Holomino Cameron Browne (c) 2007 Holomino is a domino-style game with special tiles and big scores.

Rules

Tiles: A holomino is a hexagonal tile with bites taken out of alternating corners and each of the three remaining corners assigned a different number between 1 and 6. There are 40 unique holominoes, which are kept in a sack.

Start: Each player randomly draws three holominoes to form their pool. Pools must be visible to opponents and are the subset of tiles that the current player may play from each turn.

To start the game, a tile is drawn randomly from the sack and placed in the middle of the playing area.

Play: Each turn, the current player draws a random tile from the sack to supplement their pool, giving them four tiles to choose from (unless the sack is empty). They must play one their pool tiles adjacent to at least one existing tile such that all neighbouring tile edges and numbers match.

Players must move if possible. If the current player has no legal moves they must return one of their pool tiles to the sack and pass that turn.

Scoring: Players score points for any circular holes formed on their move. Each hole is worth the sum of the three matching number pairs around the hole.

 For example, this hole is worth: (3 + 2 + 5) = 10 pts.

If two or three holes are formed on the same move, then the scores from each hole are multiplied together.

Aim: The game ends when any player runs out of tiles or all players pass in succession. The player with the highest score wins.

Notes

 The minimum hole score is:         (1 + 2 + 3) = 6 pts. The maximum hole score is:       (4 + 5 + 6) = 15 pts.
 The maximum possible score for any move is to complete three maximal holes, as shown on the left (before) and right (after): (6+5+4) x (5+4+6) x (4+6+5) = 3,375 pts.                     This is rare!
 Blocking: The figure on the right shows a blocked position. No tile can be played there as no tile has two 3s, hence this hole will never be closed.
 There are 20 ways to combine the digits {1, 2, 3, 4, 5, 6} into triplets: 123, 124, 125, 126, 134, 135, 136, 145, 146, 156, 234, 235, 236, 245, 246, 256, 345, 346, 356, 456. However, each combination may be oriented either clockwise or anticlockwise around each tile, as shown on the right. There are hence two unique tiles for each triplet of digits and a total of 40 unique holominoes.

Considered in isolation, there are nine tiles that will match one existing corner, four tiles that will match two existing corners (unless identical), and one tile that will match three existing corners.

Strategy and Tactics

Given the potential for making such huge scores, the losing player can always hope to make a comeback by arranging a double or triple hole. However, this means taking more risks.

Multiple holes are difficult to achieve but worth the reward. For any position in which a multiple hole may be formed next turn, only one possible tile will complete the move.

Do not set up a multiple hole play unless you own the tile that will complete it, otherwise there will be a 50% chance of the opponent drawing the tile to steal the points.

The fact that the supplementary tile is drawn from the sack before each move means that players cannot plan their next move with absolute certainty; the opponent will have one random tile draw before then.

It can be a good move to offer the opponent a low-scoring hole if this leads to a higher-scoring opportunity in the future (sacrifice).

Get your opponent to do your work for you. If the opponent's options are limited, try to make them play forced moves to your advantage, for example, making them play a tile that gives you a multiple hole play.

Use blocking moves to stop the opponent forming double holes. Also use blocking moves to limit the opponent's options - but not yours!

Summary: Players should strive to set up multiple holes for which they have the key tile and which the opponent cannot immediately block.

Variants

Sane Scoring: Sane scoring is an alternative scoring method that produces less ridiculous scores and should be used if you like your games well-behaved rather than chaotic and unpredictable.

The sane score for each move is the sum of all hole scores multiplied by the number of holes. For example, the maximum possible sane score produced by three {4, 5, 6} holes is ( (4+5+6) + (4+5+6) + (4+5+6) ) x 3 = 135 pts.

Sane scoring reduces the chance of either player stealing the game with a lucky move and means that the better player will generally prevail.

History

Holomino tiles and rules copyright (c) Cameron Browne, July 2007.

Holominoes are named for their ability to form holes with neighbouring tiles.

Holomino can be played on Richard's PBeM server where it is called "Holo". Check out the help file for more details. Please challenge me (camb) to a game any time.

Holomino is also available for online play at YourturnMyturn, Jij Bent and Brettspielnetz.ne (Holomino page).

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