Other Wise

Money can buy you privates

One of the 1839 playtesters argues convincingly that $2700 is too much starting capital for 1839. When playing, that feels right, it does seem too rich, but the numbers don’t make sense to me. Both games have a non-sellable B&O-type private for $220, so ignoring that:

  • Maximal total private sell-in value in 1830 is .

The privates in a given game of 1839 are semi-random, but the face value of the random portion ranges from $400 to $680

  • Smallest maximal private sell-in value in 1839 is .
  • Largest maximal private sell-in value in 1839 is .

That’s variously $260 and $540 more than 1830. In a 4-player game of 1830, privates generally sell as a collective set for a little under a 40% premium over face value, or 70% of maximal sell-in value. 1839’s privates shouldn’t be any worse than 1830’s in sum, and are often better due to useful special powers. That gives baselines for total expenditure:

  • 1830: $560
  • 1839: $742 – $938

Which puts the baseline additional expenditure on 1839’s privates from $182-$378 more than 1830. While I haven’t done a formal permutations analysis as to where the average total value is for 1830, my sense is that it sits around $1,150, which gives $245 more in overage. As such, adding $300 to the game’s starting capitalisation seems not-reasonable. Yeah, a bit rich, $15ea too rich in a 3-player game, but surely not overwhelmingly so? Or is the richness seen more as a product of the dutch auction for the privates rather than 1830’s traditional reservation auction?

39 steps of 1839

Early playtests of 1839 have been promising, but have not gone well. The game has played smoothly enough, it has clearly shown that there is an interesting game in there, but also that the then current incarnation wasn’t it.

But, it is getting closer. Perhaps it is time to review where it has gotten to.

Map

First, some background context as much has changed:

ps18xx map

Track and stations

  • Companies may place up to two tiles per OR, one of which may be an upgrade.
  • The second tile is optional, and has an additional cost of $20 if placed.
  • All companies have 5 station markers.
  • Stations cost the value of the revenue centre where they are placed, multiplied by the number of hexes with that companies station markers after the placement.
  • A revenue location counts for revenue only once, no matter how many trains hit it.
  • There are exchange markers. An exchange marker is a second station marker placed underneath where the company already has a station maker.
  • Each company may have one exchange marker on the board at a time.
  • An exchange marker allows a company to count that revenue centre once for each train that hits it.
  • An exchange marker also makes that station market not-blocking. Other companies can run trains through it and lay track on the other side.
  • A route ending at another company’s exchange marker counts that revenue center normally.
  • A route passing through another company’s exchange marker counts that location for $0 revenue.

Train roster

The trains have stabilised as to definition, even if not as to count:

Colour Type Cost Rusted
yellow 2+ $100 by blue
green 3+ $200 by brown
blue 5+ $400 by red
brown 7+ $700 by gray
red 5D $1,000 by black
gray 7D $1,500 permanent
black FLOOD $2,000 permanent

Train notes

  • +trains don’t count dits and off-boards but do count cities, and pay all three.
    • (Currently being considered) This would mean that off-boards don’t count against train-length, but also don’t satisfy the definition of a route.
    • I’ll almost certainly have to reduce off-board revenues if I adopt this notion.
  • D-trains count and pay only cities and pay but don’t count off-boards, and then pay double that total.
  • FLOOD-trains pay the sum of every revenue center that could be reached with infinite numbers of infinite trains and infinite track-reuse.
  • At the start of each SR a marker notes the smallest brown-or-larger train currently in a company.
  • If a company still owns one of those trains two SRs later, the game is over.
  • As a result, brown trains may be permanent, but probably won’t be. Red trains will probably be permanent, but also may not be. Gray and black trains are always permanent.

Privates

Privates? Yeah, they’ve gone haywire. Five privates are always in the game.

    • Cost: $40
    • Revenue: $5
    • Blocks: H7
    • Power: Owning company can place an additional yellow track tile or upgrade, in addition to their normal build, closing the private.
    • Closed: When power used.
    • Cost: $160
    • Revenue: $20
    • Blocks: nothing
    • Power: Owning company may place a tile (can be an upgrade) and station marker (must be both) at K16 or L3 for 80f.
    • Closed: When power used.
    • Cost: $160
    • Revenue: $20
    • Blocks: J7
    • Power: Owning company may place a station or exchange marker for free
    • Closed: When power used.
    • Cost: $220
    • Revenue: $35
    • Blocks: F13 and G12
    • Power: Comes with the presidency of a random company picked during setup. Company is automatically parred at $94. Flevoland bypass automatically built when closed.
    • Closed: When that company buys a train.
    • Cost: $300
    • Revenue: $25
    • Blocks: C10 and D9
    • Power: Comes with a 10% certificate of a (different) company randomly picked during setup. Owning company may place a station or exchange marker for half cost. Afsluitdijk built when sold.
    • Closed: In red phase or when power used.

There are then 10 more privates which are shuffled face down and then drawn randomly until the total face value of the drawn set exceeds $400. The drawn privates are then used in the game and the rest put away:

    • Cost: $60
    • Revenue: $10
    • Power: Comes with a $20/$10 token that may be put in any port location, permanently increasing the revenue of that location by $20 for that company and $10 for all other companies.
    • Closed: When the power is used.
    • Cost: $120
    • Revenue: $20/$0 (No revenue when owned by a company)
    • Power: Owning company has a 50% discount on all terrain costs.
    • Closed: In red phase.
    • Cost: $160
    • Revenue: $20
    • Power: Owning company may mark a train as obsoleting rather than rusting.
    • Closed: In red phase or when the power is used.
    • Cost: $180
    • Revenue: $20
    • Power: Owning company has a discount on train purchases: Green $100, Blue $150, Brown or later $200.
    • Closed: In red phase or when the power is used.
    • Cost: $200
    • Revenue: $20
    • Power: All towns are +$10 revenue for the owning company.
    • Closed: In red phase.
    • Cost: $200
    • Revenue: $20
    • Power: Owning company may buy a train, including as an emergency purchase, at any time in its operations.
    • Closed: In red phase.
    • Cost: $200
    • Revenue: $25
    • Power: Owning company may convert a town to a yellow city for a 40f terrain fee as the company’s upgrade tile lay.
    • Closed: When power used.
    • Cost: $220
    • Revenue: $15
    • Power: Owning company may add $10 to every revenue center encountered by one of its trains.
    • Closed: In red phase.
    • Cost: $250
    • Revenue: $?/$0 (Nothing when owned by a company)
    • Power: Owning player is paid the revenue value of each previously unconnected revenue location connected by track to a station marker for the first time by a company controlled by the player.
    • Closed: In red phase.
    • Cost: $300
    • Revenue: $0
    • Power: May be converted by the owning company to any single train prior to brown phase. Auto-converts to a brown train at the start of brown phase.
    • Closed: In brown phase.

Private notes

  • The auction starts with the player with the #1 player card and proceeds in player card order with the #1 player next in rotation after the player with the largest player card number.
  • Each player in turn may pass or do one of:
    • Buy one of the displayed private companies at a purchase price of the face value of the private company minus the total cash currently placed on the private company.
    • Place 10f from the bank on any private company.
  • If the total cash on a private company reaches its face value, the next player in turn order must acquire that private company at no cost.
    • A player that passes may act in a future round of the private auction.
  • The private auction ends when all players pass in sequence, or all private companies have been acquired by the players.
  • At the end of the private auction, the player order for the upcoming stock round is set using the numbered player cards in ascending order of remaining player cash. – Tied players retain their prior relative order.

Foreigners

  • There are 8 foreigners in the game, one each for each off-board.
  • Each is a 10-share incrementally capitalised company.
  • They are grouped in three countries: Germany, Belgium, and Overseas.
  • Each foreign company has a private income slot and they share a common country treasury.
    • A train may not run from an off-board to another off-board of the same country.
  • Foreign companies are parred at the largest legal par available the first time a train is run to them, and operate from then on.
  • When a company runs to an off-board, 20% of that the total run for that company is put from the bank on the income slot for that foreigner.
  • When a foreign company comes to operate, the money on the income slot is put into that country’s treasury, and then all the shares of the off-board pay 10% of the total cash (rounded up) that was in the income slot (paid from the bank).
    • As such, they have crap dividends.
  • The foreign company then buys all of their own shares they can from the Open Market, using the country treasury.
  • And then buys all the trains it can with any remaining monies. Any bought trains are discarded from the game. Any phase related changes happen immediately.
    • Thus investing in the foreigners accelerates the train rush.
  • Foreign company shares do not count against certificate limit.

Stock

  • The stock market is identical to 1843’s except that all the coloured sections have been made white.
  • There are no pars. Everything sells at the current stock price.
  • Shares of a company may not be sold until that company floats.
  • Selling shares does not change stock price.
  • At the end of an SR:
    • Shares in the open market move the stock price down once per share for public companies.
    • Shares in the open market move the stock price down once for foreign companies.
  • Public company stocks move right only if their total dividend equals or exceeds their stock price, otherwise they fall left.
  • Foreign company stock prices move right if they pay any dividend at all, otherwise they fall left.
  • Both move up for being all sold out at the end of SRs.
  • The game ends if a stock reaches a price of $500.

A failure of noodles and limited touching

1839 has been lurching forward somewhat like a dyspeptic hedonist.

Privates

In May I attacked the privates:

    • Cost: $20
    • Revenue: $5 (or $0?)
    • Blocks: One side of Amsterdam.
    • Power: Player can build an additional yellow track tile for $20 from their personal cash for any company of which they’re the president (any terrain costs must be paid by the company treasury), during that company’s operation and in addition to that company’s normal track build.
    • Notes: Closed if sold to a public company or if power used. Power can be used in yellow phase.
  1. 1
    • Cost: $40
    • Revenue: $5+
    • Blocks: ?
    • Power: Gets additional revenue of %20 of any terrain costs (rounded up) paid by any company. Terrain costs range from $80 – $120. Terrain tends to be where track wants to go.
    • Cost: $60
    • Revenue: $5+
    • Blocks: ?
    • Power: Additional revenue of $5 for every train certificate bought by any company. When owned by a company, can mark a train as obsoleting rather than rusting ala the VdL in 1843.
    • Note: Closes when its power is used.
    • Cost: $80
    • Revenue: $5+
    • Blocks: ?
    • Power: 18OH-style revenue of $5 for every revenue location connected to a token for the first time.
    • Cost: $100
    • Revenue: $20
    • Blocks: The teleport locations
    • Power: D&H style teleport for the cost of terrain at the target (one of which is $free but out of the way, other $120 and highly desirable).
    • Note: Can be bought in yellow for face value. Closes as soon as its power is used.
    • Cost: $120
    • Revenue: $20
    • Blocks: Connectivity to Rotterdam
    • Power: Either a 30% discount on a train purchase OR (exclusive) a token that can be placed under one of its station markers or on a dit. Every company that runs a train to/through that location pays half (rounded up) revenue of that location to the owning company’s treasury from the bank OR (exclusive, 3/4 player game only) may teleport/place a token in a space reserved/blocked by the discarded company for free.
    • Note: Closes when the power is used. Revenue token is removed in brown phase.
    • Cost: $150
    • Revenue: $25
    • Blocks: Blocks Afsluitdijk.
    • Power: Comes with a random %10 share (cf VdL/M&H). Owning company can place a station marker for free, or can place an additional/extra station marker (one more than normal for the company) for $100 (may be done out of order?).
    • Note: Closes when the power is used. Afsluitdijk is built when private closes.
    • Cost: $220
    • Revenue: $35
    • Blocks: Flevoland bypass.
    • Power: Comes with a random 20% presidency which is parred at $94 (cf PLM).
    • Note: Closes when that company buys a train. May not be bought by a public company. Flevoland bypass is built when it closes.

These are auctioned in an 1830-style auction. Everything, including the trigger, will block something of importance. Purchase price by a major can be from $1 to 200%. The random share allocations, as well as which company is out of the game in a 3 or 4 player game, are determined during game setup before the auction. All privates close in brown.

After that is done one 10% share of each of the 8 off-board companies is auctioned in an 18Neb-style auction with a starting price of $60, with the extension that when all players pass all bid items are bought for their bids and everything remaining gets $5 cheaper. Repeat ad absurdum, must “buy” if $free. Note: The off-boards are parred at the highest then-legal par the first time a train is run to them. Until then their shares are not liquid. Off-board shares do not count as paper.

Summary: 16 things are auctioned before the ISR.

Priority is then sorted in order of ascending cash for the ISR (not sure about this?). At the end of all subsequent SRs priority sorts in order of descending cash (cf ’43 and ’44).

Trains

In June I went to work on the trains, which as-expected, changed everything. I should have known better than to touch anything else first.

First, all of a company’s train-routes must intersect, and at least one of them must end in an off-board. But additionally, each revenue location may be counted only once, no matter how many trains included it as part of their run (ala 1873)2. This of course will require all the station marker counts to be revisited.

Additionally presidents may buy up to 60% from the IPO but may buy past 60% from the Open Market. If they reach 80% their paper limit goes up by one each time. 80% of a company may be in the pool, but no more than 50% may be sold in a single sale. Share distribution is identical to 1849 with the second 20% share always being heavy.

But back to the trains:

Colour Type Count Cost Rusted Est. Run Cost/Run
yellow 2 x5 $125 by blue $40 0.32
orange 2+1×2 x5 $200 by purple $70 0.35
green 3/5×2 x5 $500 by brown $160 0.32
lime 4×2 x5 $600 by red $210 0.35
blue 4/6×2 x5 $700 by red $220 0.31
purple 5×2 x5 $800 by gray $270 0.34
brown 5Ex2 x9 $1,000 by gray $360 0.36
red 6ED x9 $1,200 by black $360 – $480 0.35?
gray Double-D x9 $1,400 $500? 0.36?
black Flood x9 $1,600 $750?? 0.46??

In short the lower train ranks are split Poseidon-style with the last trains of the rank (eg orange after yellow) being over-sized and more expensive, but rusting one rank later than the first trains of the rank. Unlike Poseidon I’m thinking of not making the rust-later trains a choice: the half-new technology is the only thing available.

  • Note: Green phase still does not start until the green trains, brown-phase with the brown and gray with the gray.

The definitions and prices of the upper trains are uncertain. I’m modestly happy up to red with maybe a $25 adjustment here and there on the prices. I suspect the big trains might get a bit more expensive(!).

  • E trains are infinite length, best-N-stops.
  • The current idea for the 6ED is either infinite length and double the best 6 stops, or infinite length and the best 6 stops with the company’s stations doubled (ie not quite as good).
  • A Double-D would be a standard diesel that doubles everything (seems like a Bad Idea).
  • A Flood would be every revenue location that the company could see from all of its stations assuming infinite trains of infinite length (ie an 1873 diesel).

Given the smallness of the map and the large number of tokens, a diesel-equivalent train seems a weak idea. Other notions are welcomed. I like the simplicity of running a Flood for the late game.

The estimated runs for the big trains are atrociously bad. They depend intimately on track development and I’ve a hard time predicting that far into the game. The lower estimates are fairly reasonable if a bit optimistic.

The train counts are likely also poor. The intent is that with trains running for a ~third of their purchase price and with no cheap single trains ala 1843, that trains will move quickly enough that the players are always under capital pressure.

It is also assumed that companies will run out of capital and that presidents will need to pay out of pocket for trains starting fairly early and likely 2-3 times per game for some companies. As trains are not cheap and revenues are not high until the end-game (when they can be huge) this is hoped to be interesting. In partial support of this I’m tempted to use 18India-style dividends of anything between $0 and $INCOME/10 with the stock price falling to the left if the total dividend is smaller than 50% of the stock price or rising if the total dividend is equal to or more than 50% of the stock price.

Game End

  • Bankruptcy still ends the game.
  • $500 stock-value still ends the game at the end of that OR (ala 1843).
  • The game also ends at the end of two sets of ORs during which the smallest brown-or-larger train owned by any company did not change during both sets of ORs (ie didn’t rust).

The intent is that the brown trains might be permanent (not often, but might be), the red trains will usually be permanent, and the gray trains will always be permanent (if they come out).

Stations

The new trains are causing the station marker counts to be re-examined. If some train types explicitly reward stations, then the total number of stations per company should not be as disparate as they are now (currently between 2 and 4 inclusive). The temptation:

  • All companies have 2-3 stations after their home-station.
  • Stations are more expensive: eg $50, $75, $100 for a company with a weak home-station; or $100, $150, $200 for a central company with a strong home-station.
  • There should probably be a private which has a power of offering its owning company either an additional station marker, or a discount on an unplaced station marker.
Footnotes
  1. Since May I’ve become convinced that #2 is both overly powerful and excessively fiddly. A flat $20 per terrain built (or likely $15) would be simpler and as effective for the game.
  2. The primary effect of this is to reduce early revenues and the importance of big-city tokens.

Instantiated aliens

Introduction to the foreigners

Many of the Double O games have a concept of “foreigners” who buy trains at the end of sets of Operating Rounds. This not only keeps the trains moving in the presence of timid train buyers, but makes the distribution of available trains in a given game uncertain. I borrowed this idea in 1843, extending it so that the foreigners would not just buy a train at the end of every set of Operating Rounds, but if they bought the last train of a rank they would also buy the first train of the next rank as well, thus lurching the game forward and shortening the train distribution and speeding the train rush even more.

Extending the system

1843’s extension worked well, accomplishing most of what I expected in providing an addition tool for players to affect the rate of the train rush1. But for 1839 the abstract and infinitely well-funded foreigners didn’t sit well. I want a way to represent the hurdy gurdy jolting of how the Netherlands was tossed about on the technological and political waves of its geographic neighbours. Additionally, the 1843 model seemed as if the game were providing a control knob for only one half of the control system and that it would be inherently more interesting if player controls for both ends were somehow implemented, thus providing some level of tension between the two in influencing the train rush.

The specific thought is for:

  1. The foreigners to be limited in their train-buying by their capitalisation.
  2. Players to directly affect the rate at which the foreigners can buy trains by affecting the foreigner’s capitalisation.
  3. Company operations to affect the train rush rate in the normal manner through their train buying, but also by affecting the foreigner’s capitalisation.
  4. A lumpy rush/dawdle train-buying pattern by the foreigners which is yet deftermiistic and player-predictable.
  5. An implicit brake on the system such that if the foreigner’s train buying did rush and suddenly buy many trains, it would then slow down and some provide respite.

Proposal

  • Each off-board would be a 10-share company that “floated” as soon as a public company ran a train to them.
    • The initial stock price of the off-board company would be the highest par price available in the current game-phase.
  • The off-boards would effectively be incrementally capitalised companies2.
  • Public companies would be required to run at least one train to an off-board if possible3.
    • A thematic addition could be that all of a company’s routes must intersect, ala 18604.
  • As public companies operated, the bank would pay 20% of the company’s total revenue5 to each off-board included in one of their trains’ routes.
  • At the end of the Operating Round, after all public companies had operated, the off-board companies would run in descending order of stock price, and would pay dividends, from the bank, to their shareholders based on an assumed revenue of the total amount collected from the bank for public company operations.
  • The off-board stock price would then move in the normal way (dividend, no-dividend etc).
  • The accumulated revenues and dividends would then be swept to the off-board company’s treasury.
  • The off-board company would buy-back any of its shares in the pool for current market price it could afford6.
  • If the remaining treasury funds are sufficient, the off-board company would buy as many trains as it could afford from the supply.
  • Trains would generally run for a third of their purchase price (ala 1843).
  • Off-board shares would not count against certificate limit7.

First order effects

The general expectation is that some off-boards would be more popular in the early game, as they are (generally) the highest revenue locations on the board and route development to them could be shared, thus accentuating early revenue generaton. Additionally, the constraint of running at least one train to an off-board would encourage route and revenue generation near the off-boards first, and then moving inland as train lengths grew and the map developed.

The capitalisation of the off-boards should scale fairly directly with company activities. In the early game the off-board shares are severe under-performers and thus unattractive for player investments. However players could trash off-board stock prices, in the process marginally capitalising the off-board for the delta between the purchase price and the re-purchase price, and further reducing the off-board’s capital raising from future share sales.

Conversely, in the later game the off-boards become prime investment opportunities. Public shares are starting to become significant liabilities, and some off-boards may well have 4+ public companies running to them, lifting their average dividends above the average dividend of the public companies. And of course the off-board shares would not count against certificate limit — making them extremely attractive for increasingly flush and potentially paper-tight players.

The flight of capital from the public companies to the off-boards would initially accelerate the train rush due to the increased capitalisation from the share purchases (making public company shares even less attractive), but once the initial burst of trains have been bought, the capitalisation rate of the off-boards should slow due to the loss of the dividends from the purchased shares.

Train buying models

Assuming N operating companies, the off-board capitalisation should approximate 8, distributed across the participating off-boards. Assuming each company has 2.5 trains (reasonable after the first tranch), and that trains run for an average of one third their T purchase price, the rate of off-board capitalisation in terms of train purchase cost approximates . Or more directly, if 3 companies are operating, each with 2.5 trains, and are each running to the same off-board, then that off-board will raise ~enough capital in each OR to buy one train.

What about a late game scenario of 8 operating companies each with 2 trains, collectively running to all 6 off-boards, 4 of the companies are running to 2 off-boards, 5 companies are running to the Ruhr off-board (as it is the most valuable), and all of the off-board shares have sold out?

First let’s look at the Ruhr’s income (where T is the purchase price of a train): In other words, ignoring escalating train pricing, the Ruhr will be purchasing a train every other Operating Round, and two trains every third Operating Round. Ooof, train rush!

What about the ~three other off-boards with only one such active company? They’ll be buying one train every seven and a half Operating Rounds.

And the ~three off-boards being run by two companies? They’ll be buying a train every 3.75 Operating Rounds.

Summing the above: That’s just a smidge (13.34%) under an average of two trains being bought by the off-boards per Operating Round. But of course train-prices are not constant. The unpopular off-boards are going to lag and buy and lag.

The result should be that that train cost progressions should make the off-board’s purchases bursty. As rusting events progress, the base train-cost will rise faster than revenues and companies will run out of capital and be replacing their trains under the Emergency Train Buying Rules, and thus only running a single train rather than the two trains modeled above. At the crudest level this should not merely halve the train-buying rate of the off-boards to just under one train per Operating Round, but to somewhat less as the unpopular off-boards will tend to chase and miss the ever-rising train prices, thus delaying their purchases.

The actual train buying rate will be the sum of a number of wave functions with each off-board running on its own cycle, decelerating as the train prices rise and accelerating as the companies fill with and run fresh trains. When the trains rush quickly, the off-boards will lose their source of capitalisation and slow their purchases. However the accumulation of capital in their treasuries injects latency into this system, even as the revenues fall due to train rusting events, the marginal off-boards will increment over a purchase price threshold and buy a train. The result, I hope, should be an unstably punctuated equilibrium!

Footnotes
  1. Specifically: the doubled trains gave players the ability to exchange capital for increased revenue, and single trains the ability to exchange train rush for train movement flexibility and lower capital expenditure.
  2. Shares would bought and sold for current market value with purchase prices paid to the company treasury and and un-bought shares paying dividends into the off-board company’s treasury. All the public companies however would be standard 1830-style with full capitalisation at 60%.
  3. This fits thematically with the Netherlands transit/port role for its neighbours.
  4. In this way a company’s routes as an evaluation function of a company’s network would somewhat model the Netherlands role as a transit port for raw materials and finished goods moving among the neighboring countries.
  5. Rounded up to an even multiple of 10 for easier arithmetic.
  6. This may be an unnecessary optimisation.
  7. Thematically they would be members of foreign stock markets and thus not subject to domestic restrictions. However players would still be limited in their total holding of a single property.
  8. Yes, part of the reason for this post was to play with the LaTeX module for WordPress.