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Tuesday, 05 October 2021 09:24

Quantum Chess

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 

Tuesday, 17 August 2021 08:14

Frontier Space War 3

Alternative Tactical Spacecraft Combat System.

When opposing vessels meet at a system, transfer all conflicting vessels from the main interstellar board to the combat space tactical board above. Only one vessel of any type per square. Position the defending vessels on any of the nine central squares, or on immediately surrounding squares if defending with more than nine vessels. Then place attacking vessels on any of the squares that lie five squares from the middle square.

Defender moves first, defender second, and then turns proceed alternately.

All vessels may move during a turn and all vessels may either move then fire or fire then move. Any vessel may fire at any designated target within range regardless of anything in the intervening spaces.

Any hit destroys any vessel. The combat power of any vessel depends entirely on the range at which it can score hits.

To score a hit, a vessel must throw a number equal to, or greater than, twice the number of squares away that the designated target lies.

Thus, a target one square away requires a throw of two or more, a target two squares away requires a score of four or more, a target three squares away requires a score of six or more, and so on.

Vessels use dice of different sizes to represent their combat power.

Battleships – D12 dodecahedron. Battlecruisers – D10 di-pentagon. Cruisers – D8 octahedron

Destroyers – D6 cubes. Frigates  – D4 tetrahedron.

Fortresses – D20 Icosahedron.

D12, D10, and D8 vessels may move one square per turn, D6 and D4 vessels may move two. D20 Fortresses remain immobile.

Thus, vessels have the following chances of scoring a hit at each of these squares: -

Squares            First      Second      Third     Fourth     Fifth     Sixth.

Score for hit      2             4                6           8             10         12.

Battleship      11/12         9/12         7/12       5/12        3/12      1/12.

Battlecruiser    9/10        7/10         5/10       3/10        1/10.

Cruiser               7/8          5/8          3/8         1/8.

Destroyer           5/6          3/6          1/6.

Frigate               3/4          1/4.

Combat continues until only vessels from one side occupy the combat space. Vessels which manage to move off the combat space have escaped and must move to a new position on the  main interstellar board in their next main board turn.

This system allows smaller faster vessels to rush heavier more powerful vessels, it also allows smaller vessels to assist heavier vessels in attack or defence or escape.

Vessels may attempt to pass through enemy held systems by escaping the combat space.

Defending vessels may attempt to abandon a system by escaping the combat space.

Friday, 17 July 2020 20:41

Frontier Space War 2.

Frontier Space War 2. Multiplayer or Solitaire.

Outline. This strategy game models a possible future in which various groups have colonised the nearest habitable star systems and then started to dispute territory, economics, ideology, and alliances. It can accommodate up to five players or alternatively a single player can play each faction in turn to evolve a narrative and perhaps put names to all the star systems and major warships.

The structure of the game can support a variety of backstories. Backstory ‘A’ relates a geopolitical expansion of various human factions into space. Alternative backstories appear at the end.    

Backstory A. In AD 2050 humans discover a warp-drive mechanism that can enable ships to travel to star systems within 20 light years in about 3 months. This fortuitous discovery came at a time when ecological, climatic, population, and political crises on Earth had almost reached breaking point. European backed missions settled large numbers of people on habitable planets in six nearby star systems forming what became known as the Terran Sphere governed according to Synarchist principles by a vast self-perpetuating bureaucracy.   

Over the following decades various factions dissatisfied with the philosophy and politics of the Terran Sphere of seven worlds ventured further into space to colonise other worlds.

Eurasian backed colonists established Vostok on Soviet Neo-Communist principles where hierarchies of endless committees decide everything.

Colonists backed by the Americas established Kalifornia on Darwinian and Capitalist principles where wealth and power and a certain amount of democracy decides everything.

Various mystically and religiously inclined groups, particularly the New-Age-Ecumenicists backed the establishment of Nirvana which operates as an Aquarian Theocracy run by those considered the most enlightened.

Exactly who initially conspired to back the establishment of R’lyeh remains a matter of ongoing debate, but it attracted a mixed consortium of misfits, occultists, illuminati, anarchists, rebels, devils, and chaoists who eventually settled for the collective name of Goths. R’lyeh operates as a Magiocracy run by those considered to have the most magical charisma by popular acclaim.

Within a century the four splinter factions based on Vostok, Kalifornia, Nirvana, and R’lyeh colonised secondary systems in their vicinities and developed increasingly distinct cultures and slightly divergent technologies. Despite interstellar trade and commerce, tensions over resources and the control of unaligned worlds led first to the Treaty of Terra which recognised spheres of influence and neutral worlds, and then to its breakdown as diplomacy failed and factions started building warships and interstellar struggles began.

The conflict plays out with each faction using limited numbers of huge and expensive vessels. Factions can also employ specialised command vessels denoted as Flagships which add to the combat capabilities of flotillas of ships and which factions can exchange in alliances. Some backstories attribute the enhancements conferred by flagships to AI computers, others to genetically enhanced human capabilities.

 

 

Factions.      Philosophy     Colour         Capital World      Flagship AI Capability

Imperials      Synarchists     Silver          Terra                    Tactical Attack and Defence

Soviets         Communists    Red             Vostok                 Tactical Defence

Capitalists    Darwinians     Bronze        Kalifornia             Tactical Attack

Aquarians     Mystics          Green           Nirvana                Psychic Defence

Goths           Occultists        Purple          R’lyeh                  Psychic Attack

 

The following chart shows the ideological relationships of the five factions.

                        

                       Individualist

                                  l

                                  l

       (Goths)               l              (Capitalists)

                                  l

                                  l

Magical -----------------(Imperials)----- Rationalist

                                  l

                                  l

      (Aquarians)         l               (Soviets)

                                  l

                                  l

                         Collectivist

 

Types of Vessel.

Cost   Type                                                                    Dice             Number available/Faction

5       Fortress                                                           – Icosahedron D20.           4 (all)

5       Battleship                                                       – Dodecahedron D12         2 (1A, 4I)

4       B-Cruiser/H-Cruiser/P-Battleship/Monitor.  – Octahedron D8         (2G, 2A, 2C, 2S)

3       Cruiser (Frigate/Fortress Carrier).                 – Cube D6                           4 (6I) 2I 1

2       Destroyer                                                       – Tetrahedron D4                6 (all)

1      Frigate                                                            – Tetrahedron D4                 (10I)                                            

5      Flagship                                                           – Tetrahedron D4               3 (4I)

 

Star systems have production values 1, or 2, or 3, or (5, Earth), shown by relative size.

Sequential turns. Throw for first turn.

 

1) Count production from all occupied systems. Purchase extra vessels if possible and place at a Fortress. If no Fortress, purchase one if possible and place on a home system. Factions may store unused production as markers at a Fortress. The number of ship pieces provided reflects the maximum that a faction can maintain.

* Occupied means either a system held by a ship or fortress or a home territory not occupied by a rival.

2) Move any number of vessels from any star system to any adjoining one connected by a jump route. Frigates and Fortresses can only move if carried in a Frigate or Fortress carrier.

3) Black holes act as long-range jump ports, 1 turn to move directly from one to any other one.

4) Settle any conflicts arising. Risk protocols – up to 3 attack dice against up to 2 defence dice. Players may advance chosen ships into a round of combat in a concealed fashion and then mutually reveal them if desired.

Flagships. Act as combat modifiers to a whole flotilla, (all of a Faction’s vessels at a system).

Tactical AI, Supercomputer using massive parallel calculation. Attack or Defence.

Dice                          Tetrahedron   Cube   Octahedron     Dodecahedron     Icosahedron

Attack or Defence          +1              +2           +3                      +4                       +5

Psychic AI, Quantum computers with a mysterious degree of prescience. Attack or Defence. Roll each dice thrice. Use the highest of 3 rolls.

Initial dispositions, numbers and production values of star systems, and total.

7 Imperials     53 222 11 (16)

8 Aquarians    3 2 111111 (11)

6 Goths           3 22 111 (10)

8 Capitalists   3 22 11111 (12)

8 Soviets        3 22 11111 (12)   

14 Neutrals    222 11111111111 (17)         (Total systems, 51)

Combat Resolution, in each round attacker and defender must put forward at least one piece.

Attacker puts forward up to 3 units. Defender puts forward up to 2 units. Roll appropriate dice. (Adjust for flagships if present.) Pair off dice, attacker highest against defender highest, defender second highest against defender second highest, to determine casualty numbers, defender wins draws. Each side removes the appropriate number of casualties at will, (irrespective of the ship’s dice scores).

Flagships do not need to participate in a round of combat to lend their enhancement to all vessels (including themselves) in a flotilla. A flotilla can only use one flagship to enhance it.

Rounds of combat continue until either all attacking, or all defending forces become eliminated. Or by mutual agreement participants can decline combat. Any non-home territory with more than one faction occupying it does not contribute production.

Treaties.

Any Faction may send a Flagship to assist an allied Faction. It then acts under the control of the receiving Faction. However, the Faction which gave it retains two options: -

a) In its own turn the donating Faction can reclaim it and order it to move.

b) At any point during combat involving the Flagship, the donating Faction can order it to change sides.

Special heavy vessels, dice modifications: -

(Aquarians) Dreadnought – D20 attack or defence, cost 6. (Instead of a second battleship.)

(Aquarians) Heavy Cruiser - D12 defence

(Capitalists) Pocket Battleship, (Goths) Battlecruiser - D12 attack

(Soviets) Monitor – D20 attack, D4 defence.

(All) Fortress in Carrier – D20 in attack or defence. Fortress Carriers can be scrapped to allow rebuilding elsewhere.

Starting Positions.

Each Faction places a Fortress at their capital, and one turns worth of produced ships anywhere on their home-worlds. A second round then begins, and conflict can occur.

Ships may remain on black holes, but no production can occur there.

Victory Points. – Control of Earth +1. Control of another Faction’s Capitol +1. Loss of own Capital -1. Ending with more territory +1. Ending with less territory -1.

The Imperials start with more territory and productive capacity, but rival factions surround them. Alliances prove crucial to the outcome.

Alternative Backstories.

B, Alien Powers. The five factions represent Humans plus four other Alien species with advanced technology that all acquired interstellar capability at about the same time.

C, Neo-Feudalism. The factions represent the five ‘Great Houses’ that developed the biotech that gave them personal dominance over humanity and the ability to devise warp-drive. Flagships represent the personal command ships of senior family members and/or their clones.

Thursday, 07 November 2019 15:20

Frontier Space War

Herewith a recent sci-fi board game system. The board represents space using star systems as nodal points connected by posible jump routes. All movement takes place simultaneously on the declaration of pre-wriiten destinations for starships. Combat between opposing ships that land on the same star system takes place by the simultaneous revealing of ship order of engagement and chosen tactical cards, the effects of which appear on the combat octagon charts. The system does not use dice or other sortilege procedures, everything depends on trying to anticipate an opposing commander's intentions in movement and tactical combat. Does this make it a game of chance or not?

The various classes of starship and the starsystem bases all consist of various nuts and bolts and masonry anchors and plumbing fittings painted matt mettalic. Such pieces have the advantage of standing upright and not cluttering the board, vessels of the same class all have the same appearance, and the pieces have a pleasing weight. Combat takes place only at star systems. Although the system used a 2D board to represent 3D space we can consider the stars as lying both above and below the plane of representation.

Legemeton flotilla threatens a Terran position.

Legemeton ~ Little Green Men of unknown origin and appearance. 

Frontier Space War.

A boardgame system for modelling interstellar conflict as it may develop in coming centuries. This system uses concealed simultaneous choice of movement and concealed simultaneous choice of combat tactics rather than sortilege procedures to model the uncertainties of conflict.

1) Starships in the FSW Universe.

Common Classes of Vessel.

Common Name      Firepower       Defences              Cost  

Battleship                     5                     5                       5

Cruiser                         3                     3                       3

Destroyer                     1                     1                       1

Factory                         1                     1                       5

Reinforcement Vessels.

Common Name      Firepower      Defences               Cost

Battlecruiser                5                     3                         3

Heavy Cruiser             3                     5                         3    

Frigate Carrier FC       3                     3                         3          (Carries up to 5 Frigates)

Frigate                         1                     1                     2 for 1.     (Not jump capable)

 

2) Ship Movement in the FSW Universe.

At each turn all ships on all sides can move simultaneously.

All ships that move must move two star systems, slingshotting via an intermediary system at hypervelocity. (The presence of other ships at the intermediary star makes no difference)

Commanders write down the next position of each of the ships under their control on a log-sheet and then all commanders reveal their secret orders and move their ships accordingly.

A log-sheet for a small flotilla might look like this: -

Ship           Initial position      1st Move,      2nd Move,    3rd Move,    4th Move,       etc  

Battleship          N36                     D43            H67    

Cruiser              N36                    X14             L65

Destroyer          N36                    D43             H67

Destroyer          N36                    D43             H67  

Destroyer          N36                    X14             L65

Here the flotilla starts at star system N36. On successive moves the flotilla splits in two with a pair of Destroyers accompanying the Battleship to D43 and then on to H67, whilst the other Destroyer goes with the Cruiser to X14 and then to L65.

3) Ship Combat in the FSW Universe.

When opposing vessels meet at a star system, combat occurs if any commander elects to attack opposing vessels. Combat proceeds by combat rounds until only the vessels of one side remain, the others having become destroyed or having managed to evade, or all commanders elect not to attack further.

A combat round begins with the Assignment of vessels. Commanders put forward a piece concealed within a hand against an enemy commander who must then put forward a concealed piece and then both reveal them simultaneously, until all attacking ships become paired.

If one side’s ships outnumber that of the other, then the commander(s) of the greater number may then assign any spare ships to join in where desired.

Combat rounds then take place between vessels assigned against each other. Each commander selects a tactical card for a vessel and puts it forward, both commanders then reveal their tactics and consult the tactical chart to assess the result.

If vessels from both sides survive their individual duels, then any vessels which did not evade successfully can go through another cycle of assignment and combat rounds. Ships which manage to evade during a combat round can voluntarily de-evade and participate in another cycle of assignment and combat rounds if desired.

Where more than one vessel becomes assigned to attack a single vessel the commander(s) of the multiple vessels may order them to attack individually and put forward a concealed tactical card for each. In this case commanders assess the effects of each of these chosen tactics against the single tactic chosen for the single vessel. Alternatively, the commander of the multiple vessels may coordinate Destroyers or Frigates with other vessels (subject to certain restrictions below) and chose a single tactic for them.

Ships coordinated together on a single tactic simply pool their firepower and defences and act in effect as a single more powerful vessel.

Restrictions on the grouping of Destroyers or Frigates arise from the telemetry problems associated with closely coordinating their actions:

a) A single Destroyer or Frigate can coordinate with a heavier vessel such as a Cruiser or a Battleship or a Jump Carrier or a Factory.

b) Two Destroyers or Frigates can coordinate with each other.

c) Destroyers or Frigates cannot coordinate with vessels from different allied civilisations.  

The arrows on Combat Octagon 1 show the effects of eight possible tactical choices upon each another. A thick arrow shows that one ship has scored 3 against another. Middleweight arrows add a score of 2. Lightweight arrows add a score of 1. Red arrows or red circles show a score of 1, 2, or 3 against both ships.  

If adding the arrow score to the firepower of the ship that scored the hit gives a number higher than the defence value of the target, the target ship becomes destroyed. In the unforgiving environment of space, shield and generator breaches invariably prove fatal.

Dotted lines show that a vessel which has chosen tactic 7 or 8 has achieved an evasion. To achieve an evasion against multiple opposing ships, a ship must evade them all.

When Ships attack Factories based on planets, commanders use Combat Octagon 2 in which they have fewer tactical options.

When a Factory comes under attack, commanders treat the Factory in the same way as a Ship for the purposes of Assignment. If all defending Ships have become destroyed or have managed to evade, the attacking commander may simply declare an evasion of remaining attacking Ships if an attack no longer appears worthwhile.

After the resolution of all combats, another turn begins, and commanders write new movement destinations for all the Ships they wish to move.

Thus, a complete turn consists of the following three phases.

a) Spending of Ship Units to create Ships which appear at the Factory.

b) The writing of movement orders on a ship-log. The mutual revealing of movement orders and the implementation of movements.

c) Combat resolution.

e) Production of Ship Units at Manufactories which lie on planets and have not moved during the turn. (Only one Manufactory can operate at any Planet.)

4) General Notes on Scenarios, Strategy, and Tactics in the FSW Universe.

a) The FSW system uses Topological Nodal Mapping of the contested areas of space. Points on the map denote star systems. Yellow points or markers show stars with inhabitable rocky worlds in an appropriate temperature range. Blue and Red points show stars which do not have such planets, Ships can go to such systems or slingshot past them whilst jumping but they cannot establish bases there. In most areas of space, uninhabitable star systems outnumber habitable ones by about five to one. Lines joining star systems show those within navigational range of each other and hence the possible ‘jump routes’.

Two dimensional representations of contested areas (with the stars and jump routes understood as projecting both above and below of the plane of representation and with some jump routes thus perhaps appearing to cross each other) prove most convenient. The scale of the map in relation to the sizes of the pieces should allow for the unambiguous positioning of groups of pieces around any star system.

To settle larger battles at star systems commanders may temporarily move all involved pieces off board to a convenient space and then replace the surviving ones on the board afterwards.

b) Scenarios.

In Tournament Scenarios both or all commanders start with equal forces on a board with an appropriate (if somewhat unrealistic) symmetry, and the contest continues until one side achieves set victory conditions such as the elimination of all enemy Factories or Ships or the establishment of a set number of new Factories.

Initial set ups and dispositions should ensure the dispersal of forces between well separated Bases to avoid excessive force concentration and cataclysmic battles too early in the scenario.

Asymmetric Scenarios.

Empire Building. Players start with some Factories placed and strive to expand their spheres of influence. Alliances may form and break.

Raids. An empire can over-extend itself by providing insufficient protection to peripheral areas or to areas where it has started to establish new Factories. This may offer opportunities for cost effective raids by smaller vessels against areas defended by too few heavier vessels. Deep Penetration Raids against Factories designated as politically important can also justify the commitment of heavy warships.

Convoy Operations can involve moving Factories or designated warships carrying items of great value from one side of an area to another against enemy interdiction.

Insurrection Scenarios can arise after cyber-warfare and/or political propaganda causes some Factories and Ships to rebel and fight for independence.

Tactical Notes. Jump Carriers enter combat with their Frigates already launched. Thus, a fully loaded Jump Carrier could in some circumstances engage several opposing ships by effectively reconfiguring itself as (3+1), (1+1), (1+1). Alternatively, the Jump Carrier could attempt to evade carrying its Frigates.

The civilisations from which fleets originate may not wish to allow commanders to become too powerful and may limit the number of replacements and reinforcements they can build.

5) Diplomacy and Treachery in the FSW Universe.

Scenarios involving more than two players provide opportunities for the making and breaking of alliances.

The simultaneous movement of ships requires trust between allies, and treachery can exploit this.

During a multi-player battle of several combat rounds, ships can change allegiances.

Diplomacy can proceed openly and/or by the passing of private notes.

The complexity of FSW lies above that of ‘family game’ but below that of ‘afficionado game’. However, game aficionados can easily complicate to game to any required degree of sophistication by adding house rules.

Whilst a two player game becomes a straight conflict based on bluff and an asymmetric rock-paper-stone type combat, multiplayer games tend to also involve elements of Diplomacy and Poker.

The rules do not forbid the use of psychic powers.

 

 

Wednesday, 08 May 2019 19:16

Spacehulk

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.

 

Wednesday, 12 September 2018 11:39

Square Rigger Chess

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 2Nd 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 3rd Rater with a Speed of 2 and a Turn of 2 can do in a move with mainly starboard turns.

The nimble 3rd 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 3rd 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. 

 

Saturday, 15 July 2017 18:12

The Necronomicon Mythos Simulation

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. 

Tuesday, 25 April 2017 20:53

Game of Thrones Risk Deluxe Solo

Game of Thrones Risk Deluxe.

I enjoyed the Game of Thrones so much that I arranged to receive the board game for xmas. Okay, so it follows the usual Risk format which provides a reasonable ‘beer and pizza’ evening for 5 or 7 student age people if you play it straight. However the beauty of the map and the pieces led me to wonder if I could get more out of it by using it to tell a longer story as a one player game over a number of evenings, rather as one might enjoy reading or writing a novel within defined parameters.

Herewith my rough house rules: -

Setup on the Westeros board only.

Each house occupies all of its own territory, plus use the red pieces for the Iron Islanders.

Use the blue pieces for neutral territories (Vale of Arryn, Riverlands, Stormlands.)

Place the blue citadel on Kings Landing as a second Baratheon citadel.

Each territory generates 1 troop unit, as does each town and each port, citadels generate 3 units.

Each town and port and citadel generates 1 (100) gold.

Ships – I used the galleons out of ‘Civilisation’, you need about 10 ship markers. Each house starts with one, except the Iron Islanders who have 2. They begin and end turns in ports.

At each player turn, 1) adjust forces and income as above. 2) move any troops 1 space within occupied territory. Spend income if desired on fortifications, catapults, knights, reinforcements, or treachery.

Costs, fortifications, catapults, knights, ships, 3 gold each.

Treachery, to subvert an adjoining enemy unit pay 1 gold and throw a 2 or less on a D6, pay 2 gold and throw a 4 or less, or pay 3 gold and throw a 5 or less to change that unit to one of the active players own house. This only works at all if all units on a territory plus knights become subverted, otherwise it all fails, and the gold wasted.

Attack any neighbouring territories from ones you initially own. Ships carrying troops may attack up to 4 ports away, and may sail around the bottom of the map but not the top.

The usual rules of combat apply but with the following modifications, you can employ multiple knights and catapults, so towards the end of the game the 8 sided dice get used more. (you may need an extra 8 sided attack dice)

Citadels offer +2 to defenders on dice but only if the defenders elect to retreat to the citadel for a siege. Attackers can elect not to assault but to lay siege, in which  case they own the territory, towns, and ports associated. If after 3 turns the siege remains in place, the defenders become eliminated.

Naval warfare. If a defender elects to defend an attacked port with ships then each ship can have a fighting crew of up to 3 troops plus up to 3 knights and one catapult if available, it may also carry another 3 troops as transports but not combatants. If a ship losses all three combat troops it becomes sunk, along with transports.

Ships can land troops on any territory to which a white line points even if it doesn’t count as a port, but then the ships must retire to their nearest friendly port.

Undefended ships in ports become automatically captured if attacked by crewed ships.

The single player should play each house in turn, considering the strategic options as they arise. Obviously alliances will become a critical consideration and part of the developing narrative. One simple rule can suffice here; any house breaking the terms of an alliance has to forgo all of its income in its next turn.

Objective- dominate Westeros, or at least form a stable alliance between the surviving houses.

Extra feature, when the last of the blue neutral pieces become eliminated the Undead as blue, begin to invade the The Gift. Roll a D8 to see how many appear each turn. They attempt to move south 1 territory per turn rolling D8s. Destroyed opposing pieces become replaced with undead pieces if they capture territory.

 

 

 

Monday, 22 February 2016 14:34

Favorite Games

Herewith a list of games that have particularly intrigued me over the years, some remain in print, some you can find easily on the net, others remain personal creations or in development. Games have made a considerable contribution to my thinking since an early age, not perhaps as much as books, yet interesting games function a bit like a books, and not only do they have a stories to tell in their structures but you can evolve stories as you play them or adapt them.

Careers. https://en.wikipedia.org/wiki/Careers_(board_game) I came across this at about age 12. I knew little about the world in those unsophisticated times and attended a grammar school where the English Master (a wily and provocative old cove) would occasionally announce ‘You are here to be educated as clerks, like your fathers’. Fortunately the school also had a science department, although nobody had a clue what you could do with a science education except become a science teacher. The school gave no career advice, it assumed you would either take one of the plentiful clerical jobs available at the time, or go to university and think of something whilst there. The game of Careers thus seemed an astonishing eye opener. Choose Wealth, Happiness, or Fame, join a whole series of professions, buy a yacht, in short; choose an Identity! All this seemed to sit in my subconscious till the mid-1970s, an era of plenty when career-anxiety seemed to give way to the search for personal identity in my peer group. I guess that I have always looked at life as a sort of board game. A lot of the assumptions built into the Careers game now seem simplistic but eventually it would perhaps have some influence over what I wrote in EPOCH, but more of that in a following article.

The Game of Nations. This came out in the 1970’s to model the then current oil crisis. Players control abstract Middle –Eastern oil producing territories and vie to get wealth that they can spend on oil extraction, tankers, and pipelines, or on taking over adjoining territories. The game system does not involve dice but it does have uncertainties built in with event cards. Players can buy Politicians, Secret Agents, Monarchs, Dictators, and Guerrillas in an attempt to subvert or conquer additional territories. Today we should perhaps consider adding Theocrats as well, and making the map less abstract and updating the events cards.

The Russians currently seem to play a strong hand in Syria. The West has perhaps made a mistake in supporting the ‘moderate’ rebels. Both sides need Iranian cooperation and support but if the Iranians come out of this on top then all hell may break loose if they go head to head with the Saudis.

 Diplomacy. This classic game of early 20th Century European alliances represents one of the few games which model WW1 in an interesting way. Apart from the naval battle of Jutland the battles of WW1 mainly got settled by terrible attrition rather than by interesting tactics and manoeuvres. In Diplomacy we see the bigger picture as nations make secret alliances and agreements off board and then simultaneously reveal their strategies to see what results. Historians argue constantly about the causes of WW1, but in this model scenario, war seems virtually inevitable if the game represents the actual diplomatic system of the time. The game however does really need 5 or more players, but you can play it over many days with perhaps a move a day, and with secret diplomatic notes passed around at tea and lunch breaks.

Axis & Allies. The basic Axis & Allies game models WW2 from after it has started and Japan has attacked Hawaii and the Germans have attacked Russia. It can accommodate five players but it works well with just two. Basically it works a bit like the simple strategy game of ‘Risk!’ where you get extra forces for conquering more territory, however the forces consist of various types of land, sea, and air units which makes it far more detailed and engaging. Subsequent versions have striven for yet more detail and realism. The initial game suffered from the structural quirk that Japanese commanders with any sense should disengage quickly from the pacific and attack Russia in the east, thus virtually ensuring an Axis economic victory. However for historical reasons, notably the Nomonhan Incident, the Nazi-Soviet Non-Aggression Pact and an Oil Embargo, they adopted a Pacific strategy. The critical role of oil supply in WW2 does not seem well reflected in the basic rules.

Buck Rogers – Battle for the 25th Century. This quirky game never became very popular but you can get second-hand versions quite easily. It has an Axis and Allies type strategic structure but set in the inner solar system with spaceships and spacefaring troops disputing the control of Mercury, Venus, Earth, Mars, the Asteroids and various orbital facilities. It has the extraordinary feature of a variable geometry board. The Planets move around the Sun and you need to plan spacecraft trips accordingly. The basic game has some complications that I don’t find worthwhile; I have preferred to adapt the rules to make it more like Axis & Allies and also to use the Risk 2210 sci-fi pieces to provide more choices of troop type. 

Discworld. Ankh-Morepork. Something extraordinary happened here and then a tragedy occurred. Perhaps by some happy chance a really good game got cobbled together in Ankh-Morepork, (two attempts to make sequels to it fell badly flat) but then after the death of Sir Terry Pratchett something went wrong with the rights and the publishers had to stop making it. Sets can now fetch several hundred pounds. The game has a bit of everything, it seems a bit like turbo-monopoly with assassination and magic, although amassing property may not necessarily win you the game because you don’t know which characters your opponents play. It works best with four players and it contains enough randomness and pageantry from the books to make it surprising and enjoyable for aficionados and beginners.

Space Raid.  Interstellar board game design presents two major problems, firstly how to represent 3D space on a 2D board, and secondly how to allow for the vast distances and speeds involved. The designer needs to invoke or invent some reasonably credible but as yet undiscovered physics.

In designing Space Raid, I opted for sheets of black board with numbered or named stars on them joined by pale green lines representing possible jump routes between them of lengths of up to a few parsecs, to produce a sort of spider web or network of jump routes with the stars at the nodes and with most stars connected to between 2 and 4 others by jump routes. On the board the jump routes have different apparent lengths to represent the reality of the stars not all lying in exactly the same plane, but perhaps lying in the thickness of the plane of a spiral galaxy.

The starships move using (hypothetical) gravity focussing devices. By focussing the gravity drive exclusively on a nearby star, a ship accelerates towards it and achieve an immense velocity fairly quickly.  It then performs a slingshot manoeuvre around the star and as it hurtles away it uses the gravity focussing drive to brake against the star to eventually bring itself more or less to rest around another nearby star. Thus each time a ship makes a jump it leaves one star system, hurtles through another without stopping, and ends up in a third. Two further quirks of relativistically dubious speculative physics also occur in this scenario, initiating a jump sends out a non-local gravitational hyperwake through the system so all ships know when another has jumped, but not to where, plus all jumps take a very similar amount of time, irrespective of differing distances.

Rather conveniently this leads to the situation where all ships on both sides can jump simultaneously but commanders don’t know the destinations of their opponent’s ships. So both sides secretly write down the next destinations of their ships and then both reveal them and move their ships and see if any have arrived at the same star systems, in which case combat begins. Plus ships passing through a star system in the middle part of their two star jump have such an enormous velocity that interception and combat remain impossible, however they can deploy kinetic energy weapons in passing, basically dropping rocks on very large targets like planets to create massive devastation. No defence exists against this except to intercept them well before they get within jump range of a star system with a base or colony on one of its planets. This does not seem unreasonable, the capacity for flight soon brought with it the capacity to wreck entire cities; the capacity of interstellar travel would probably bring with it the capacity to wreck entire planets. Players may agree to a treaty forbidding such tactics, or a severe loss of victory points if they break it.

When opposing starships end up in the same system they can attempt to engage or evade each other using a variety of sensors, cloaking devices, and evasive tactics, force shields, particle beam weapons, and missiles. Each ship has a variety of factors for these and duelling proceeds through the use of asymmetric combat polygons. Ships can also exchange fire with orbital bases or with planetary bases.

Tuesday, 16 February 2016 19:47

Asymmetric Combat Polygons

Asymmetric Conflict Polygons

Uncertainty in games can come from either building in randomness with dice or shuffled cards or some other sortilege procedure; or from scenarios where players lack information about their opponent’s intentions.

Simultaneous Play often yields a system that models real life scenarios rather well. In this, the players secretly record their intended plays and then all reveal their orders and compare them to see what happens. The game of ‘Diplomacy’ which simulates the political alliances and military balances in Europe from 1900 onwards provides a classic example of a game based on simultaneous play with concealed intentions. Only rarely does peace prevail until 1914.

Some people find the use of dice or some other random mechanism unappealing as it can make the best laid plans come to nothing for no reason except bad luck, and it prevents any detailed analysis of a game afterwards.

The game of Scissors-Paper-Stone, sometimes called ‘Roshambo’, may well originate from the Han Dynasty era in China. It has attracted a considerable amount of study and competitive play, and computer algorithms exist against which humans can play. Although no strategy can consistently beat purely random play, competitions and algorithms remain interesting because few people can consistently play randomly and a good player or algorithm can anticipate the non-random choices of an opponent based on their previous choices.

Nevertheless the game remains rather trivial although the principle has become incorporated into some games to settle combats between pieces, for example in hand to hand conflict, Parry and Thrust beats Lunge, Lunge beats Slash, and Slash beats Parry and Thrust, or something like that. To a very simple approximation circa 1805, Artillery beats Infantry, Infantry beats Cavalry, and Cavalry beats Artillery.

Such a system of conflict resolution leads to a quick and easy type of duelling done with hand gestures, or with cards selected and put forward and then exposed. Yet in its simple form it seems little better than using dice. However by using something a little more sophisticated than a simple symmetrical triangle of outcomes we can create a facility for meaningful tactical choices with some uncertainty of outcome.

Consider the virtues of Asymmetric Conflict Polygons. An Hexagonal one appears below.

In this the six choices can represent any tactic from the exchange of fire between starships to the exchange of spells in a magical duel. The arrows between tactical choices show which choice wins and the weight of the arrow can show by how much. Each player in the duel has six cards marked with the tactical choices and both draw a card and then they simultaneously expose them and find the result. The asymmetries in the chart make some choices more favourable than others, depending on the powers of the pieces involved, however obviously the opponent will appreciate this.

The actual chart shown has the design feature that no choice offers guaranteed immunity from a full hit, but some choices offer greater chances of some kinds of hits.   

 

We could display the information on such a polygon with a simple 6 x 6 chart, however the polygon itself gives a much easier to use representation of the effect of one tactical choice upon another and the opportunities for second guessing the opponent.

Conflict polygons can also model the effects of offensive against defensive tactics where the attacker draws an attack tactic card and the defender draws a defensive tactic card.

In solo play an asymmetric polygon can allow the player to compete with intelligent choices against random choices generated by dice rolls. 

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