The Game Mechanics
A die is perfect when the number of pips on the face of the die equals the number of dice neighboring it, regardless of those dice ownership and pips.
The first example figure below shows a part of a board with 6 dice. The dice five and three are perfect (it is shown with the highlight background), other dice are not perfect. The dice one and two are not perfect, because they have more neighbors than needed for perfection.
The perfection status is not permanent. If now we move the die one (as the second figure shows), then the die five goes regular, while the dice two, four and one itself (at its destination) become perfect.
The Basic Rules
Initially the board is empty. Each player holds 12 cubical dice of a distinctive colour (first player owns blue dice, second player owns red dice). In 3-player variant, each player owns 9 dice (third player owns green dice).
Players take alternating turns. Each turn you must roll one of you own dice and then place it in any vacant hex on the board rolled face up. You may choose either to take the moving die from the hand, or from the board. Thus, the board is getting filled, and some dice become perfect.
Get six or more of your dice perfect before your opponent does the same.
A game may end in a draw and not necessarily ends by the winner's move.
Manipulating their own dice only, players affect perfection status of opponent's dice as well, that creates a collision. At the same time the goal is virtually impossible to achive using only your own dice.
The spicy part is that at any single move significantly many dice could be affected -- theoretically, up to 12 dice could achieve the perfection or lose it by a single move. In other words the goal of the game is very fragile, which gives the game a great drama. Thus the game is not about your ability to get higher perfection score as fast as you can, but to create an advantageous position that allows you to flip as many dice as you can. Apparently this reasoning could be applied recursively to itself -- this makes the game non-trivial.
The Game Variants
In order to improve the gameplay, we offer you several modifications of the basic ruleset. Here we specify only the difference to the "BASIC" ruleset.
Players hold 13 dice, and the objective is to achieve perfection of 7 or more dice.
This variant generates significantly longer and even less luck-dependent games.
Players observe the next dice-roll one turn ahead.
Before the game starts you must roll one of your dice, and put it onto the table rolled face up -- this is your indicator. All players do the same and everybody sees all indicators. On each subsequent move a die chosen for rolling becomes the indicator, and the indicator moves on the board. The sequense of actions within a move is unchanged: first you decide which die to roll, then roll it, see the outcome, and then you take the indicator die and put it on the board, replacing the indicator die with the newly rolled one.
This variant uses 1 additional die for each player (to play the role of the indicator). "STRATEGIC" can be played with the "PRIMES" and "BASIC" objectives as well, if you play it "BASIC" you need 13 dice, and if you play it "PRIMES" you need 14 dice.
This is the most advanced variant, giving you plenty of information to make well crafted moves. It is played with 13 dice and with the objective "PRIMES".
Before the beginning of the game, you must roll all your dice one-by-one, thus creating the sequences of dice (the order is important, only the head of the sequence goes to the board during the game). All players do the same and everybody sees all sequences. During the main phase of the game, if you decide to remove a die from the board, you must roll it and put it to the tail of your sequence, otherwise you do not roll anything and proceed to the dice placement phase of your move. For dice placement you take a die from the head of your sequence without rolling it.
This is the variant without uncertainty, all die rolls are determined in advance. It is played with 13 dice and with the objective "PRIMES". It also requires a sheet of paper and a pencil.
Before the beginning of the game, players negotiate about the length of the game and then roll a die as many times as many moves they intend to make. They write down all rolls outcome in a sequence (note: all members with odd indexes belong to the 1st player and the rest to the 2nd one). The game proceeds normally, but instead of rolling a die each player uses the first number from the written sequence and strikes it out. If the sequence is exhausted the game result is considered a draw. (It is apparently safe to reuse unused tail of the sequence in a consequent game.)
This variant is particularly convenient for playing with physical dice
Players can not take imperfect dice from the board. The goal is to deprive your opponent of possible moves. When a player can not make a move the game ends and the winner is the player who made the last move.
All variants of the game can be played with 3 players, in this case each player owns 9 dice for "PRIMES" and "GROSSMEISTER", and 10 dice for "STRATEGIC"