# Variants: 1830 Cardgame

Variants to consider for the new 1830 cardgame:

• Move the hand management to after the turn order auction:

1. Players auction for turn-order before discarding their hands down to 3 cards.
• Address the turn order auction as well:

1. First to pass will go last, second to pass will go second to last, etc with the last remaining bidder going first.
2. Winning bidder pays their bid, all other bidders pay half their bid rounded up, except for the player last in turn order who pays nothing.
3. After the turn order auction, players reseat in turn-order order.
• Remove and reduce the silly trackable information:

1. Players keep their initial hands of action cards face-down on the table before them (but may of course inspect them freely).
2. Drawn cards which are kept in the hand are put face-up on the table before them.
3. All played cards in the discard piles may be freely examined and counted at any time.
• Increase the information level of the draft:

1. In addition to the three cards for the action draft, also lay out the next three cards, face up, that will be drawn to replace drafted cards.

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