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Published: 05 October 2021

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Quantum Chess, or WPD Chess, (Wave-Particle Duality Chess).

Herewith a simple way to represent quantum effects in a game of chess by the addition of a small number of additional rules.

All the normal rules of chess apply and in addition: -

1) Any piece that can move to two or more empty squares can move to two of them at once by splitting the piece down the middle. (Either saw all pieces in half beforehand or use two pieces in place of each one at the start, on a board which can accommodate two pieces per square comfortably.)

2) Whenever a half piece interacts with an opposing piece, either by taking it or being taken by it, the other half of it instantly re-joins it, and both halves then occupy the position of the taken piece or both halves become eliminated if one of them gets taken.

3) A Player moving a half piece must also move its corresponding other half.

4) Halved pieces occupy squares and block movement and support and threaten other pieces in the same way as whole pieces.

These four rules lead to a challenging but playable game that has many intriguing properties.

A whole piece represents the piece in ‘particle’ mode, it has a definite position. Halved pieces represent the piece in ‘wave’ mode, it could occupy either position, but it will come to occupy a definite position only when it interacts.

At the end of a game, a record of the game that does not include the moves of all the half-pieces that ‘disappeared’ because their corresponding half interacted, will still look like a standard game of chess although some of the moves may appear as legal but as very strange choices.

The following picture shows a representation of Quantum Chess in the early stages of a game, using doubled pieces rather than pieces sawn in half. (The numbers on some of the pieces make it easier to remember which pieces go together.)

White has taken the Black Kings Pawn with Kings Knight.

Black has replied by moving its Kings Bishop to two possible places simultaneously, one possibility puts White’s King in check, the other possibility threatens White’s Knight.

White now has a quantum problem. White must take its King out of check by either moving it or by moving its Queen or Queen’s Bishop to block, or its Queen’s Bishop Pawn to both block and threaten the ‘possible presence’ of the Black Bishop.

Black can then take the White Knight and the entire Black Bishop will then occupy the White Knight’s square, thus removing any threat to its ‘possible presence’ by  the White Pawn.

Black has effectively used a quantum trick to threaten two pieces at once with two possible presences of its Bishop and then taken the White Knight. The result of this manoeuvre looks like a legal move in ordinary (particle) chess, but White’s failure to  protect its Knight remains inexplicable if the match record does not include the possible wavelike moves that later disappeared.

Quanta take off and land like particles, but they seem to fly as waves. We can only observe their particle behaviours but from their particle behaviours we can infer their wavelike behaviours.   

Imaginary phenomena can have real effects.

Herewith the world’s first fully operational Quantum Chess Piece!

Note the cunning base design which gives extra stability to each of the two halves and helps to secure them together.

Handmade from an ornamental curtain rail endpiece, a length of 2x2 inch softwood, and a disc cut from a length of batten, it took hours with chisels and files, followed by a delicate sawing in half. I don’t have a lathe. I doubt that I’ll try making the other 31 pieces this way.

If anyone wants to manufacture these in say plastic, please let me know, the pawns, rooks, queens, and kings would only require one mould each to this design as they have rotational symmetry about their long axes, the bishops and knights would probably require two moulds for each complete piece.

There follows some general musing on the physics/metaphysics of Quantum Chess: -

Probability – the two halves of each piece represent, in some sense, the probability of its presence on a particular square.

‘Quantum Entanglement’ – the two halves of each piece remain instantly linked over any distance by rule 2 which states that whenever one of them interacts with another piece by taking it or becoming taken by it, then the other half of it undergoes a ‘Wave Function Collapse’ and instantly re-joins the interacting half.

‘Quantum Superposition’ – we can regard the two halves of a piece as representing a quantum superposition when they occupy the same square.

‘Quantum Ontology’ – this model offers as many questions as answers about the reality underlying quantum phenomena: -

Does a piece in wave mode ‘really’ exist in the same way as a piece in particle mode? The wave modes can undoubtedly influence the progress of play, but we can still create a record of the game that does not include them or break the rules of ordinary ‘particle chess’.

Does the wave function collapse of an interacting piece look remarkably like retroactive causation?

If each particle piece can do two different things at once by splitting into two wave modes, does this imply Multidimensional Time?

Technical notes on play -  the rigorous application of the standard rules of chess plus the additional quantum chess rules, only allows pawn particles to split into waves on their first move when they can move one and two squares forward simultaneously. There seems no reason to forbid a player moving the two wave components of a particle piece to the same square to recreate a single particle piece, but this will rarely prove advantageous.

Checkmate and ending the game – Placing the opposing whole King in checkmate wins the game and so does placing either half of an opposing King. Note that a player with half a King in apparent checkmate may have the option of taking an opposing piece with its other half thus evading checkmate. At the end of a game players can elect to collapse any remaining wave positions by moving either one of two halves of the same piece to a square occupied by one of them, but the two halves of a halved checkmated King must move to the square in which checkmate occurred. This restores the semblance of an ordinary game of standard chess.  

Quantum Chess, Q-Chess, WPD-Chess, Copyright Peter J Carroll 09/10/2021 

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Published: 08 May 2019

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Herewith the Exuberant Desolation, perhaps the first of a series of starship models made entirely from scrap materials from the beach and surrounding construction projects. It may eventually form part of a fleet for the spaceraid game here, or perhaps it will feature in a sci-fi novel.

After all, the best games work rather like novels which tell a memorable story with the added advantage that readers become participants and editors within limits.

Perhaps the Exuberant Desolation's AI accidentally achieves full self-awareness and sentience, absconds from the Synarchist Fleet, and spends centuries as a privateer wreaking havoc, gathering allies, and spreading rebellion and revolution.

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Published: 12 September 2018

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Square Rigger Chess models the manoeuvre and combat of square rigged naval ships of the Napoleonic period. No element of chance enters into this system, the results depend entirely on player skill and the chosen starting conditions, to this extent it functions as a chess-like game. This modelling system depends on several simplifications for game play: -

The division of sea areas into squares. The orientation of all ships and firepower and wind direction, in just 8 possible directions. The characterisation of ships by just 3 factors, Firepower, Speed, and Turning ability. F, S, and T.

Firepower. – (the combined effects of cannon + carronades + mortars + musketry), ships begin with a firepower factor of 2, 3, 4, or 5. In attack a ship may allocate its firepower factor in any directions preferred up to the maximum of its firepower as shown in the Fire chart following: For example, a 2^Nd Rater with a firepower of 4 could direct all its firepower of 4 in a starboard (right) or port (left) broadside, but not both. It can only use a maximum of 2 units of its firepower (4 – 2 = 2) fore or aft and only a maximum of 3 units (4 – 1 = 3) off the port or starboard bows or off the port or starboard stern, thus it could for example simultaneously fire 2 units of its firepower fore and the other two off the starboard bow, (or any other direction chosen). In combat the attacker assigns firepower factors to chosen directions first.

The effect of attacking firepower falls off with distance, by 1 per every square after the immediately adjacent square effect shown below. (See the Distance Fire Chart later.)

Ships defending against Fire use their Firepower factor in the same way, assigning part or all of it to various directions to try to cancel the effects of incoming fire, however it does not decrease with distance. This curious seeming rule reflects the fact that the vulnerability of ships rose in precisely those directions where they could use the least of their firepower.

Any ship which receives from any direction more firepower than it assigns to that direction takes one ‘Hit’ for every unit of firepower that it loses by. Merchant ships have defensive ‘firepower’ only.

Speed and Turn. In a player turn ships may move one square forward for every Speed factor they have and may turn 45 degrees (one eighth of a full circle) for every Turn factor they have.

The chart below shows what manoeuvres a 3^rd Rater with a Speed of 2 and a Turn of 2 can do in a move with mainly starboard turns.

The nimble 3^rd Rater starts on square 1, its initial position shown in black. It can end its move in any of the positions shown by red ships by using some or all of its 2 Speed and 2 Turn capabilities. Note that it could also use turns to port instead of starboard to end up in the positions and orientations shown by the white ships and that it could also make other orientations on squares 4 or 7 using turns to port. (Not shown).

The heavier ships have less manoeuvrability than a 3^rd Rater, and manoeuvrability declines as ships take Hits (see damage chart).

Wind direction and intensity also affect manoeuvrability (see wind rules and chart).                                                                                   

Ship Classes.

First Raters. F5, S1, T1. These rare lumbering behemoths with 100+ guns have huge firepower but poor speed and manoeuvrability.

Second Raters. F4, S1, T2. As above but these monsters with 84 guns do manoeuvre slightly better.

Third Raters. F3, S2, T2. These faster and more manoeuvrable 64-gun warships serve as the main workhorses of the line of battle.

Frigates. F2, S2, T3. These fast and highly manoeuvrable 44-gun warships can bring vital extra fire support when heavier ships engage.

Distance Fire Chart.

Firepower has its greatest effect into adjacent squares, but ships may also use their firepower at greater distances. Basically, subtract one from the effect of assigned firepower for each additional square. Thus, if the vessel below has a firepower of 4 and assigns it all to a starboard broadside that broadside can only have an effect of 3 on any one square marked X, or 2 on any one square marked Y.

The Non-Adjacency Rule. Ships on the same side must leave at least one empty square (orthogonally or diagonally) between themselves when ending their player moves.

This rule may seem slightly unrealistic, although friendly ships did try to keep at least a ships length between themselves.

This rule allows for the use of the classic manoeuvre of ‘cutting the line’ without the complications of modelling collisions. Ships on opposite sides can occupy adjacent squares, and they will often do so to disrupt enemy formations and to direct the fire of several ships to a single target.

The above chart shows a flotilla of red ships engaging a flotilla of blue ships. Note that whilst several ships from either side have moved to squares adjacent to enemy ships, no two ships on the same side lie orthogonally or diagonally adjacent to each other.

The non-adjacency rule does not apply inside of harbours, friendly ships may moor and manoeuvre alongside each othear, ships may also lay adjacent to friendly ships that have struck their colours.

Damage Chart. As ships take Hits, their Firepower, Speed, and Turning abilities decline as shown on the following chart. Players should place damage markers on their ship markers as appropriate to show their status.

Any ship reduced to 0 0 0 ‘Strikes its Colours’ and remains immobile and inactive for the rest of the battle and subject to towing away for repairs or as a prize afterwards, if the victor has a mobile ship spare to do this, otherwise the victor may elect to scuttle it.

Wind Chart. Players set the wind direction and intensity before play, the wind can come from any one of 8 directions. Players may also make some provision for a change of wind during the game if desired.

Moderate Wind simply prevents movement directly into the wind (square riggers could not do this), however they can turn into the wind and then turn to 45 degrees to the wind and effectively tack in a zig zag in a generally windward direction.

Stronger winds also deny movement directly into the wind and additionally allow for greater movement with the wind as shown in the chart below. The numbers on the squares represent the number of squares a ship can move in that direction for the expenditure of a single speed point. Ships can move twice as far with a following stronger wind.

General notes on scenarios and tactics. Players should practice with small numbers of ships at first. Larger flotillas and fleets may require the command of several Commodores or Admirals each in charge of a squadron, as coordinating the movement and fire of many ships becomes a challenging task.

Scenarios can include convoy interception (see note on transports and merchant ships), chasing down and capture of slow enemy heavy ships by more numerous lighter ships, harbour blockades and attempted breakouts, and fleet battles for naval supremacy.

Transports and Merchant Ships usually effectively consist of unarmed versions of naval ships, with the heavier ones having less speed and manoeuvrability. They take damage and strike colours in the same fashion.

Play takes place by alternate moves. In each player move players may move all their ships in any order so long as the final positions of their ships does not break the non-adjacency rule. Attacker and defender then both assign firepower in exchanges of fire, calculate Hits and place damage markers.

The following 2 charts show for extra clarity, firstly the effects of fire from diagonally orientated ships, and secondly the effects of stronger wind from diagonal directions.

Shore Batteries. These defend harbours and effectively act like static ships with high firepower. They should have precisely designated fields of fire. They take firepower damage in the same way as ships.

Commanders should learn to recognise the lines of squares which stretch out from the port and starboard bows and the port and starboard sterns of any ship, for these represent the ‘true diagonals’ of the ship itself, (whether the ship lies orthogonally or diagonally on a square), for these define its fields of fire and defence.

Note that Frigates begin with no ability to fire directly forward from their bows, or directly backwards from their sterns, and no defence against fire from these directions either. Theoretically negative values for defensive firepower do not invite extra damage hits, negative values simply count as zero. 

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Published: 15 July 2017

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The second expedition to the Necronomicon Mythos by Psychonauts of Arcanorium College continues to produce strange and unanticipated results.

From Hastur I received the following inspiration to complete a task that has bugged me all my life, to make some sort of simulation or boardgame that models the magical quest itself.

I have made many games in the course of a lifetime that model various real and imaginary scenarios, with the underlying thought that if you can identify the mechanisms underlying any system then you can perhaps understand the dynamics of it, and perhaps do it better in the game of ‘real’ life. Strategy Games certainly seem to sharpen the mind, and may bring us some focus on the Human Condition.

Yet most of the games involving magic that I have collected or read the rules of seem unsatisfactory. Magic typically appears only as a combat modifier in battle games, rarely as the focus of an activity or a quest in itself.

In this Hasturian inspired simulation the Elder Gods and their Knowledge and Power stand as metaphors for the abilities we humans seek in the quest for personal and species survival. They represent abilities we need to survive the future, not ghastly eldritch cosmic adversaries bent on our destruction, although with careless use they could have that effect.

Hastur may appear as an empty yellow robed void, countless aeons old, a well of cosmic indifferentism, yet it seems to take an occasional whimsical interest in promising species, perhaps to allay its existential angst awhile.

The concepts of the simulation may seem cruel and cynical; individual questors inevitably die although they may achieve much before senescence and mortality take hold. The numbers used to represent various factors all come from my calculations in an attempt to render the simulation realistic.

Oddly, the whole thing begins to look strangely autobiographical although several treasures still elude me. My own mistakes and that of others have become obvious during the course of many runs of the simulation. The virtues of maintaining a high Sanity, particularly in the early stages of a quest, become all too apparent.

Build it, try it, and send feedback and questions.