Cameron Browne (2008)
Lambo is a tile placement game in which players strive to form closed groups of their colour.
Tiles: Two players, White and Blue, share a common pool of 48 hexagonal bridge tiles. Each tile contains a white bridge and a blue bridge, and may be oriented in three ways such that the corner colours are the same for each rotation. The small circular slices are called tips.
Figure 1. Three rotations of a bridge tile.
Start: The game starts with a single tile in the middle of the playing area.
Play: White places a single tile adjacent to the starting tile such that edge colours match, then players take turns placing two tiles per turn, adjacent to each other and at least one existing tile such that edge colours match.
Figure 2 shows a typical starting sequence: starting tile, White move, Blue move.
Figure 2. Typical starting sequence.
Aim: The game is won by the player who forms a closed group of their colour containing at least one bridge (a bridge group). Only one tile need be played if that tile wins the game for either player.
For example, figure 3 shows a game won by Blue who has enclosed a blue bridge group containing one bridge. The closed white group contains bridges so doesn't count.
Figure 3. A game won by Blue.
Tiebreaker: If a move closes bridge groups for both players then the mover loses. If the tiles run out before either player wins (rare) then the game is won by the player with the largest group (counting bridges) otherwise the game is a draw (even rarer).
Single holes enclosed on all six sides, as shown in Figure 4, represent a special case. A player cannot place the first tile of their move in such a hole (unless that tile immediately wins the game) as it would then be impossible to place the second tile of the move adjacent to it.
Figure 4. A hole.
Figure 5 (left) shows a situation in which either player may fill a hole by closing their group; however, they would lose by doing so as such a move would also close an opponent's group (right). Such unplayable positions of mutual disadvantage are called seki in Go.
Figure 5. A losing move for both players (seki).
However, White can quickly turn the position to their advantage by playing the two tiles shown in Figure 6 (left). This move closes the group except for the freedoms within the hole, which White can close on their next move to win (right).
Figure 6. White resolves the seki to win.
It's theoretically possible for Blue to achieve a similar win from the position shown in Figure 5 (left). However, this is unlikely as it would require at least nine tiles to close the surrounding Blue group and White is only three tiles away from a win.
This example shows how a group adjoining a single hole may be closed if the rest of the group is closed first. However, any group adjoining two or more separate holes is safe from closure; holes may therefore be used strategically as attacking moves (one hole) or to ensure group safety (two holes).
Strategy & Tactics
Players should look for moves that simultaneously achieve two disjoint threats, which constitutes a guaranteed win unless both threats can be nullifed by an adjacent tile pair. For example, Figure 7 (left) shows that three tips in a row are a guaranteed win if left undefended, as their owner can form two disjoint threats next turn (right). This is true for both players in this example.
Figure 7. Guaranteed win for the next player.
Figure 8 shows another danger pattern (the triskelion) in which White can force a win if it's their turn to play, by creating two disjoint threats as shown. Although White will never be presented with this exact pattern – there will always be four tiles placed after the second move – the principle holds for a number of similar patterns: look for disjoint groups, three or less moves from completion, that can both be reached with a single tile pair.
Figure 8. White can win.
Figure 9 shows a more subtle danger pattern; White has already lost this game even with next move. This can be proven using similar techniques to those used in the solution of Puzzle B below.
Figure 9. White has already lost.
Attacking players should be able to form an immediate threat almost every turn, which can be useful for limiting the opponent's replies. For example, Blue threatens to win from their very first move in Figure 2, forcing White to play at one or both of the red dots to stay alive. However, overly aggressive play can prove disastrous if the opponent's developing position is ignored; a much safer approach is: connect the opponent's most dangerous threats each turn to nullify them. This may give the opponent the largest group, but it's unlikely that the game will last long enough for that to matter.
The requirement that tile pairs be placed adjacent to each other makes it harder to spoil double threats set up by the opponent. This means that games are more likely to end in a kill rather than players being able to continually defend until the tiles run out.
White to play two adjacent tiles and set up a win (easy).
Can Blue play two adjacent tiles to survive?
This was the way that the game was originally played, however it was found to make defensive play too easy, resulting in players developing the board without real purpose and leading to too many draws. The adjacent placement constraint introduces the hole threat and tightens the game up considerably.
Eat Enemy: In this version, a group wins if it eats (surrounds) two or more enemy groups. The enclosing group may be open or closed. The eaten enemy groups may be of any size. For example, Figure 11 shows a game won by Blue who has formed a Blue group eating two White groups.
Figure 10. Blue eats two White groups to win.
If a move achieves this for both players then the group that eats the most enemy groups wins, else the mover loses.
If the tiles run out, the game is won by the player who eats the largest enemy group, if tied then the player who eats the most enemy groups, if still tied then the game is drawn.
Must Contain: Winning groups must be closed and contain (eat) at least one enemy subgroup. For example, Figure 11 shows a "must contain" game won by Blue (left) and a game with a closed but non-winning group (right).
Figure 11. A Blue win (left) and not a win (right).
If the tiles run out before either player wins, then the game is won by the owner of the largest closed group; if tied then the owner of the most closed groups; if still tied then the game is declared a draw.
The "must contain" version is more balanced as White is not immediately under attack from the very first move. It is more relaxed as every move is not an immediate threat to be answered, which allows more subtle play to develop; it still rewards clever play and allows satisfying killer moves, but threats must be constructed rather than simply being available each turn. The "must contain" rule is also more elegant from a theoretical standpoint as it removes the explicit "must-contain-a-bridge" minimum group size constraint.
Lambo tiles and rules by Cameron Browne and copyright (c) Cyberite Ltd 2008.
The name Lambo is derived from the fact that the game is a sort of "Lite Mambo".
Lambo 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.
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Site designed by Cameron Browne © 2007. Last modified 18/7/2007.