# Let run the maps of foreign lands

I’ve finally (ha!) gotten around to preparing three of the maps I put together for commercial publication for free print-and-play:

### Age of Steam: Wales

Age of Steam: Wales features a lot of terrain, multiple track gauges, and different Links for narrow and standard gauge track. The result is a remarkably smooth game which rewards track and expense planning more than most maps.

Playtester feedback (which stretched over a year) consistently rated this game highly with couples (which surprised me).

### Age of Steam: SE Australia

The changes in Age of Steam: SE Australia are large, sweeping and easy to under-estimate. More work went into this map and the analysis behind it than any other two maps I’ve designed put together (other than Denmark). There’s a lot of months spent with spreadsheets in there. But that’s what happens when you rework the a game’s economic system from scratch.

Age of Steam: SE Australia introduces an entirely new economic system, more dynamic and player responsive than Age of Steam’s default system, and one which bears surface similarities to Steam’s system (but was developed long before Steam’s release), but puts much heavier focus on accurate long-term planning and precise execution than Steam’s system – most especially end-game planning starting in the very early game.

And yet it seems so simple and fluid on the surface. No more income reduction until the very late game, simpler expenses calculation, several limits relaxed…so nice and easy…and then it isn’t. If anything the game is tougher and crunchier than classic Age of Steam…but it is easy to miss that until the late mid-game when you’re suddenly painfully haunted and crippled by your early game.

### Age of Steam: Denmark

Age of Steam: Denmark is the culmination of the changes started in Age of Steam: SE Australia; taking the new economic system introduced there and carrying it all the way forward to also rewrite how Links are handled with an entirely new and somewhat ground-breaking definition of the Locomotive action.

Without reservation, I recommend three players here. Try dominating the Locomotive action every single turn until the early late game…and then upgrading all the way to your end-game Links in one step (and a lot of income). There’s a fundamental opportunity for a fully viable (but not dominant) hail mary approach to the game here that’s simply not seen in other maps. That, and auction price management becomes an even bigger deal than usual.

Age of Steam: Denmark marks the zenith of my explorations into Age of Steam.

Enjoy!

# 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 $(20+40+70+110+160)*2 = \$800$. 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 $(40+160+160+300+400) = \$1,060$.
• Largest maximal private sell-in value in 1839 is $(40+160+160+300+680) = \$1,340$. 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:

### 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. 1. . • 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. 2. . • 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. 3. . • Cost:$160
• Revenue: $20 • Blocks: J7 • Power: Owning company may place a station or exchange marker for free • Closed: When power used. 4. . • 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.
5. .
• 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: 1. . • 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. 2. . • 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.
3. .
• 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.
4. .
• 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. 5. . • Cost:$200
• Revenue: $20 • Power: All towns are +$10 revenue for the owning company.
• Closed: In red phase.
6. .
• 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.
7. .
• 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.
8. .
• Cost: $220 • Revenue:$15
• Power: Owning company may add $10 to every revenue center encountered by one of its trains. • Closed: In red phase. 9. . • 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.
10. .
• 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: 1. . • 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. 2. . 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. 3. . • 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.
4. .
• Cost: $80 • Revenue:$5+
• Blocks: ?
• Power: 18OH-style revenue of $5 for every revenue location connected to a token for the first time. 5. . • 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. 6. . • 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. 7. . • 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.
8. .
• 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+1x2 x5$200 by purple $70 0.35 green 3/5x2 x5$500 by brown $160 0.32 lime 4x2 x5$600 by red $210 0.35 blue 4/6x2 x5$700 by red $220 0.31 purple 5x2 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.

1. Since May I’ve become convinced that #2 is both overly powerful and excessivelyoq 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. qq

# Chain link fences on the prairie

A quick simulation run on a 9x9 board ran for over 2,500 turns. Repeating on a 7x7 board with a somewhat dumber greedy algorithm hit 900 turn before I got tired. This is clearly unreasonable for a tabletop game.

1. Keep the board size no large than 7x7. While 6x6 is tempting, the side-length being a natural multiple of 3 is overly pleasant. 5 or 7 are more attractive and 5x5 appears to be clearly too small.

2. Give a marker to the start player. After the player with the marker takes a turn, they must place an unmarked level 1 tile of the highest level the player is qualified for1 on an empty square of the board, if possible without causing a glob. If a glob is formed, the resultant tile is left unmarked. After their turn they pass the marker to their right (against the flow of turns).

3. Among the objects that can be placed during setup are a variously large number “rocks” which create dead squares on the board and thus break up object formation globs.

4. When three ore more level 4 objects glob, the active player is awarded a VP tile…which is placed on the board with a player marker and otherwise acts as a “rock”.

5. The game ends N rounds after the first VP tile is placed.

1. humans > animals > vegetables.

# Making Ground

Making Ground:1 a placement game of terraforming for 2, 3 or 4 players. The 4-player game is a partnership game.

### Components

A board of squares, perhaps 7x7 or 9x92. A large number of tiles in three families (vegetables, animals and humans) with four ascending ranks per family (eg grasses, bushes, trees and forests in ascending order for the vegetable family). Coloured player markers. (Optional) A small number of “rocks”, or tiles used to mark parts of the board as dead/unplayable. A bag.

### Setup

• Randomly assign turn order.
• In a 4-player game, opposite pairs of players are partnered.
• Put a small number of tiles from the first two ranks of each family in the bag.
• In turn order each player draws a tile from the bag and places it on the board on any empty square which is not adjacent to an already placed tile.
• Do this twice (thrice?).

### First move

In clockwise rotation the players optionally accept a previously proposed first move as their own (must not have previously accepted a first move) and then propose a first move themselves by placing a level 1 vegetable tile with two of their markers on the board. A move is accepted by replacing the player markers on the proposed move with one of the accepting player’s markers.

There is then a second round, in the same order, of the players that did not accept a move on the first round (necessarily true of the first player, but may be others). On their turn they must accept a previously proposed move.

The game then starts with the player to the left of the player to last accept a move3. All subsequent turns are in clockwise rotation.

### Basic gameplay

A set of three or more orthogonally adjacent tiles of the same family and rank glob and become a single tile of the same family and the next higher rank which is substituted for the tile that created the triggering glob. If the set of globbed tiles, including the newly placed and upgraded tile, was orthogonally adjacent to three or more tiles of the same family and the new higher rank of the placed tile, then the placed tile is globbed to the next higher rank etc. In this way multiple levels of globbings can occur with a single tile placement.

All the constituent globbed tiles of the final upgrade set are removed from the board and are returned to their owning players.

Special cases:

• Removed tiles without owners (ie those added during setup) are awarded to the active player.

• An animal glob must consume an adjacent vegetable tile of the same or lower rank if possible (active player choice of which).

• Likewise, a human glob must consume an adjacent vegetable tile of the same or lower rank if possible.

• The consumed tile is removed from the board and returned to its placing player, or the active player in the event of an unowned tile.

• Players accumulate a private supply of tiles that have been returned to them.

• Three tiles of the same family and rank in a player’s supply automatically and instantly upgrade into a single tile of the next higher rank in the same family with the globbed tiles being returned to the general supply.

• Three tiles or more of the fourth rank on the board or in a player’s upgrade into a VP chip.

• Upgraded tiles are returned to the general supply.

### Player turn

On their turn the player must place one tile on the board along with one of his player markers4.

• Players are always allowed to place level 1 vegetable tiles from the general supply.
• If they collectively have at least three level 2 vegetable tiles on the board or in their personal supply, or at least one level 3 or 4, they may instead place level one animal tiles from the general supply.
• If they collectively have at least three level 2 animal tiles on the board or in their personal supply, or at least one level 3 or 4, they may instead place level one human tiles from the general supply.
• Instead of placing level 1 tiles from the general supply, players may place any tile they currently hold in their personal supply.
• Placed tiles are marked with one of the placing player’s markers.

Any automatic upgrades are then executed, along with tiles being returned to their placing players and any resulting upgrades and tiles in player’s supplies.

If there are no empty squares left to place a tile on a player’s turn, the game is over.

### Game end

The game ends when all players pass in rotation, or the board fills such that no further tiles may be placed.

#### Scoring

• Vegetable tiles on the board are worth 2, 4, 8 and 16 points respectively based on level. Tiles in player’s supply are worth half that.
• Animal tiles on the board are worth 3, 6, 12 and 24 points. Tiles in player’s supply are worth half that, rounded up.
• Human tiles on the board are worth 4, 8, 16, 32 points. Tiles in player’s supply are worth half that, rounded up.
• VP chips are worth 50 points 5.

The player or partnership with the most points wins. In a 4-player partnership game, the score of the partnership is the lowest of the scores of the individual members of the partnership.

1. Mostly a thought model at this point.

2. The size will likely vary with player count.

3. Questionable: May be the first player as nominated before the game started instead.

4. There’s a good argument that in the event of a player’s placement resulting in a glob/upgrade, that they then get an additional turn, but this may prove analytically overwhelming.

5. Yes, an odd number.

# 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.

Assuming N operating companies, the off-board capitalisation should approximate $company revenue + dividends = 0.2N + 0.2N = 0.4N$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 $(0.4 * 2.5)T/3 = T/3$. 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): $5 * 0.2 * 2T/3 = 2T/3$ 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? $0.2 * 2T/3) = 0.4T/3$ They’ll be buying one train every seven and a half Operating Rounds.

And the ~three off-boards being run by two companies? $0.4 * 2T/3) = 0.8T/3$ They’ll be buying a train every 3.75 Operating Rounds.

Summing the above: $2T/3 + (3 * 0.4T/3) + (3 * 0.8T/3) = 1.86T$ 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!

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 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. $\frac{d}{dx}\left( \int_{0}^{x} f(u)\,du\right)=f(x)$

For most of the last year I’ve been working on the development of 18FR-RCE in order to address an excess of False Decisions and degenericy with the 6-trains and 7-trains. Much was changed, not least the renaming of the game to “1843”, and more was learned in the process1. I also hope to release a ps18xx implementation in the near future.

1. Not least of which was around the discussion of can versus may in rules writing

# A different horse's gripping hand

Virtual graphs, virtual networks, connectivity expressed by derived relationships rather than represented directly… I last wrestled with these concepts in Corrupt Beneficence. In this post I’m waving an 18xx/route-building stick at them. The following discusses a possible mechanical representation of the operational side of 18xx as a card game.

Imagine cards. There are cards which simply represent railroad track and cards which represent revenue locations (cities and towns). Some revenue locations are also the home stations of various companies. Thus, for instance, the NYC card might also be the home station of the NYNH&H.

The director of a company, say the B&O, would have a card before them for Baltimore. On the Baltimore card they’d place a token for the B&O’s (home) station. Other revenue locations (non-home stations) would have spaces for companies to place stations ala the normal model. If player were running a different company than the B&O, they would have a different card of a different revenue location for that company’s home station if enough cards for that revenue location exist in the game

During the course of the game the B&O president would place track cards adjacent to the revenue location. Cards could be placed on each of the four sides (perhaps limited by game phase), forming a stack or route leading away from that location. The president might also place revenue locations at the ends of such stacks, assuming that the stack contains enough cards to satisfy that revenue location (eg the Lancaster card might require 3 track cards before it can be connected/placed).

And this is where the network enters. There are multiple copies of the revenue location cards. Thus for instance, the B&O may place track from Baltimore to Lancaster and thence to Chicago. Meanwhile another, say the C&O places track to NYC, and then Chicago and thence Scranton. There would be two Chicago cards, one on the B&O’s network, and one on the C&O’s network. Indeed a company might have the same revenue location on several of the routes that fan out from the edges of its home station.

This is where the network enters. All those repeated Chicago cards are the same location. Thus in the above example the B&O might run a train from Baltimore -> Lancaster -> Chicago (transitioning to the C&O’s network) -> NYC -> Scranton. In fact a route might transition across several different company networks as they connect shared cities into their routes. And in the above example the B&O might drop a token in Chicago (and thus on all the Chicago cards), thus allowing them to run trains out of every route in every company’s stack that contains Chicago. As companies acquire tokens in other company’s networks, they might also place track and revenue locations directly on those networks (where visible from their tokens) instead of onto the networks directly attached to their home stations. A virtual implied network, all build from cards!

# The great affair is to move

Now that 18FR-RCE is getting publisher attention (more on this later), I’ve been working on two more designs: 1845 and 18RT. 18451 has been in flight for more than a year now, but 18RT has replaced it as the smaller, simpler vehicle for trialling some of the core notions of 1845 while also exploring its own area.

18RT?” I hear you cry? 18RoadTrain, an 18xx-inspired game set around the road trains of Australia, although in this case many Baltimore & Ohio inspired notions have been sneaking in as well.

### Map

The current notion is for the map to cover the area from Darwin in the Northern Territory, down through Alice Springs to Adelaide in South Australia, and thence Melbourne in Victoria, and across to Brisbane in Queensland2. Perth (Western Australia), Tasmania and the various major ports would be represented by off-boards, the Nullarbor Plains likely being implied by a token surcharge in the Perth off-board or extreme terrain costs for a single hex connection there. The primary focus of the map however would be a morass of dits and terrain surrounding the cattle ranches, metal mines and other bulk-export production centres.

### Companies

The general idea is for a slew of private companies with 1870-esque revenue bonus tokens, accelerated track-builds, terrain discounts and the like. The general idea is that these would either be assigned to major companies ala many David G Hecht games, or sold (at close to cost) to major companies ala 1846.

I’d like to also represent, if only partially, the excessively poetic GSR and Ghan. Wrapping them in a revenue-based private is an obvious route, but perhaps less interesting. Instead I’ve been toying with the idea of a president-less investment vehicle (akin to the bank of England in 1848) which pays liability-less revenues as a function of both the current train technology level and much of the connection between Adelaide and Darwin has been built. Something similar might be also done with the (recent) iron ore connections to China, the Tasmania produce connection, the vast emergent wine industry etc, but in those cases in a manner which more directly connects to major companies operating in those areas.

I’m currently toying with 8-10 major companies which can be incrementally capitalised or fully capitalised at the president’s choice3.

### Trains, err, Trucks

A first notion is to change how trains are managed. Of course they’re not really trains, but bear with me as calling them trains makes the 18xx-relevant language easier:

• Unlimited trains per technology level
• No train limits for companies
• Maintenance fee due for each train at the end of that company’s operation of: ((current_tech_level - train_size)^2-1)*10. ie the sequence of $10,$30, $80,$150, $240 etc. • A company may research the next technology level and upgrade all of its trains (for a$fee) to the next available train-level. When doing so the company may not run the trains that are upgraded. This may happen multiple times in an Operating Round with increasing expense for each acceleration.
• If no company researches the next available technology level in a given set of Operating Rounds, then the game does immediately before the Stock Round.
• The definition of a legal route is changed. Only stations and off-boards count against train-length. Dits count for revenue but not against length. At least one train’s route must intersect both one of the company’s station markets and a small town/dit. All subsequent trains must either intersect one of the revenue locations touched by a previous train and a dit and a city, or must intersect a station marker (in a city) and a dit in the normal manner. As a result, a single station marker can support many possible train routes that spread out somewhat like a peacock’s fan from a single starting station (ie a sort-of flood-fill)4.
• A company which pays a dividend and cannot profitably run a given train (ie income from the train is larger than maintenance fees) must discard the train (for no recompense).

### Track

The next area of exploration is a tentative form of impermanent track combined with an inversion of normal revenue allocations:

• Dits (towns) are generally worth more than cities and upgrade to be worth a lot more. Specifically dits appreciate faster and further than cities when upgraded.
• Bush “track” is represented by narrow gauge track.
• At the end of each set of ORs all narrow gauge track is removed from the map (dirt roads wash out with the rainy season)
• Most of the centre of the board is terrain interspersed with single and double dits.
• Yellow narrow gauge track can be upgraded to green standard gauge track, which is not removed at the end of the set of ORs
• Single dit track does not upgrade (ala 1830).
• Yellow double-dit narrow-gauge track can be upgraded a green tile to a mix of a narrow-gauge route and a standard gauge route. In this case at the end of the OR the tile is demoted to a green single dit of a higher revenue.
• Yellow narrow gauge double-dits can also be upgraded green track with to both sides being standard gauge.
• Green double-dit standard gauge cites can be upgraded to (standard) green/brown 4-exit cities.
• The offboards which ring the map allow train (gangs) which run to them to double-count N dits for revenue.

### Stock market

I’m interested in varying the rates of appreciation at different sections of a stock market, as well as stock markets which don’t have the traditional triangular shape5. What if the market had a different shape? What if the top-edge of the market weren’t flat? What if the rate of appreciation across the market were non-uniform in an interesting manner? What if navigating the marker’s new particulars were significant to gameplay?

A first toy idea is below6:

 40 45 50 60 70 80 95 110 125 145 165 190 220 255 295 340 390 450 520 600 690 795 915 1050 1210 1390 1600 35 40 45 55 65 75 85 100 115 130 150 175 200 230 265 305 350 405 465 535 615 705 810 930 1070 1230 1415 35 40 45 50 60 70 80 90 105 120 135 155 175 200 230 260 295 335 380 435 495 565 645 735 840 960 1095 35 40 45 50 55 60 70 80 90 100 110 125 140 155 175 195 220 245 275 310 345 385 430 480 540 605 680 30 35 40 45 50 55 60 70 80 90 100 110 120 135 150 165 185 205 230 255 285 315 350 390 435 485 540 30 35 40 45 50 55 60 65 70 75 85 95 105 115 125 140 155 170 185 205 225 250 275 305 335 370 405 25 30 35 40 45 50 55 60 65 70 75 80 85 95 105 115 125 135 145 160 175 190 205 225 245 265 290 30 30 30 35 40 45 50 55 60 65 70 75 80 85 90 95 105 115 125 135 145 155 165 180 195 210 225 25 25 25 30 35 40 45 50 55 60 65 70 75 80 85 95 105 115 125 135 145 160 175 190 205 225 245 25 25 25 25 30 35 40 45 50 55 60 65 70 75 85 95 105 115 125 140 155 170 185 205 225 250 275 20 20 20 20 25 30 35 40 45 50 55 60 65 70 80 90 100 110 120 135 150 165 185 205 230 255 285 20 20 20 20 20 25 30 35 40 45 50 55 60 65 75 85 95 105 120 135 150 170 190 215 240 270 300 15 15 15 15 15 20 25 30 35 40 45 50 55 60 70 80 90 100 115 130 145 165 185 210 235 265 300 15 15 15 15 15 15 20 25 30 35 40 45 50 55 65 75 85 95 110 125 145 165 190 215 245 280 320 10 15 15 15 15 15 15 20 25 30 35 40 45 50 60 70 80 90 105 120 140 160 185 215 245 280 320 370

#### Market Details

• The top row appreciates by 15% horizontally. The next row down by 14%, the next row again by 13% and so on down to 8%. Then the next row down by 9%, 10% etc back up to 15%. The result is a market that’s heavily skewed towards stock-appreciation at the edges, but is flat and uninteresting in the middle – that same middle that the shape of the market pushes all shares towards.
• The magnitudes of the stock-price increases toward the top, especially in the second section, and are thus rather large7. It is hoped that this will provide a balancing tension between being dividend/income-centric versus portfolio/stock-centrism.
• Arrows on ceiling cells by walls point down and to the right for when stocks bounce on the ceiling or hit the wall.
• Similar arrows for floor cells merely point vertically up (no acceleration).
• Red cells are possible pars (some will likely need to be removed)
• Players may buy past 60% from the Open Market.
• The coloured sections in the corner may be removed, or if they remain, are unlikely to have traditional definitions.

#### Stock price movement

• Up or follow arrow if 100% in player hands
• Right (at least) once if total dividend is larger than price
• Right twice if total dividend is more than double price and company is incrementally capitalised8
• No movement if total dividend equals price
• Left if total dividend is less than price but larger than half of price
• Left and down if total dividend is half of price or less
• Down on stock sales (possibly once per sale rather than once per share)
• Down if shares in the Open Market at the end of a Stock Round (maybe)

### Game Events:

• Yes, a stock can pay a dividend and move right or up and find its price reduced as a result. Of course it can also pay an inadequate dividend and move left or left and down for the same reduced price result. Simply consistently paying dividends is no longer enough to prosper.
• (Not shown) the stock market is divided into diagonal stripes. Companies start with a limited and small number of station makers. As their stock prices move right across the various bars, they are allowed to buy and place additional station markers.
• On the sale or research of the first 6T all share prices fall to the floor, move left (if possible), and then fall to the floor again. (This ordering is deliberate and specific) Again, like 18FR-RCE’s all-the-trains-rust moment, this is in recognition of World War II. It is generally hoped that this will happen when several companies are near or shortly past the market constriction around $1059. • The result of the steeply banked par values and stock-appreciation differences, encourages fully capitalised companies to par high in order to maximise capital and ease getting their price through the passage. • Conversely, incrementally capitalised companies do not want to par high as later shares will (almost necessarily) be much cheaper than the initially parred shares, and will proportionally fail to raise capital. However parring an incrementally capitalised company low simply fails to raise enough capital to be viable. 1. And more on 1845 later as well. 2. ie everything except Western Australia. 3. This may change. I do want to provide a choice regarding capitalisation, but I want it to be a real choice where both answers are frequently correct. 4. I am also toying with using something like 1873’s train-multiple concept here. 5. After 1828’s market which has a large new triangular section bolted on the end-tip of what is otherwise a normal triangular-shaped market. 6. The gray sections are for calculations and are not part of the market. 7. eg$210/share should a stock reach \$1,600/share

8. The notion is to have both incrementally capitalised and fully capitalised companies, at the player-choice per company, with the choice as to which to prefer and when being difficult.

9. Recently termed the stock anus or sphincter in local discussions.