Power Grid’s market system with the two layers of plants is interesting and provides a deceptively large degree of control and prediction. It really is quite clever while presenting a surprisingly predictable pattern. Space Race has the problem that while it models something akin to the 18XX train rusting progression, the intended sequence is so short (3 layers) that incentivising player progression is worse than tetchy. I’m not sure I can learn from Power Grid here, but it is tempting.

A possible address is to model the total productive capacity of the system, to cumulatively sum the total production to date. As that total production volume crosses pre-set thresholds the next layer becomes available and of course as the third layer is entered all level 1 factories rust. This could essentially arithmetic sum could be modelled in several ways, actually tracking total production volume as a calculated sum or simply having bits from a limited supply which are discarded as they are used¹.

With such an approach it becomes tempting to add a fourth level of factory, a pure consumer. We could call it the Centre Of Government or some such silliness (themed after Asimov’s Foundation universe?). It would either be notably expensive or force auctioned at another production volume threshold. There would be only one CoG, and while it wouldn’t necessarily rust the level 2 factories² it would consume both level 2 and level 3 goods until the end of the game, with all fees and payments recorded as usual for route-based deliveries. Variously interesting curves could be applied to the system. Perphaps the market value of the CoG pseudo-product would likely decline continuously, forcing a race between additional factory construction/operation, run-away CoG ROI and endgame acceleration? Similarly a race could be constructed between the level 2 and level 3 factories based on the game-length required for equivalent profit volume³?

Such a system has advantages. The level 1 factories would be (mostly) unprofitable but failing to buy into them would allow those that do to be extremely profitable and to have undue leverage into the level 2 factories and economy. The real value of the level 1 factories would be to establish market relationships for exploitative level 2 factory upgrades which would actually be profitable. This would of course also require ensuring a limited supply of Level 2 factories (possibly by spacing rules rather than count?). The level 3 factories would then be similarly constrained⁴. And likewise for the level 4 CoG factory: placement constricted by neighbourhood. Such placement rules could be quite interesting and offer an attractive short-long planning aspect.

Methinks I should spend more time in the shower.

I generated a 7-depth Penrose tiling last night. It took most of the night.

Axiom:
  [N]++[N]++[N]++[N]++[N]
Rules:
  M=OA++pA—-NA[-OA----MA]++;
  N=+OA–PA[---MA--NA]+;
  O=-MA++NA[+++OA++PA]-;
  P=–OA++++MA[+PA++++NA]–NA;
  A=
Angle:36

The tiled SVG’s generated by the L-System are prone to very high rates of duplicate elements. They’re also extremely slow and system intensive to process under Inkscape as the entire graph is rendered as a single bazillion-point object. Handling the performance problem is simple enough: Inkscape/Edit/Select_All and then break up the object with Inkscape/Path/Break_Apart. Ahh, much better.

Handling the duplicates is tougher. There are simple duplicate elements, PATH elements with identical attributes and vertices and there are path elements which are identical except that they list the vertices in a different order. The former are easy to remove. Just fold the raw XML document so that all PATH entries occupy but a single line, sort the PATH elements and then remove all duplicates. In my case I just extracted the PATH elements to an external text file, wrote a quick XEmacs macro to make each PATH element single-line and then did:

$ sort outfile.xml | uniq 

Voila! All identical PATH elements removed. This simplistic dupe-removal reduced the file size by approximately 30%.

I looked at removing the duplicate-vertex elements but found it too hard for a quick hack fix. In short I’d have to extract all the path elements and then the vertices for each element, sort them and then do duplicate removal. That was more than I was willing to be bothered with. However while wandering the data I noticed that there were many 7 vertex elements whose vertices precisely overlaid the vertexes of other elements (exception: a small few elements at the edge of the graph). With the exception of the ones at the edge of the graph, they were all redundant. Remove them:

$ grep -v "path.*M.*L.*L.*L.*L.*L.*L"  outfile.svg

While a plain white mesh is pleasantly clear, I had the idea of colouring the tiles to give a bit of a stereoscopic effect.

The effect of which is to assign a fill colour to two thirds of the elements, a different colour for each third

I like it.

I’ve been playing with the L-System support in Inkscape, generating Penrose Tilings. Damn this is clever neat nifty fun!

Axiom: 
  [N]++[N]++[N]++[N]++[N]
Rules:
  M=OA++pA----NA[-OA----MA]++;
  N=+OA--PA[---MA--NA]+;
  O=-MA++NA[+++OA++PA]-;
  P=--OA++++MA[+PA++++NA]--NA;
  A=
Angle:36

Just drop that into Inkscape/Effect/Render/L-System (put all the rules on one line) and you should get this:

Increase the Order value and it will iterate more, drawing a larger graph. Be careful though as execution time grows exponentially as the number of iterations grows.

Some other L-system-derived graphs produced with Inkscape:

Axiom:
  f
Rules:
  f=-f+f+g[+f+f]-;
  g=gg;
Angle: 60

Or perhaps more entertainingly:

Axiom:
  W
Rules:
  W=+++X--F--ZFX+;
  X=---W++F++YFW-;
  Y=+ZFX--F--Z+++;
  Z=-YFW++F++Y---;
Angle: 30

Yes, that’s a single continuous line in what is known as a space filling curve. Wander about Wikipedia or with a search engine and you’ll find many other little L-system programs for other tilings or space filling curves. Plug them in and play! They’re not only a heck of a lot of fun but such curious tilings can easily form the backdrop for interesting games and there are many many such interesting patterns.

Attempting a taxonomy of player interaction along a scale of increasingly personal relations:

Absent interaction

The simplest form: there is simply nothing the players can do to affect each other and thus no form of profitable reaction to another player’s choice or inversely, prompt a player to change course in reaction to your choice. Games absent interaction are the poster children for Multi-Player Solitaire.

Recognition interaction

There’s no requirement for understanding or predicting the other players, merely recognition that they exist and have potentials that may affect the results of your game. qDominion (usually) falls in this camp (there are small exceptions). Knowledge of the specifics of the other players is rarely if ever useful, but an overview of the gestalt of all the other players en masse is useful. Do any of them have any of XYZ cards? What is the rate of consumption of the QRS card stack across all players? The answers to such questions can profitably inform play choices.

Predictive interaction

Ahh, the first tremblings of mutual-perception! The question isn’t what effects a player may enforce on another, but rather how correct choice-prediction (and thus correct counter-counter-counter-counter–ad-infinitum-choice-prediction) may be translated into an advantage. The classic recent case is Race for the Galaxy; a game in which there are significant efficiency gains for drafting on other player’s choices. Predictive interaction is a slippery beast as it has a strong harmonic in Personal Interaction and a weaker harmonic in Personal Direct Interaction.(see below).

Direct interaction

Players intimately affect each other, contructively, obstructively and destructively. They may help each other’s success, obstruct success, or directly destroy or foul each other’s success. I sank your battleship! The effects can range from the relatively subtle taking of a limited resource another had planned on taking themselves (eg roles in Puerto Rico, actions in Age of Steam, station markers or track tiles in the 18XX) to the very direct destruction or removal of player value (eg stock trashing and loot’n’dump in the 18XX, conquest and possible elimination in Risk, dumping a high point pain card on an opponent in Sticheln, or almost any player-interaction in Diplomacy).

Direct interaction can be sub-divided into Impersonal and Personal types

Personal Direct Interaction is the targeted subset of Direct Interaction and a weak harmonic of Predictive Interaction (due to the requirement of accurate player incentive/value prediction in foiling player’s personal success). The qualifier is that the subject is explicitly and deliberately targeted. Something isn’t done to all players or to any random player, but specifically to specific player with deliberate (ill) intent for that specific player’s success. Settlers of Catan‘s monopoly card card (all other players give the player all their resources of a given type) and calling time in Galaxy Trucker are usually Impersonal Direct Interaction as they are indiscriminate effects. In contrast encouraging a large bribe in Intrigue and then reneging on the implied or promised deal, building walls in another player’s presumed territory, using “their” resources” to cut them off from “their” buildings, or simply conquering a player’s temples and territory and annihilating their military and conquering their territory in Antike is Personal Direct Interaction.

Personal interaction

The return of subtlety. Here the ticket isn’t to recognise or even so much to predict, but to comprehend the player(s) intimately. The challenge is to not only predict their immediate choices, but their patterns, their strengths and weaknesses as players, their intersection of character and individuality with the game and by the advantage of exploiting that intimate and intensely subjective comprehension, to beat them. Personal Interaction is a strong harmonic of both Predictive Interaction and Personal Direct Interaction (see above).

Observations

It is worth noting that the above divisions aren’t quite linear or evenly spaced along the not-quite-a-scale. That’s a problem with the soft-sciences: straight lines aren’t. Most noticeably Personal Interaction is variously orthogonal to both forms of Direct Interaction and the line between Subjective Interaction and Direct Interaction isn’t quite straight through Predictive Interaction.

Apocryphally, women as a gender are commonly said to dislike the destructive sides of Direct Interaction. I’ve not noticed that gender bias but several of the players I commonly play with (mostly male FWVLIW) share that trait: they are only interested in constructive positive-sum games. Additionally different players have various detection and preference ranges for the interaction levels they prefer. While I can detect the inter-player interaction among players of Race for the Galaxy it is too diffuse and impersonal to appeal to me. Similarly Impersonal Direct Interaction has little appeal for me. In contrast one of the chaps I play with¹ simply isn’t comfortable with any form of Personal Direct Interaction where-as another chap pooh-poohs and avoids anything which doesn’t operate at the deepest level of Personal Interaction.

I’ve played Jeroen Doumen and Joris Wiersinga’s Duck Dealer twice. It is a tough game to grok.

Update: In fact the game is sufficiently difficult to grok that almost all the below is flat out wrong. It is hogwash. Beware. I’ll be writing up a correct summary of the game after it reaches broad release.

• Duck Dealer is a perfect and certain information logistics game very much in the spirit of Roads & Boats and Neuland but with its own unique take
• Don’t be deceived by the light and funny theme
• Duck Dealer is a deceptively direct re-interpretation of Merchant of Venus
  • The theme, core nouns and board-patterns are similar
  • The play decisions and game character are violently different
    • Duck Dealer is a mentally demanding forward-looking planning-festival. Merchant of Venus is a much lighter and simpler affair of delivery optimisation with occasional opportunities
• Three players is probably the sweet spot, maybe four with experienced players
• The first phase of the game is ship improvements
• The opportunity cost of ship improvement is usually prohibitive later in the game
• Each pattern of ship investments establishes a natural rhythm for that ship; the rhythm at which it takes energy and then acts
• The balance of colours on the ship likewise establishes a natural activity-type rhythm
• None of the choices of combinations for game-start ship configuration are obviously bad but each one strongly suggests a different ship development tack and thus resulting rhythm
  • I suspect that the game’s initial turn order plus the ship configurations of the player’s ahead of you in turn order is a key factor to smart initial ship configuration decisions
  • I also suspect this reflects strongly into suggested ship configurations
    • It is clear that the random distribution of initial mines and the consumer tile ordering affects this and in fact defines these choices
    • It is not at all clear to what extent this is true in practice given human’s struggle with the decision space of the game
• Coarsely (there are exceptions) the larger/more equipped a ship is the longer its rhythm
• The heart of the game is managing your ship’s natural logistical rhythms against the emergent opportunity costs as the game/board develops and new buildings (tiles) are placed
• It is viable to stay with an undeveloped 8-speed ship with two discs and a cargo hold
• The undeveloped ship strategy is the most programmatic (fewest significant decisions), most risky and most subject to interference from other players
  • Undeveloped ships are dependent on rapid short-term opportunity exploitation which in turn requires frequent actions and results in a short/fast game
  • If the undeveloped ship dawdles the better equipped ships will out-pace them
  • If multiple players do run undeveloped ships they will drive a short/fast game that will likely seem to be decided arbitrarily
    • I find longer games with more developed ships more interesting
• The more ship improvements the players do, the longer the game will be and the more of the board will be developed
• Just one undeveloped ship moving fast and staying focussed can drive a fast/short game
• The value of Build/yellow decreases during the game, sometimes precipitously.
• Build/yellow can be worth a lot early in the game
• Exception: Heavily built ships with two movement can reliably profit from Build/yellow energy to place Galactic Infrastructure (cubes on routes) to help manage their naturally short (2) movement distance
• The bigger your ship is the more often Galactic Infrastructure (cubes on routes) is more useful than privilege markers on tiles
• Teleports are remarkably hard to place usefully
• Clever teleport placement may invert some of these observations
• I have yet to see a clever teleport placement
• With rare exception there are more VPs for building factories and flipping consumer tiles than doing milk runs stuffing goods into an already flipped consumer
• Establishing and then running a production loop is almost invariably less profitable than focussing on building factories and flipping consumer tiles
  • This is directly opposite from Merchant of Venus’ reward patterns
• Exception: Ships with huge hold-spaces (7+ capacity?) can profit enormously from a well-optimised production loop (ie privileges claimed on all steps) on a 25/10 consumer.
• The usual reason players act is that they become unable to sustain comprehension of their intended move. Their mental stack overflows, they lose track and so they act instead of continuing to search for the optimal risk/value return for energy accumulation. This is often (almost always) a mistake.
• Usually getting more energy and doing more later is markedly more efficiently profitable
  • Unless someone gets there first
• The game is all about acceleration curves against game length
• Each player’s ship investment has a pay-off curve
  • A undeveloped ship is faster to build, runs more quickly but makes fewer points per natural action
  • A big ship takes longer to build and runs more slowly but makes more points per natural action
• The players emergently determine the game length
  • Which player’s ship’s reward-curve/opportunity-exploitation-rate/game-length sums best when the game ends is the core question of the game

The recent play of Muck & Brass has been occupying my sleeping nights and bedraggled shower time. I’ve no great conclusions other than that 5-days-for-everyone is a Bad Idea (see below). The rest is just terrain mapping.

The standard action pattern in the recent game was a spate of Expands followed by a mix of Develops and Capitalises. Typically the final actions were chosen to either force the round closed, or to put the next player in a position to force the round closed. The only times Capitalise was selected early was when either all of a player’s companies were broke or in the late game in order to float more secondary companies in order to extend game length (it was set to end in the sixth General Dividend with only two companies left operating but we called the game early mid the 5th round due to other constraints).

Unlike Wabash Cannonball early capitalisations were not seen as critical early moves, in part due to the high opportunity cost of the Capitalise action (time), but also because there are simply so many shares available (10 unsold shares) and relatively little to differentiate among them. The result is that Muck & Brass is mostly not about temporary emergent alliances but about the old standards of arbitrage, opportunity and tactical position.

In a four player game the dance is straightforward:

1. Stay low/early in the turn order to get more Expands for your companies
2. Buy lots of shares (difficult when you’re low in the turn order)
3. Buy shares that players lower than you in the turn order also have so that you profit from their activities
4. Try to keep your own shares undiluted

The lack of a Chicago-style golden target to create a discontinuous value set is the main characteristic that precludes temporary emergent alliances. What alliances there are, are happenstance collisions of mutual interest rather than deliberately managed affairs. As such the player relationships are much closer to Preußische Ostbahn’s management of temptation and exploitation than Wabash Cannonball’s forthrightly collusive work-together-and-we-both-make-more.

In our game, because of the high opportunity cost for capitalisation, Capitalise was usually used as a round ender to re-invigorate a cash-less company or to setup turn order for the next round. Thus the first round looked something like:

• (E7/D5/C3)
• P1-E2/2 P2/E2/2 P3-E2/2 P4-D1/2 P4-E2/2 (E3/D5/C3)
• P1-E2/4 P2-E2/4 P3-E2/4 P4-C3/5 (E0/D5/C2)
• P1-C3/7 P2-C3/7 (E0/D5/C0)

The second round was a little more interesting as London started to be developed, thus freeing up a host of other possible Develops for other companies:

• (E7/D5/C3)
• P1-E2/2 P2/E2/2 P3-E2/2 P4-D1/2 P4-D1/1 P4-E2/3 (E3/D4/C3)
• P1-E2/4 P2-E2/4 P3-E2/4 P4-C3/6 (E0/D4/C2)
• P1-D1/5 P2-D1/5 P3-C3/7 (E0/D2/C1)
• P1-P1-D1/6 P2-D1/6 (E0/D0/C1)

The third round was similar, but with even less Capitalisation:

• (E7/D5/C3)
• P1-E2/2 P2/E2/2 P3-E2/2 P4-D1/2 P4-D1/1 P4-E2/3 (E3/D4/C3)
• P1-E2/4 P2-E2/4 P3-D1/3 (E0/D3/C3)
• P3-E2/5 P4-C3/6 (E0/D3/C2)
• P1-D1/5 P2-D1/5 (E0/D1/C2)
• P1-D1/6 (E0/D0/C2)

Such a lower rate of capitalisation encourages companies to run with broke treasuries, for positions to be more heavily invested, and for strong player differentiation, both positional and financial (low cash high income versus lower income and high cash). It also encourages players to forgo Capitalise and instead Develop heavily as it has similar effects on income (and slows the game down). From a design perspective these are all desirable patterns, not least the slowing of the game.

The players clearly valued Expand higher than the other actions. I’m not convinced they were wrong. Getting to London is critical for most companies and building out of London not only offers a larger income delta than any other activity (once London been developed once), but also positions for ready mergers with the three companies surrounding London. In our game the B&GR built 5 connections out of London. When London was developed up to $9, that was $45 income for the B&GR: $14/share just for London alone!

Consider a hypothetical 4th round of a game:

• (E7/D5/C3)
• P1-E2/2 (port/merger) P1-C3/5 P2-E2/2 (port/merger) P2-C3/5 P3-E2/2 P4-E2/2 (E3/D5/C3)
• P3-E2/4 P4-D1/3 (E2/D4/C3)
• P4-D1/4¹ (E2/D3/C3)
• P3-E2/6 (float or merger) P3-C3/9 P4-E2/6 (float/merger) P4-C3/9 (E0/D3/C3)
• General Dividend (two players past 6 days)

Four secondary shares were sold. There is potentially only one company left in the mix. The game could have just ended. Or, more likely there are less ports and mergers as there’s just not enough money in the other companies/players for the Expands required for ports and mergers. The players early in turn order are likely to have shares in companies with cash for ports and mergers:

• (E7/D5/C3)
• P1-E2/2 (port/merger) P1-C3/5 P2-E2/2 (port/merger) P2-C3/5 P3-E2/2 P4-E2/2 (E3/D5/C3)
• P3-D1/3 P4-E2/4 (E2/D4/C3)
• P3-D1/4 (E2/D3/C3)
• P3-D1/5 P4-D1/5 (E2/D1/C3)
• P3-D1/6 P4-C3/8 (E1/D0/C2)

Two secondary shares just sold and one arbitrary share was capitalised. Assuming that mergers were done instead of port builds there could be as few as 3 companies left in the game. Assuming instead that P4 had a share of a company that could merge with a single expand the last actions set could have been:

• P3-D1/6 P4-E2/7 (merge) P4-C3/10 (E0/D0/C3)

In which case there could potentially be only two companies and the game would be over depending on what share P4 force capitalised. P4 has three choices:

1. Capitalise the first share of any secondary company. This clearly makes sense if P4 will win as the game ends
2. Capitalise the second share of a secondary company which is already connected to a company in which P4 is invested. This assumes that one of the earlier players capitalised the first share of that company. In practice this usually means either the NER, LNWR or GWR and only makes sense (again) if P4 is will win as the game ends
3. Capitalise the second share of an unconnected company. This will put three companies back in the game causing the game to not (yet) end.

The choice-set is interesting because P1 and P2 control whether #2 is even present as a choice, and which company fits #3 (likely one near their investments). Neat!

More immediately useful is that without the forced 3 days for the merger there’s a reasonable potential for a merger storm in the fourth round that instantly ends the game. The real problem is that it is absurdly difficult to control or predict the values generated by such a merger storm from the preceding rounds making the game results essentially a crap-shoot. Scratch that idea!

The other perspective is that ports effectively offer several values to minor investors:

• Cause a special dividend
• Impoverish a company such that it can’t afford to drive future mergers
• Ability to capitalise a share that encourages a merger-via-Capitalisation along with its related Special Dividend (ie a connected secondary company)

Mergers deliver all the above plus the following:

• Accelerates game-end condition
• Builds a combined treasuring which is likely large enough to afford another merger or port

Mergers are generally better for major investors as they provide two forums for special dividends for their heavily invested shares. Ports conversely offer only one future venue for additional secondary dividends but protect other investment’s special dividend capacity from predation by a steamrollering behemoth.

The other advantage for forced 3 day capitalisations is that players are now encouraged to capitalise more heavily in the early rounds in order to get enough cash into their companies to afford special dividends be they from ports or mergers. However this early capitalisation rush exposes another phantom that pushes back on such heavily capitalisation. Imagine the following perhaps not-quite-so-fantastic evolution:

• P1 is invested in the L&MR (possibly even a minor investor), Expands to a port in Liverpool and force-capitalises the NER
• P2 is invested in the L&SR (possibly also minor), can’t afford a nearby port and so merges with the EUR or LB&SCR for a special dividend. P2 then force-capitalises the NER to make a L&MR/L&SR/EUR/NER merger for yet another special dividend.
• P3 is desperately behind and merges the LB&SCR or EUR into the new huge agglomerate, thereby removing the merger possibility from the agglomerate and securing their share’s dividends. P3 Capitalises something. Anything.
• P4 has a potentially remarkably ugly decision as there are only two companies left in the game, the huge agglomerate and the B&GR.

That’s two actions spent for 3 special dividends. Oof. What’s different is that huge gobs of money have just been thrown into the mix by the three mergers. P4 is really wishing he owned a good spread of the northern companies at this point. Double oof.

The new map fits on 18”x12” paper easily enough with broad empty swathes down the edges. It is a bit tetchy at that scale. A few of the short links such as York/Selby, Preston/Blackoool and Dover/Canterbury get to be awfully short – going smaller would present significant clarity problems. For the Europeans printing on A3 is the best bet despite being a smidge shorter than the not-quite Super-B I’m working with here. (I’d test that conjecture here if I could find a reasonable supply of A3 or Super-B paper about San Jose).

I’ve updated (increased) the port costs back to within reason. If ports are too cheap then they are used exclusively rather than mergers. As the goal of ports is to a provide way for minor shareholders to drain gobs of cash from companies and to thereby ensure that they are not able to cause mergers, the cost of ports has to be high enough to provide the needed drain and yet low enough to prevent casual use. (ie more than $30 but not too much more) Meanwhile other players push for mergers as they solidify share positions and aggregate treasuries for further dividending activities.

Unfortunately the empty spaces along the edges of the new map aren’t large enough to fit the income track or the bank pool spaces. Instead I’ve made a separate tracks page that will fit comfortably on letter or A4 for those details:

And of course some rules polishing. The changelog:

• Ports and mergers cause a (forced) capitalisation
• Forced capitalisations cost 3 days! (This is big)
• Added rules section for forced capitlisation
• Sized bank described as ~$4K
• Pumped port values most of the way back up
• Removed several ports
• Clarified glossary
• Clarified double build language
• Development rule WRT London clarified to account for Liverpool and York.
• Added scoretrack page.

The forced capitalisations for ports and mergers is a huge question. There are good reasons to think it is a great idea, as a control on late game velocity, but also good reasons to fear it slows down the effective rate of capitalisations in the late game which in turn delays the rate at which secondary companies enter the game and that is a problem. I’m finding modelling this problem fiendishly difficult; it is so sensitive to exact player positions and incentives that I’m not yet able to predict broad pattern behaviours.

In partial response I’m considering changing the round-end determinant yet again. Currently it is two exhausted actions or two players at or past 6 days. While that’s a nice pattern it is also a wee bit slow. The new thought toy is to end the round on two exhausted actions or when all players have used at least 5 days. In a 6 player game that ensures that all rounds will end on two exhausted actions. With lower player counts it will often be all players at 5 days. Hmmmm.

New rules.

Changelog:

• Reduced port fees (perhaps too much)
• Auctions clockwise from capitalising player (faster and simpler)
• Clarified multiple home stations for merged companies
• Fixed action supply length and colours on map
• Correction: Capitalise may be chosen for any available company or one of their own shares
• Clarified that non-floated company treasuries are discarded when scoring
• Clarified that merger-forced capitalisations take 3 days (Okay, added)
• Clarified that merger-auctioneers are not required to bid
• Fixed language about summing incomes for auto-merges

New rules.

Updated map:

Updated rules.

I have not adjusted the port prices. But the new days language is used for the action track and the action track length has been reduced from 7 to 6.

Four of us had a go at Muck & Brass with the new action system this afternoon. In short, it was wonderful, really wonderful and far less unstable than the earlier version. Early conclusions:

• It was more intuitive to describe the action system in terms of days than points. Actions take days (time) and the players take turns in the order in which they are available
• Ending on 7 days or two exhausted actions is too rich. It wasn’t terrible but we always ended on actions rather than points. 5 days may be too short but it is clearly either 5 or 6 days
• The secondary companies are odd. Simply, odd. It is tempting to have them float on one share, but that feels too large a change for their modest oddity. I’m not sure they need to be addressed but it is tempting
• The Foreign ports are probably over-priced by ~30%
• 3 Capitalisations, 5 Develops and 7 Expansions seems right
• The requirement for London to be the most valuable city forces the early game into an expansion frenzy. This is good, but I’d forgotten it in my earlier thought cases.
• One player strongly disliked the action/time track being way from the geographic map. That’s easy enough to fix.

In all, an excellent outing.