Cameron's Mambo Page

Play: The opening player starts by placing a tile, either side up, in the middle of the playing area. Thereafter, players take turns placing a tile, either side up, adjacent to at least one existing tile. Tiles must be placed so that their edge positions and colours exactly match those of adjacent tiles.

Any space in which the colours of three corners are decided by neighbouring tiles constitutes either a null point or an auto move as described below.

Null Points: Any space with three corners of the same colour constitutes a null point at which no tile can be played. For example, if a space has two red corners as shown below (left) and a tile is placed such that the third corner must also be red (middle) then the space becomes a null point (right).

Null points are marked 'X' and indicate dead end points that stop growth, as no tile can possibly be played there.

Auto Moves: Conversely, any space with three corners of mixed colour is automatically filled with the only tile that will fit there. For example, if a space has two red corners as shown below (left) and a tile is placed such that the third corner must be blue (middle) then the space is automatically filled with the appropriate tile as part of the move (right).

Aim: The game is won by killing an enemy group (stopping it from further growth) as shown in the following examples. Groups can be killed by closing them (left) or blocking their growth with null points (right).

If a move kills groups of both colours then the mover loses. If the tiles run out before a group is killed then the game is won by the player with the largest group (counting dominant tiles) otherwise it is a draw.

The small coloured region on each tile side is called a wedge and the large coloured region a bridge. The important distinction is that each bridge forms a link between two same-coloured corners through which neighbouring groups may connect, while each wedge constitutes a dead end that terminates connections from neighbouring groups.

The side with the red bridge is described as the tile's red-dominant side and the side with the blue bridge is described the tile's blue-dominant side. It is generally better for the current player to place a majority of tiles of their dominant colour each turn, unless circumstances dictate otherwise.

Auto moves are the key to tactical play in Mambo. Use auto moves to place multiple tiles in order to set up multiple threats with a single move.

The larger an opponent's group is allowed to grow, the more growth points (freedoms) it will have and the harder it will be to block. Try to keep the opponent split into smaller disparate groups that cannot be easily joined together. Null points are the easiest way to keep subgroups separated.

Every time a player places a tile of their dominant colour, they also place a wedge of the enemy's colour. A good move will use this enemy wedge to the mover's advantage, for instance by closing an enemy group, causing a favourable auto move or starting a new but weak enemy group that can be threatened.

If the opponent has the momentum and threatens to expand a large unstoppable group, a player can steal the initiative by creating a splinter group of the opponent's colour elsewhere and threatening to surround it, forcing an immediate and inconsequential reply from the opponent.

The figure on the right shows an even worse position for Red, who has two vulnerable wedges which cannot both be defended next turn - Red will lose from this position no matter whose turn it is to play. Beware of stray wedges near null points.

Cold Fronts: The adjacent pair of Blue wedges shown below (left) may look inconsequential but they actually constitute an emergency for Blue. If Red plays move a then Blue must reply with move b to stay alive*, allowing Red to apply the coup de grâce with move c to win the game. It pays to keep an eye out for this subtle threat or games will end quickly.

* Blue actually has an alternative move b that also delays the loss, however the end result will be the same.

Ladders: Groups with a single freedom may be forced to follow a sequence of ladder moves as shown. At each step, Red plays at the only point that will keep this group alive (they have the choice of two orientations but must play the red-dominant side) and in each case Blue's reply perpetuates the ladder to the next turn.

Note that Red makes the ladder zig-zag at each step which means that the enclosing pieces are split up into multiple smaller groups as the ladder grows. Blue must abandon this ladder or risk losing the game due to the "largest group wins" rule; this is a natural balancing mechanism so that ladders do not dominate the game and lead to easy wins.

Table Etiquette: Once a player has placed a tile then that move stands and must be completed - players cannot change their mind halfway through the auto placements and undo the move.

The following table lists the number of tile states that may be played at a given empty board point, depending on the number of coloured corners surrounding it (described as that point's degree of freedom):

Coloured Corners	Tile States
0	6	(opening tile)
1	3
2 (mixed)	2
2 (same)	1
3 (mixed)	1	(auto move)
3 (same)	0	(null point)

Some variants are played with territory scores (see below). The territory score of an individual loop enclosing n enemy junctions will be (3n + 1), as demonstrated below:

Territory scores for loops enclosing 0, 1, 2 and 3 enemy junctions.

The total territory score for a given group will therefore be a sum of digits from { 1, 4, 7, 10, 13, 16, 19... } rather than a sum of arbitrary digits. This increases the chances of two groups with a similar number of loops having the same territory score, and also makes it easier to count a group's territory at a glance.

The "+ 1" term in the (3n + 1) equation has the effect of rewarding greater numbers of loops within a group. For example, two loops each surrounding one enemy junction (8 pts) are worth more than one loop surrounding two enemy junctions (7 pts).

The following examples show some designs made with Mambo tiles. These are not necessarily positions that could emerge during a standard game.


*A Red head eating a Blue group.*	*A Mambo monkey.*


*En garde!*	*A Mambo fish.*

Variants

Limited and Full Auto Moves: Automatic moves at spaces with three corners of mixed colour are described as limited auto moves. By contrast, full auto moves involve the automatic placement of the appropriate tile as soon as any known point (space enclosed by two corners of the same colour) occurs. This eliminates null points from the game except in rare circumstances and allows some interesting variants.

The following example shows move a (left) that creates a space with three corners of mixed colour to the left and a space with two same-coloured corners to the right. Using limited auto moves, only the left space is automatically completed (centre). Using full auto moves, both spaces are automatically completed (right).

Move a.

Limited auto moves.

Full auto moves.

The rationale behind limited auto moves is that a space with two same-coloured corners has the potential to become either a null point or a forced placement if left uncompleted (recall that three same-coloured corners constitute a null point that can never be played).

Mambogo: Mambogo is played with full auto moves. The game ends when the tiles run out, and is won by the owner of the group with the most territory (number of enclosed junctions). If scores are tied then the game is won by the player with the most territory enclosed by all of their groups, otherwise the game is a draw.

The following example shows a game in progress, with red and blue groups each enclosing 8 pts of territory:

A game in progress, with red and blue territory scores marked.

Both players are currently tied on territory, however Blue has the edge as the Blue loop on the right will give them 1 more pt of territory in the event of a tiebreaker.

Territory is achieved by closing loops. There is a trade-off between trying to form a large number of small loops or a small number of large loops, which score more highly but are harder to make.

Mambogo is easier to play and less demanding than standard Mambo and leads to more attractive patterns emerging during play. Unfortunately, players are able to form self-perpetuating patterns that lead to easy wins in some circumstances.

Mamba: Mamba is played with full auto moves (i.e. no null points). A player wins by forming a group of their colour with four loops of any size. If a move achieves this for both players then the mover loses.

If the tiles run out before the game has been won, then the player with the largest group loses, else the game is a draw. Only the dominant tiles in each group are counted.

Mamboa: Mamboa is a combination of Mambo and Mamba with limited auto moves; a player wins by killing an enemy group and/or forming a group of their colour with two loops of any size. If a move achieves either or both of these conditions for both players then the mover loses.

If the tiles run out before the game has been won, then the player with the largest group wins, else the game is a draw. Only the dominant tiles in each group are counted. [Note: Mamboa uses the rule that the largest group wins, as this solves ladder problems that may arise when playing with the "kill a group" rule.]

The example below shows a Red win in Mamboa. Red has achieved both winning conditions, although only one is required. Null points also feature much more heavily in Mamboa.

A game of Mamboa won by Red.

Mambo is named for the abstract patterns that emerge during play, which can be reminiscent of the weird tribal artwork of Reg Mombassa.

The general play mechanism has not changed since the game's inception, however the winning conditions have undergone a number of revisions. The territorial rule set was thought to capture the best elements of earlier rule sets (enclosing enemy groups, loop formation, group connectivity) while avoiding their drawbacks (ladders, null points) to provide a faster-flowing and less taxing game at the expense of depth, however the emergence of self-perpetuating winning patterns somewhat detracts from this version. Despite a number of proposed revisions, the original kill-a-group version continues to provide the most interesting and challenging form of the game.

Thanks to Stephen Tavener for extensive play testing and excellent suggestions during the game's development.

Mambo can be played on Richard's PBeM server - check out the help file for more details. Many thanks to the server regulars who helped test the game. Please challenge me (camb) to a game any time.