pair, is captured and removed from play. There is one important exception:
  • A piece on the far wall is safe from capture: any opponent's man that explodes onto its square is instead eliminated itself.

explosions explosions explosions
Chain reactions
If an explosion and the resulting dispersal of men causes other squares to surpass capacity, these all explode as part of the same turn. The order in which to perform them is up to the player.
An example can be given right from the start: if white opens with 1.b2a1, this causes a1 to surpass capacity, dispersing its contents to b1 and a2. The latter therewith also surpasses its capacity and in turn explodes its men to b2 and a3.
All has settled down in the rightmost diagram. This is not at all an unusual opening move.

Strategy
Strategy is fairly obvious: you need an explosion from the far wall to get beyond. Side columns explode fastest, so a7 and e7 appear obvious targets for white to get his men on.
The drawback of this strategy is that, if successful, it gets a man across on the sidecolumn on a8 or e8, where a defender can block it with a single man on b9 or d9. If however the attacker next successfully targets the same square again by a second explosion from the same square on the wall he wins because this would cause the square on the eighth row to explode.

Breakthrough © MindSports

Newbie #1 - Newbie #2 (0-1)
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Trackgammon
Trackgammon is backgammon type game for 2-4 players who each play individually. Each player has a segment of the board and a stack of 5 discs of subsequent diameters. The boardsegments fit together to a board for 2, 3 or 4 players as indicated.
Each player has a 14-points track in front of him and places his stack on the leftmost point.
explosions

The track follows the player's side of the segments, as indicated on the 2-player board, so player's interact only on the centerpoints. The light lines near the center of the 3- and 4-player layout are not actually part of the board, but indicate how the tracks switch from one segment to the next.

Object
The object is to move one's stack along the track to the other side, disc by disc according to the throw of two dice, and come in first in the process.

Rules
  • One player moves first, after which player's take turns clockwise. On his turn a player throws two dice.
    • If the throw is unequal, the player moves his discs accordingly.
    • If it is a double, the player must add the reverse side of the dice and move his discs accordingly.
    Thus on his turn a player has either two or four moves at his disposal and he may use them for the same or different discs as he pleases. However, he may only move top discs, and every number of eyes must be moved seperately!
  • A move may be forwards or backwards as the player pleases, counting onwards in the opposite direction if it passes over the begin- or endpoint of the track.
    A player may not pass (part of) his move, but a disc may land on the point it started from if it passes over the begin- or endpoint of the track.
  • A disc may never land on a smaller disc, nor may it move over an opponent's smaller disc.
  • If a disc lands on a disc of equal size it takes its place, while the 'captured' disc returns to its starting point, where it is inserted according to size.
  • A disc may freely land on any larger disc, which then, for the time being, is blocked.

Every number of eyes must be moved seperately. If a player for instance throws 3-5 on his first move and uses them to move the top disc 5 steps and the second disc 3, and if on his next turn he again throws 3-5, then he won't be able to move the third disc 8 steps, because the 3 and the 5 must be moved seperately, and both points are blocked by a smaller disc.

Entering
Since no disc may land on a smaller one, the last one out must be the first one in.
In the initial position the 'next disc to enter' is the largest one, for every player. Once the largest one has been moved to the endpoint, the second largest one is the 'next disc to enter'. Thus, in any stage of the game, every player has exactly one 'next disc to enter'.
  • All moves follow exact count, except the 'next disc to enter': once it has reached the endpoint, the remainder of that part of the move may be discarded.

Every player is entitled to the same number of turns as the first player who enters all his discs, so after this has happened, one or more players may be entitled to an 'afterthrow'. Players may finish ex aequo that way.

The doubling die
If played for stakes, a doubling die may be employed much the same way as in Backgammon. If in a multi player game, a player leaves on a double, his discs remain where they are as if he were still in the game.

Trackgammon © MindSports
No applet



Recent additions
Although I'm not actively inventing, I can't help stumbling over the occasional game. That happened with Query.
Hexdameo may either be considered 'Hexdame with linear movement' or 'Dameo translated to the hexgrid'.
Chakra's reason for being is a very special 'piece', the transmitter, consisting of two parts that are part piece, part square, dreamed up with Ed van Zon, a long long time ago.

The games in this section have been put here provisionally, with just the bare bones rules.



Chakra
Initial positionChakra's reason for being is a very special 'piece', the transmitter, consisting of two parts that are part piece, part square, dreamed up with Ed van Zon, a long long time ago. The housing was provided by a Chess game that in itself had no reason for being. The object is checkmate and stalemate is a draw.
  • The King moves like the king in Chess.
  • The Queen moves like the queen in Chess.
  • The Samurai (to the right of the King) moves like a rook or a king.
  • The Monk (to the left of the Queen) moves like a bishop or a king.
  • The Monkey moves like the knight in Chess.
  • The Courtesan moves like the king in Chess, but has a special relationship with the King: whenever a Courtesan can 'see' her King along a straight or diagonal open line, she controls the lenght of this line, up to the King in one direction, upto the next obstacle in the other, including if the obstacle happens to be an opponent's piece.
  • The Pawn moves like the pawn in Chess but may not move two steps initially.
  • The Transmitter consists of two parts called chakra's. In some respects a chakra is a 'piece': on his turn a player may move a vacant chakra, just as any other piece. A chakra moves like a king or a knight, depending on which side is up (square or circle respectively). After the move the player may flip the chakra as part of the same turn. A chakra is also a 'piece' in that an opponent's piece may move onto, but not over it. Thus a chakra can interpose on a staight or diagonal check. A chakra may never move onto another chakra of either color.
    The only piece that can capture a chakra is the opponent's King. It can only do so by capturing a vacant chaka: if the chakra is occupied the King, if doing so doesn't lead him in check, can only capture the piece, but not the chakra.
    In all other respects the chakra is a 'square' as much as it is a piece, and a player can move over his own chakra's as if they weren't there.

    Basic property
    The basic property of the Transmitter is this: If a piece moves onto a vacant chakra of it's own color, and the other chakra is either vacant or occupied by an opponent's piece, then the piece is transmitted to the other chakra, capturing the opponent's piece as the case may be. If the second chakra is occupied by a piece of like color, the Transmitter doesn't work and the result of the move will be the player occupying both his chakra's.

    Note that a pawn can be promoted instantly by having one chakra in front of it, and the other on the backrow. A pawn is promoted to any piece previously lost by its side. Note also that a King can give check and even deliver checkmate through a Transmitter!

Chakra © MindSports

No applet



Query
BoardQuery is a connection game in which the players, Black and White, take turns to put one stone on a vacant c8 intersection or two stones on two vacant c4 intersections. Black moves first, after which White is entiteld to a swap.
  • White tries to connect the upper and lower side of the board, Black the left and right side, following the lines of the board. The cornerpoints belong to both sides.

Query © MindSports

No applet



Hexbushka
Initial positionThe diagram shows the board and the pieces in the initial position. The only difference with Bushka is the hexboard.

Hexbushka © MindSports

No applet



Hexdameo
Initial positionThe diagram shows the board and the pieces in the initial position. The only difference with Hexdame is the presence of linear movement: an unbroken straight line of men may move forward as a whole, in any of the three main directions, provided the cell in front is vacant.

Hexdameo © MindSports

No applet



Mephisto
An initial positionMephisto is a game for any number of players.
You need:
A domino set, five different colored pawns, five correspondingly colored dice, a one minute sandtimer and as many beer infested beta-nerds as the room will accommodate.

This is how we played it:
  • The dominos are laid out in a 7x8 grid, no blanks on the edge, no blanks orthogonally adjacent (except the double-blank of course).
  • Players set their stakes (jawbreakers for instance, or beer) The pawns are placed on five blanks. The dice are thrown, the timer is set.
  • Each pawn must move orthogonally, exactly the number of steps that is on the corresponding die. The track may not lead onto any square twice (including the starting square). A pawn may not move onto or over an occupied square.
  • Object:
    Players now all try to visualize how to move the pawns so that the highest possible score is reached. There are two kinds of score: a nominal score and a street

    Nominal
    If the pawns in the endposition are on different values, the score is the total of these values, for instance 6+6+6+5+4=27.

    Street
    If the pawns in the endposition are all on the same value, the position is a street. The highest possible nominal score 6+6+6+6+6=30 is also the lowest possible street. The lower the value, the higher the street.
    The highest street of 5 blanks is called Mephisto, but remember all pawns must end on a different blank than the one they started from!
  • If a player sees a first score or a score that tops the previous bid, he calls out: 28! ... street6! ... street4! ... .
    When the timer stops it is turned and the player with the highest bid must realize it within a minute, moving the pawns according to the rules. If he succeeds he wins all stakes, if he fails he must pay every player his stakes.
  • If a player calls out Mephisto!, the timer is turned immediately and the player must realize it in the same time it took him to visualize it.

Mephisto © MindSports

No applet