Isaac Bickerstaff (Verkisto) posted new share images for Wabash Cannonball and the Erie expansion (Wabash.pdf, Erie.pdf) a while back. I’ve dawdled on doing anything with them as I was mostly content with the originals and wasn’t yet sure how I physically wanted to produce them. This afternoon I finally got off my kiester and made them.

A laser printer produced good enough copy. I’d hoped to mount back-to-back copies so as to make double-sided shares (unthematic but simpler to handle), but in testing that proved overly difficult within the desired tolerances. The next stab was at cold laminating and then cutting to shape. The plastic laminate would add thickness and the paper would provide its own colour (on one side at least). I’ve done this before for other games, and it works well enough. But fate had it that the cold laminator was on the other side of town, an Office Max was in the middle, and I needed to stop at the Office Max anyway to get some more wet erase pens for Pampas Railroads since my red pen exploded last week¹. Oh, and I’d just bought a few bags of penny sleeves for Tahuantinsuyu’s cards. A quick check revealed that Isaac had thoughtfully sized his share images to fit penny sleeves perfectly!

1. Two packs of 3”x5” index cards from Office Max
   • One in five colours (red, blue, yellow, green and purple – available in rainbow and day glo, I chose rainbow as slightly more pastel/muted)
   • One in stripes (red, blue, yellow, green or purple against white – again picking rainbow instead of day glo)
2. One stick of liquid permanent glue with applicator
3. 20 minutes with the glue and a rotary cutter

I put the unlined sides of the cards to the back, leaving the lined sides to be covered by the glued on shares. This lets the shares effectively be double-sided without the effort of having to register both sides. While most of the colour matches are obvious, I used purple for the Wabash and purple/white striped for the Erie. The moisture content of the blue warps them almost immediately – they are now sitting in an ad-hoc vise atop my water heater to dry out into flat form. They look rather nice! It would have been nice to find gray index cards for the Wabash, but that was not to be. It is possible that other stores carry them (I haven’t researched). Isaac’s Erie share is an odd shade of purplish tannish gray rather than the straight tan of the original. A purple/while stripe seemed an acceptable compromise.

Given that we mostly play on Ted Alspach’s redraw of the map (much larger and more colourful), these replacement shares will mean that the wood cubes are the only original component I use in play. Given how much I like and admire Winsome Game’s game art in general (it is the model of functional clarity), and have repeatedly said so publicly, this is rather oddly hypocritical. Huhn.

I’ll try to remember to get some pictures posted. With luck we’ll play with them tomorrow.

The Neuland action-track, even Thebe’s simpler version, is just an action costing/selection mechanism akin to the rondel that Mac Gerdts has been so fond of using. The track controls turn order and expresses choices in terms of action versus cost where the cost is implied against turn order. Key to the whole pattern is differentiation both in terms of board position and action track position. This localises values to that the turn order ramifications of subsequent action choices are significant.

Neuland does this through the combination of three patterns:

1. Food and Wood must (nearly) always be protected through occupation/production
2. Players must consume their products each turn or lose them at the end of their turn
3. Players ending with their action market on a slow already occupied by another player must slide forward to the next free slot

The result is an accelerating wave front of consumption, driven from behind by the constant input of food and wood and fanning out into ever more orchestrally difficult complexity in the mature mature products. The wave front collapses when products must be discarded rather than consumed¹ and around point-producing buildings consume of mature/complex products, allowing the player to reset back to a simpler world² and begin the next heady climb³.

The key here is differentiation. Differentiation is required by any temporary emergent alliance game else the alliances have no value gradients to form around. Like both Pampas Railroads and Wabash Cannonball the current initial share auction in Muck & Brass establishes a couple primary points of differentiation:

1. What shares are held by whom at the end of the auction
2. Total cash holdings (and resulting turn order)

However those differences are too small for Muck & Brass. Unlike Wabash Cannonball and Pampas Railroads, companies are poorly differentiated in Muck & Brass as their long-term income potentials are mostly dependent on action selections that surround the early mid-game (access to London and merge opportunities). Again like Wabash Cannonball and Pampas Railroads, Muck & Brass uses competition for limited action supplies to provide the rest of the differentiation. Any replacement action selection and turn order system will need to at least equal that level of differentiation if not improve on it, and there are a few problems.

Unlike Neuland, Muck & Brass does not have an oscillating wave-front of commitment. Actions will generally not be selected in large sets, rather a player will take an action (sliding forwards Neuland-style as needed) and the player furthest behind on the action track will take the next action (usually a different player). The result is that opportunity cost becomes significant – not opportunity for self but opportunity afforded to others. A large/expensive action which passes over other players affords them the opportunity to perform multiple smaller/cheaper actions before the expensive-action-player can react.

This has large implications for the numbers selected. If, for instance, all the costs are even values, then the players will rapidly sort themselves into sets, the odds and the evens, with transfers between sets occurring only on collisions⁴ All odd costs also has the same behaviour. Having the action cost values close to each other suggests that collisions will be more frequent, but also suggests that players will select actions in part to avoid collisions (they might as well spend the action they’d otherwise lose by sliding forward). The intersection of these two patterns arrives when some costs are multiples of other costs. Multiples suggest phase relationships with the parity of the modulo affecting action selection in order to avoid collisions, Additionally there’s a relationship between the size of the average action cost and the number of players. For instance if the costs are 1/2/3 and there are 5 players in the game, then after a few turns every action choice will result in a collision.

The significant attributes appear to be:

1. Odd/even spread of costs
2. Ratio of average cost to number of players
3. Density of action cost values
4. Average rate of collisions
5. Strength of set-formation among players along parity lines
6. Breath of action cost range in terms of cost-multiples

And of course:

1. Length of action track as a function of action costs as a determinant of dividend rate

Hurm. I was looking at 1/2-2/3-4 as action costs, but that seems clearly poor, especially when compared to player counts. 2/5-3/5-7 seems attractive. This is going to take some work.

As a total aside, I’ve also been toying with an extension to the Capitalisation action:

- In addition to the normal behaviours a player holding a clear plurality of shares in a company may have that company reclaim any one of its shares held by any player for a sum equal to twice the current dividend value of the share

I ran some thought models last night. They didn’t work so well. Today’s talk with Tim on #bgdf_chat summarises well enough:

[2008-08-29/12:51] <clearclaw> The Neuland action system has problems as described – it forces all players to ally equally.

[2008-08-29/12:51] <gamesonthebrain> How so?

[2008-08-29/12:52] <clearclaw> You want to make money on every player’s turn when they cross the boundary. Thus you want to invest in everything they hold a plurality in.

[2008-08-29/12:52] <clearclaw> Similarly you only want to forward companies you at least hold an equal share in.

[2008-08-29/12:53] <clearclaw> But that’s due to the definition of when/how dividends get paid.

[2008-08-29/12:53] <gamesonthebrain> Right, which can be changed

[2008-08-29/12:53] <clearclaw> Yep. Changing that constraint can change everything.

[2008-08-29/12:54] <clearclaw> I’m toying with having everything the player is invested in pays out, just to that player.

[2008-08-29/12:54] <gamesonthebrain> I did’t realize until today that Neuland’s turn order system is fairly different from Thebes

[2008-08-29/12:54] <clearclaw> That does really interesting things to the incentives.

[2008-08-29/12:54] <clearclaw> I’ve never played Thebes so can’t comment.

[2008-08-29/12:54] <clearclaw> Neuland is a favourite though.

[2008-08-29/12:54] <gamesonthebrain> In Thebes, the person in the back of the line always takes the next action

[2008-08-29/12:55] <gamesonthebrain> So the actions would be much more broken up

[2008-08-29/12:55] <gamesonthebrain> If I was on space 4 and you on 3, it would be your turn

[2008-08-29/12:55] <clearclaw> Ditto Neuland except that in Neuland players get to keep using actions until they quit, as long as they don’t pass themselves.

[2008-08-29/12:55] * clearclaw nods.

[2008-08-29/12:55] <clearclaw> That is finer grained.

[2008-08-29/12:55] <gamesonthebrain> If you took a 1 AP point action, you’d then be on “top” of me, and thus still your turn

[2008-08-29/12:55] <gamesonthebrain> Ya

[2008-08-29/12:55] <clearclaw> I’m thinking of that graining for this game.

[2008-08-29/12:56] <clearclaw> Tinner’s Trail is somewhat similar.

[2008-08-29/12:56] <gamesonthebrain> Yes… the only real difference is the fixed round in TT, and the “top” person does not go again…

[2008-08-29/12:57] <gamesonthebrain> Like you said in our chat the other day, the finer grained Thebes system might make the game substantially longer

[2008-08-29/12:57] * clearclaw pondering.

[2008-08-29/12:58] <clearclaw> I am liking the idea of paying just the active player for everything they hold though. It feels like it might work.

[2008-08-29/12:58] <gamesonthebrain> It certainly would be easier

[2008-08-29/12:58] <gamesonthebrain> Less fiddly

[2008-08-29/12:58] <clearclaw> As for game length, that’s also a question of end-definition. That can be adjusted.

[2008-08-29/12:58] <clearclaw> It also makes the play decisions, especially Capitalisation, much harder.

[2008-08-29/12:59] <clearclaw> Very odd tempos.

[2008-08-29/12:59] <clearclaw> Very hard to predict.

[2008-08-29/12:59] <clearclaw> Strange effects on alliances.

[2008-08-29/12:59] <clearclaw> I don’t think I understand what it will in fact do....

[2008-08-29/12:59] <gamesonthebrain> Sure, but at least it is completely controlled by the players

[2008-08-29/12:59] <clearclaw> There is that advantage. Players are my favourite source of randomity.

[2008-08-29/13:00] <gamesonthebrain> It’s hard to say without testing it, but it sounds perfect to me

[2008-08-29/13:01] * clearclaw grins.

[2008-08-29/13:01] <clearclaw> I have more models to run.

[2008-08-29/13:01] <gamesonthebrain> Let me know about the results… my email is gamesonthebrain@---------.com

[2008-08-29/13:02] <gamesonthebrain> As I said the other day, I have an experienced train gaming group ready to playtest

[2008-08-29/13:04] <clearclaw> Hehn. Wilco. I suspect the blog and the IRC here are the best channels until it gels.

[2008-08-29/13:05] <clearclaw> Thanks

[2008-08-29/13:06] <gamesonthebrain> Fine… I’m on here a lot more now with the new IRC channel

The real key is the control of what pays when as that drives the incentives that drive alliance formation. That prediction by the players is (going to be) the base on which they determine their interest and thus their action selections.

I’ve been wanting to get back to work on Colonial Zoo for a while now but every time I start re-assembling my thoughts they veer off and turn into odd ideas about Trade Winds and/or Muck & Brass or some collision of the two. It has been frustrating.

The main thought for Muck & Brass is that the Pampas Railroads-style action selection mechanism isn’t sufficiently expressive. It provides interesting choices, but they tend to short-term tactical due to the ever-shifting turn order¹. Both Pampas Railroads and Wabash Cannonball exploit right/left binding as a way of providing enough certainty for alliance formation. My largely certain assumption is that fixed turn order isn’t required for emergent alliances, just merely helpful. Emergent alliance formation can still operate in games with variable turn order, as seen with Han’s Riding Series.

Without admitting a problem, perhaps a more free-form action system would make the game more interestingly phase-driven and thus cast a stronger structural light on the game of mergers? Additionally such a system might offer some of the long-term certainties that are missing with variable turn order and thus allow for more interestingly strategic decisions.

The thoughts were solidified by a discussion with Tim Harrison (GamesOnTheBrain) on #bgdf_chat:

[2008-08-27/10:46] <gamesonthebrain> hmmm… JC… I just had an idea… you remember my basic description of my holy grail train game above… I wonder if the Thebes/Neuland AP thing would work well in a game like that

[2008-08-27/10:50] <clearclaw> The Neuland turn-order pattern will tend to drive a longer game.

[2008-08-27/10:51] <clearclaw> Think about it this way: How many turns per player and how many rounds per player per game.

[2008-08-27/10:52] <clearclaw> In general players should have 10-14 turns in non-epic games which feature non-trivial turns. Less and the game is too short to build interest, longer and it bloats.

[2008-08-27/10:52] <gamesonthebrain> Ya, you’re right

[2008-08-27/10:52] <clearclaw> (there are of course exceptions)

[2008-08-27/10:53] <gamesonthebrain> I do tend to like games that have a lot of short turns rather than few long ones though

[2008-08-27/10:53] <gamesonthebrain> like the rondel games

[2008-08-27/10:56] <clearclaw> The Rondel games are interesting. All the rondel really does is present a specific choice-costing structure on each turn.

[2008-08-27/10:56] <clearclaw> His next game does exactly the same sort of choice-costing, just without the rondel and thereby affords a somewhat more interesting graph of choice-relationships.

[2008-08-27/10:56] <gamesonthebrain> I’m really looking forward to princes

[2008-08-27/10:57] <gamesonthebrain> sounds like a must buy for me

[2008-08-27/10:57] <clearclaw> My sense however is that for a game turn to be interesting a player must manage 5-7 (not more!) discrete elements, and must make at least 3 significant and inter-related decisions.

[2008-08-27/10:58] <clearclaw> But that may be more revealing my own preferences than setting an abstract guide.

[2008-08-27/10:58] * clearclaw nods. It does sound interesting.

[2008-08-27/10:58] * clearclaw says things about the implications of the rule of seven etc.

[2008-08-27/10:59] <gamesonthebrain> with the AP thing, wouldn’t a successful player have to be thinking several turns ahead in order to do well? thus, it seems, they would have to be managing 5 or so elements and be making 3 significant decisions per turn.

[2008-08-27/10:59] * clearclaw nods GamesOnTheBrain

[2008-08-27/11:00] <gamesonthebrain> I agree that it might make the game way too long though

[2008-08-27/11:00] <clearclaw> That think-ahead can be one of the dimensions managed on the turn, thus allowing the choices contained within the turn to be simpler. Goa does that trick particularly well.

The brief thought is to make the following changes:

1. A Neuland-style action point track (length TBD, probably in the 7-9 range))
2. One location on the track is called out (colour or other marking)
3. Players may perform any of the standard Capitalise/Develop/Expand actions in the normal manner
4. Each action has an associated AP cost, eg Capitalise 3 AP, Develop (single) 2 AP, Develop (double) 3AP, Expand (single) 1AP, Expand (double) 2AP
5. APs result in the player’s token orbiting the Neuland-style track in the normal manner
6. Turn order is dictated by the action point track Neuland-style (very uncertain about this)
7. Should a players action take them to or past the specially marked location on the action track (cf Imperial’s Investor rondel location) then all the companies of which that player is the plurality shareholder pay dividends

Methinks I need to run some simulations.

A good understanding of Nash equilibria is necessary for understanding the implicit auction theory behind most games. Presh Talwalkar has written a rather nice casual description of them in his Mind Your Decisions blog in the artcle, The Non-Mathematical Guide to Fixed Point Theorems and Proving Nash Equilibria Exist. He similarly casually and usefully discusses Arrow’s Impossibility Theorem (central to thoroughly understanding any auction or voting system) and Pareto Efficiency in another article, Arrow’s Impossibility Theorem and The Voting Paradox. Good stuff.

A few other interesting articles from a game-design perspective:

• Strategic Commitments: How to Lose Weight and Live up to New Years Resolutions
• Why Patience Pays Off in Negotiations
• Voting Power in Israeli Judge Selection and the Shapley-Shubik Index

In all the recent discussions of Temporary Emergent Alliances (or Manipulating Others’ Incentive Structures), Wabash Cannonball, Pampas Railroads, Muck & Brass and similar games the following article fell across my browser: Game Theory in The Dark Knight: A Critical Review of the Opening Scene (Spoilers). Several of the other articles in the author’s Game Theory Series are also interesting.

Wabash Cannonball Expansion - Erie Railroad belies its effect on the game with its small size. The Erie RR is nitroglycerin in a cocktail shaker. It makes the already rather delicately knife-edged game of Wabash Cannonball even more tetchy with the penalties for mis-steps ever larger and the path ever narrower and risk-fraught.

The Erie expansion consists of a single new Erie company with a single share, 14 cubes (1 income marker, and 13 track) and a slip of paper containing the few special rules governing when and how the Erie becomes available for play. More specifically it has enough cubes to reach both Detroit and Chicago.

The Erie RR becomes available for Capitalisation when any of four specially nominated cities have track built in them by another company. The Erie’s home station is roughly in the middle of the northern edge of the board. It has no special rules except that:

• It can build into New York City at a cost of $6 for an income boost of $8
• The N-companies-out-of-shares game-end condition is increased from 3 companies to 4 companies

Functionally the Erie RR is simple enough except in the implications:

• The Erie can only be Capitalised by explicit choice. Why a player would Capitalise the Erie is a difficult question:
  • Because the acting player can win it and profit
  • To tempt another player into a posture that can then be wielded against them (push a short game against a player positioned for a long game and visa versa)
  • To drive an early/faster game-end
  • To tempt another player into sundering their extant alliances
• The player that wins the Erie:
  • Is almost certainly no longer a functioning member of any prior alliances as their incentives now orbit the Erie RR due to their high cash investment in the Erie RR
  • (Likely) explicitly postured for a long game but with greatly reduced ability to influence game length
• The Erie RR is more valuable to owners of NYC RR and Pennsylvania RR shares
  • The Erie is most likely to share cities with the NYC RR and second most likely to share cities with the Pennsylvania RR.
• Once the Erie RR opens the Development actions becomes much more interesting to all players
  • Once the Erie RR player runs out of Expansion actions, or runs out of cash, very likely their most attractive action is Development
  • If the Erie RR player can benefit multiple of their companies with Development (thus the interest in the NYC RR and the Pennsylvania RR), then so much the better.
  • Due to the steady depletion of Development actions by the Erie RR player, the Development action becomes more attractive for the other players. Their shares are less diluted with the removal of the Erie RR player’s maniacal focus on the Erie RR and Development is thus more likely to lead to a direct/tangible cash income increase for them.
  • Increased use of Development as versus the standard routine of Capitalise/Expand affords control of additional control game length and control of who is the start player for the next round.
    • It becomes easier for low player count games to end due to track cube exhaustion
    • It becomes easier (albeit likely still rare) for middle-player count games (ie 4 players) to end due to Development cube exhaustion.
    • Exact control of game length is more diffuse while the Erie RR player’s maniacal focus encourages all the players to posture more heavily toward a specific game length
• Detecting when it is no longer viable to invest in the Erie RR versus when it is too soon (not enough cash or game-control) is delicate and fraught with failure
  • The Erie RR will likely need somewhere between $20 and $30 (possibly more) in order to fully afford its own expansion opportunities
  • Due to the single share all capitalisation must occur from the initial share sale. Forest development is an unviable capitalisation source.
  • Whether or not the Erie RR will get those opportunities is uncertain
  • As only one player can Expand the Erie RR, company income growth is necessarily slow as compared to collusive Expansion alliances among other players
  • However due to lack of dilution, income growth is fast(er)
    • With a large caveat for Chicago Dividends
    • Those same Chicago-bound alliances encourage the Erie RR player to sabotage the other RRs by running them short of cubes
      • The opportunity cost of not spending that Expansion on the Erie RR is high

The Erie RR is highly attractive due to the massive potential profits. Should it get to both Detroit and Chicago it can easily pay $25/share! However as noted above this great profit potential comes with risks for all the players, not just the Erie RR-investing player. That balance of risk and reward forces the players to begin positioning themselves in relation to the Erie RR from the initial auction of a Pennsylvania RR share at the start of the game and every portion of the game after that becomes a question that also needs to be evaluated in relation to the Erie, whether or not it is in the game yet.

I recommend Wabash Cannonball Expansion - Erie Railroad only to experienced Wabash Cannonball players. Unless the players comprehend not only the base game’s arithmetic and alliance system, but also how to posture against game length and how to adroitly wield game-length control against the other players then the Erie will simply walk all over them and render the game results an opaque who-goofed crapshoot. With skillful players however it becomes a delightful game of balancing on razorblades and juggling waterballoons of nitroglycerin. It is quite the designer tour-de-force. Amazingly subtle and pervasive. It is rare that so little turns so much of a game on its ear without also breaking it. Everything is the same and yet different. Bravo!

I primarily use the Remainder Game for start player selection but there’s no inherent reason it has to be limited to that application. The pattern is simple:

1. One player calls for the start player selection, Everybody stick out some fingers. 1, 2, 3!
2. Take the modulus of the total number of fingers shown by the players by the number of player and starting at zero, count out that many players in rotation from the calling player.
3. The indicated player is the start player.

The Remainder Game is efficient, deterministic results (no repeats, roll-offs or ties possible), actually random¹, short constant execution time, works with any number of players in any situation, works with any game in any situation, clearly auditable by all concerned, and requires no equipment.

Ariel has come up with an impressive follow-on T-shirt suggestion:

Chris Johnson (fnord23) kindly noticed an error in my charts for Pampas Railroads. Corrected versions are in the normal place.