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Commentary and processes of J C Lawrence: systems architect, contrarian, theorist, sailor, hacker, virtual world designer, linux-user, aquarist, disquisitor, cat breeder, raconteur, game designer, ludophile, bibliophile, numismatist, speculator and theologiser

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Totem stack rotation

In the prior discussion I defaulted without examination to moving forward in the event of a collision1 Why?

If collisions do not trigger slides then either it must always be possible to avoid a collision (easily proven impossible in 4+ player games) or there must be an ordering function for players resident at the same action slot, perhaps a FIFO(def) or LIFO(def). Both queue forms have their interesting aspects with LIFOs perhaps being the more interesting as later players can get an instant second turn by ending atop a prior player, perhaps to the earlier player’s discomfort (making turn prediction more difficult and yet more valuable).

Stacking seems inevitably less interesting. Collision sliding offers a few clear interest-benefits:

  1. A slide moves the subject player further around the ring thus making their next dividend closer/sooner
    • Situations can be crafted which allow multiple positions to be collision-slid
  2. Collision sliding encourages players to chose actions which use/absorb the lost action point. Because this value cuts in both directions, Development gets an extra boost encouraging a slightly more Development-centric game than Expansion-centric
  3. Unpreventable slides (can) force players to waste action points in non-income producing movement

Meanwhile almost the same multiple-turn opportunity remains, just trimmed by one action point to not include the collision point.

More simply collision-sliding offers an additional decision: To slide or not to slide. Each side of that decision has significant effects on turn order — effects which are interesting for the subject player and interesting for other players to predict and arrange afore-hand.

Footnotes
  1. player ends their turn at the same place on the action track as a prior player, thus colliding and sliding forward to the next available slot. ↩

Definition: FIFO

[1] : The Collaborative International Dictionary of English v.0.48

FIFO \FIFO\ (f[imac]"f[=o]), a. [acronym, First In First Out.]
   1. (accounting) an accounting method in which goods in
      inventory are valued at the price of the most recent
      acquisition of each type of goods, and those used up from
      inventory are valued at the cost of those first acquired.
      [PJC]

[2] : WordNet (r) 3.0 (2006)

FIFO
    n 1: inventory accounting in which the oldest items (those first
         acquired) are assumed to be the first sold [syn: first in
         first out, FIFO]
See also:
[first in first out] [FIFO]

[3] : The Free On-line Dictionary of Computing (26 July 2010)

first-in first-out
FIFO

    (FIFO, or "queue") A data structure or hardware
   buffer from which items are taken out in the same order they
   were put in.  Also known as a "shelf" from the analogy with
   pushing items onto one end of a shelf so that they fall off
   the other.  A FIFO is useful for buffering a stream of data
   between a sender and receiver which are not synchronised -
   i.e. not sending and receiving at exactly the same rate.
   Obviously if the rates differ by too much in one direction for
   too long then the FIFO will become either full (blocking the
   sender) or empty (blocking the receiver).  A Unix pipe
   is a common example of a FIFO.

   A FIFO might be (but isn't ever?) called a LILO - last-in
   last-out.  The opposite of a FIFO is a LIFO (last-in
   first-out) or "stack".

   (1999-12-06)

See also:
[block] [Unix] [pipe] [stack]

[4] : V.E.R.A. -- Virtual Entity of Relevant Acronyms (June 2006)

FIFO
       First In First Out (CPU)
Close

Definition: LIFO

[1] : WordNet (r) 3.0 (2006)

LIFO
    n 1: inventory accounting in which the most recently acquired
         items are assumed to be the first sold [syn: last in first
         out, LIFO]
See also:
[last in first out] [LIFO]

[2] : The Free On-line Dictionary of Computing (26 July 2010)

stack
FILO
last-in first-out
LIFO

    (See below for synonyms) A data structure for
   storing items which are to be accessed in last-in first-out
   order.

   The operations on a stack are to create a new stack, to "push"
   a new item onto the top of a stack and to "pop" the top item
   off.  Error conditions are raised by attempts to pop an empty
   stack or to push an item onto a stack which has no room for
   further items (because of its implementation).

   Most processors include support for stacks in their
   instruction set architectures.  Perhaps the most common use
   of stacks is to store subroutine arguments and return
   addresses.  This is usually supported at the machine code
   level either directly by "jump to subroutine" and "return from
   subroutine" instructions or by auto-increment and
   auto-decrement addressing modes, or both.  These allow a
   contiguous area of memory to be set aside for use as a stack
   and use either a special-purpose register or a general
   purpose register, chosen by the user, as a stack pointer.

   The use of a stack allows subroutines to be recursive since
   each call can have its own calling context, represented by a
   stack frame or activation record.  There are many other
   uses.  The programming language Forth uses a data stack in
   place of variables when possible.

   Although a stack may be considered an object by users,
   implementations of the object and its access details differ.
   For example, a stack may be either ascending (top of stack is
   at highest address) or descending.  It may also be "full" (the
   stack pointer points at the top of stack) or "empty" (the
   stack pointer points just past the top of stack, where the
   next element would be pushed).  The full/empty terminology is
   used in the Acorn Risc Machine and possibly elsewhere.

   In a list-based or functional language, a stack might be
   implemented as a linked list where a new stack is an empty
   list, push adds a new element to the head of the list and pop
   splits the list into its head (the popped element) and tail
   (the stack in its modified form).

   At MIT, pdl used to be a more common synonym for stack,
   and this may still be true.  Knuth ("The Art of Computer
   Programming", second edition, vol. 1, p. 236) says:

     Many people who realised the importance of stacks and queues
     independently have given other names to these structures:
     stacks have been called push-down lists, reversion storages,
     cellars, dumps, nesting stores, piles, last-in first-out
     ("LIFO") lists, and even yo-yo lists!

   [Jargon File]

   (1995-04-10)

See also:
[instruction set architectures] [subroutine] [machine code] [auto-increment] [addressing modes] [register] 
[stack pointer] [recursive] [activation record] [Forth] [object] 
[Acorn Risc Machine] [functional language] [linked list] [MIT] [pdl] 
[Knuth] [Jargon File]

[3] : V.E.R.A. -- Virtual Entity of Relevant Acronyms (June 2006)

LIFO
       Last In First Out
Close

Wabash Cannonball & Erie share production

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.

Footnotes
  1. Remember folks, keep your wet erase pens in a sealed plastic bag! ↩

In an infinite field there are no tangible differences

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:

Footnotes
  1. Consumption building unavailable, blocked or too expensive ↩
  2. Roads & Boats achieves a similarly complex logistical wave-front end, but without the reset function of Neuland’s action point buildings. To contain the complexity Roads & Boats limits transports and pushes an aggressive (implied) tech tree. ↩
  3. A typical Neuland game consists of 3-5 climbs per player per game with 2-4 player turns per climb. ↩
  4. Player ends at the same point on the track as another player’s marker ↩

Getting paid by the nose

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.

Turn about is fair play

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.

Footnotes
  1. Note to self: Write article on turn order controls ↩

Casual Nash

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:

The game of theatre

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.

Early Experience: Wabash Cannonball Expansion – Erie Railroad

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(def) 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:

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

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!

Definition: tetchy

[1] : The Collaborative International Dictionary of English v.0.48

Tetchy \Tetch"y\, a.
   See Techy. --Shak.
   [1913 Webster]
See also:
[Techy]

[2] : WordNet (r) 3.0 (2006)

tetchy
    adj 1: easily irritated or annoyed; "an incorrigibly fractious
           young man"; "not the least nettlesome of his countrymen"
           [syn: cranky, fractious, irritable, nettlesome,
           peevish, peckish, pettish, petulant, scratchy,
           testy, tetchy, techy]
See also:
[cranky] [fractious] [irritable] [nettlesome] [peevish] [peckish] 
[pettish] [petulant] [scratchy] [testy] [tetchy] 
[techy]
Close

Definition: sundering

[1] : The Collaborative International Dictionary of English v.0.48

Sunder \Sun"der\, v. t. [imp. & p. p. Sundered; p. pr. & vb.
   n. Sundering.] [OE. sundren, AS. sundrain (in [=a]sundrain,
   gesundrain), from sundor asunder, separately, apart; akin to
   D. zonder, prep., without, G. sonder separate, as prep.,
   without, sondern but, OHG. suntar separately, Icel. sundr
   asunder, Sw. & Dan. s["o]nder, Goth. sundr[=o] alone,
   separately.]
   To disunite in almost any manner, either by rending, cutting,
   or breaking; to part; to put or keep apart; to separate; to
   divide; to sever; as, to sunder a rope; to sunder a limb; to
   sunder friends.
   [1913 Webster]

         It is sundered from the main land by a sandy plain.
                                                  --Carew.
   [1913 Webster]
See also:
[Sundered] [Sundering]
Close

The Remainder Game — a method for constant-time (pseudo-)random selection

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(def) 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.

Footnotes
  1. Well, nearly and close enough in practice. Ideally the number of fingers shown by each player should be in the range of zero-#players-1 or else there’s a bias away from players to the right of the calling player. In practice however as player counts are usually in the 3-5 range and most people use the fingers of one hand, this really doesn’t matter much. throw in the odd player who sometimes uses fingers from both hands and you’re near golden for all games and player counts ↩

Definition: modulus

[1] : The Collaborative International Dictionary of English v.0.48

Modulus \Mod"u*lus\, n.; pl. Moduli. [L., a small measure. See
   Module, n.] (Math., Mech., & Physics)
   A quantity or coefficient, or constant, which expresses the
   measure of some specified force, property, or quality, as of
   elasticity, strength, efficiency, etc.; a parameter.
   [1913 Webster]

   Modulus of a machine, a formula expressing the work which a
      given machine can perform under the conditions involved in
      its construction; the relation between the work done upon
      a machine by the moving power, and that yielded at the
      working points, either constantly, if its motion be
      uniform, or in the interval of time which it occupies in
      passing from any given velocity to the same velocity
      again, if its motion be variable; -- called also the
      efficiency of the machine. --Mosley. --Rankine.

   Modulus of a system of logarithms (Math.), a number by
      which all the Napierian logarithms must be multiplied to
      obtain the logarithms in another system.

   Modulus of elasticity.
   (a) The measure of the elastic force of any substance,
       expressed by the ratio of a stress on a given unit of the
       substance to the accompanying distortion, or strain.
   (b) An expression of the force (usually in terms of the
       height in feet or weight in pounds of a column of the
       same body) which would be necessary to elongate a
       prismatic body of a transverse section equal to a given
       unit, as a square inch or foot, to double, or to compress
       it to half, its original length, were that degree of
       elongation or compression possible, or within the limits
       of elasticity; -- called also Young's modulus.

   Modulus of rupture, the measure of the force necessary to
      break a given substance across, as a beam, expressed by
      eighteen times the load which is required to break a bar
      of one inch square, supported flatwise at two points one
      foot apart, and loaded in the middle between the points of
      support. --Rankine.
      [1913 Webster]
See also:
[Moduli] [Module] [Modulus of a machine] [Modulus of a system of logarithms] [Modulus of elasticity] [Young's modulus] 
[Modulus of rupture]

[2] : WordNet (r) 3.0 (2006)

modulus
    n 1: an integer that can be divided without remainder into the
         difference between two other integers; "2 is a modulus of 5
         and 9"
    2: the absolute value of a complex number
    3: (physics) a coefficient that expresses how much of a
       specified property is possessed by a specified substance
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One more winner

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

t-shirt-2.jpg

New Pampas redrawn

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

The future is not our’s you see

I previously simplified the implemented definition of a future down to:

  1. Buy goods now to be delivered at time X
  2. Sell goods now to be delivered at time Q

That was a mistake. A necessary element of the core problem of Modern Mogul is that fact that the players should (nearly) never be playing the game as it exists in present time. Instead they should be playing the game as they hope it will be some number of turns in the future. In the above simplified definition the capital is both committed and spent now and only satisfaction is delayed. The more interesting and useful form has the commitment occur now and the capital expenditure when the future matures. In this way the players will not only have to juggle the vagaries of the future market, but also the vagaries of their future liquidity as a result of market activity between then and now. Much better.