How to tell when you have made a loop

Tiles above the board surface must be adjacent to at least one previously placed tile of the same color. This implies that every tile is connected to the board surface via a continuous path of same color tiles.

Here is a small portion of the board position. These tiles might be on levels one and two, or they might be higher up. The white tile A is sitting on top of tiles C, D, F. White tile B is on tiles D, E, G. Tile A must be connected to the board surface via tile C, and tile B must be connected to the board via tile G or tile E. So, a 3-D loop must have formed here, and the black tiles D and F form part of a continuous path of opposing tiles which passes through this loop.

Regardless of what the rest of the board looks like, the game is over. White has won. You could say that white has completed a bridge over a river of opposing tiles. There must be room at both ends of this river to pass completely through the loop formed by this bridge. Tiles F and D are each adjacent to at least one vacant space, so a path (a hole) can be traced completely through the loop. The highest part of a winning 3-D loop is always the last part to be completed.


Here tile F' is now white instead of black. Although a corner of tile D' is visible next to tiles F' and G', that corner of D' is not adjacent to any vacant space, as these terms have been defined here. The river does not pass completely through. There is a blocking region in the way, as described earlier. Tiles A', B', G', F' do not form a winning loop. It is impossible to form a loop over top of a single opposing tile. You need two opposing tiles, adjacent on the same level, to form a bridge over.

A winning 3-D loop will always have the same basic pattern as shown in the first diagram above. Tiles E and G might not be the same color, and the tile arrangement might be rotated or reflected and the colors might be reversed, but you will always complete a bridge of at least two tiles which crosses over a river of at least two adjacent opposing tiles.

Board surface markers

Keep in mind there is another way to win, by forming a board surface loop. Sometimes a portion of a board surface path could become buried by other tiles, making it difficult to tell if a board surface loop is possible or not. To keep track of buried paths, there are round tokens of different colors supplied with the game. When any board surface path becomes partly buried, place tokens of the same color on top of or next to each uncovered board surface tile around the outside of this "hill" of tiles which could form a board surface loop.

For example, in this position, white is about to play at the hole indicated by the orange triangle. Before doing so, three red markers are placed on or near black tiles as shown, to indicate that those three tiles are connected to each other via board surface tiles of the same color.

Sometimes a path could never form a board surface loop because it is blocked by opposing tiles, so these markers are not always necessary.


Examples of Winning Moves

The following diagrams show an overhead perspective-less view of a small Lazo grid. Every hole on every level where a tile (usually, of either color) may be placed is shown in purple. The green grid duplicates level one. The tile to the right of the green grid indicates whose move it is. A star indicates the best move, which is either an immediate win or a forced block of an immediate win threat. A move anywhere else would not be the best move.

To find a winning 3-D loop, look for a pair of enemy tiles, adjacent to each other on the same level, which you can complete a bridge over. In diagram 1, those two white tiles are tinted pink. One of these pink tiles is mostly buried, but you can see two corners of it. A white tile sits on top of this buried tile, so the river passes completely through. Black can win immediately by playing as indicated by the yellow star.

It may appear in diagram 1 that black could also win by playing at the space indicated by the question mark. A move there would indeed connect a black tile on the board surface to a level one black tile, and this might seem to form a loop of four tiles, but there is a blocking region in the way, outlined in red, and this means the white tiles you see are not adjacent to any vacant space through this region. There is no path of white tiles + vacant spaces which passes through.



In diagram 2 it might seem that black can win by playing in the hole marked with an X, but there is only one white tile there, and a blocking region prevents the hole from passing completely through. The best move for black here is to play at the star, which prevents white from winning on the next move.




The most important thing to see in Lazo is when a move forms a winning loop.


In diagram 3 white to move has an immediate win at the star. The pair of black tiles which are here tinted blue form the river which would pass under the white bridge.



Diagram 4 shows the same basic pattern as in diagram 3. A white tile at the star completes a bridge over the pair of black tiles which are here tinted blue. Do you see how the bridge can be completed over the river?



In diagram 5, black to move can complete a board surface loop at the star. The green grid shows this loop.



In diagram 6, white to move can complete a bridge over a pair of black tiles by playing at the star.

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