Osbo Cameron Browne (c) 2008

Osbo is a boardless dice game in which two or more players strive to complete the longest celtic knot.

Rules

Pieces: Players share a common pool of six-sided dice showing knot segments on each face. Note that two of the faces are identical.

The six faces of an Osbo die.

Start: Each player has a separate playing area in which they grow their design. The game starts with a single die in each playing area showing the face with the most crossings uppermost.

Starting position for a four-player game.

Play: Players take turns rolling m dice (where m is the number of players) and placing the faces shown to extend existing path ends. Edge crossings must match edge crossings on all neighbouring dice, and as many dice as possible must be played to as many different players' designs as possible each turn.

Hence the mover will generally add one die (the best one!) to their own design and one die to each of their opponents' designs. Any dice left over due to players with no open path ends may be played wherever the mover chooses.

Each design must fit within a 5x5 grid; moves that would let a design extend beyond this limit are not allowed. For instance, if a player wished to play at point p in the following example they could not make the middle move shown, but they could make the move on the right as it keeps the design within an imaginary 5x5 window.

No move may allow a design to extend beyond a 5x5 grid.

Players whose designs have been completely closed remain active in the game and take their turn as usual; they can still extend their opponents' paths, if not their own.

Aim: The game ends when no players have any more moves (i.e. when all designs have been closed) and is won by the owner of the longest closed path. A path's length is given by the number of crossings it contains, with self-crossings counting twice.

The left player wins.

For example, the short game shown above has been won by the player on the left with a path of length 10. The player on the right has more total crossings but these are split into three separate paths each of length 8.

If scores are tied then the next longest closed paths are compared, then the next longest, and so on. If this fails to break the tie then the game is a draw.

Notes

Players should strive to maintain a single path with as many extension points as possible in their own design while attempting to split enemy designs into multiple shorter paths with limited extension points. Converge your paths, diverge your opponents'.

Dice faces with more crossings are more useful in the early game, while dice faces with fewer crossings are more useful in the end game.

Osbo is perverse in that players with completed designs - and hence no moves for themselves - still actively participate in the game and can even decide the eventual winner. This kingmaker effect is generally taboo in multiplayer game design but has been deliberately incorporated so that players must think carefully about who they attack; if A consistently hurts D, then D will take revenge when the opportunity arises (McCarthy's Revenge Rule). In fact, players with completed designs have extra blocking power as they no longer need to save the best die for themselves and will have at least one free die with which to wreak havoc. Players must therefore try to eliminate opponents without annoying them in the process. Tricky!

Another reason that players with closed designs remain active in the game is that they may not only decide the winner, but may go on to win the game themselves. Even players who have resigned and left the game may still win if they have achieved a closed path of sufficient length before retiring.

The fact that players may play to all opponents each turn makes move order less important than in other games. This provides a balancing mechanism which means that the last player does not necessarily get the worst deal.

Unfolding an Osbo die reveals that the six path segments actually form two interlinked knots if followed around.

An Osbo cube unfolded and coloured to show the two distinct knots.

An nxn game between m players will require nxnxm dice. For instance, a standard two-player 5x5 game will require 50 dice.

The highest possible score for the default 5x5 game is 72.

The highest possible score for a given nxn grid is 2 (2n - 1) (n - 1).

Grid size	Maximum score
2x2	6
3x3	20
4x4	42
5x5	72
6x6	110
7x7	156
8x8	210

This figure is determined by observing that:
1. The maximum score will be given by the longest single cord.
2. There will be 2n (n - 1) potential crossing points within an nxn grid (midpoints of internal edges).
3. n linked cords will be generated if all crossings are realised.
4. n - 1 crossings must be broken (removed) to splice these n cords into a single cord.
5. The longest possible cord will therefore have 2n (n - 1) - (n - 1) = (2n - 1) (n - 1) crossings.
6. The score will be twice this number as all crossings will be self-crossings.

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