Other Wise

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|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|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!

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|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.

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

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.

Negotiated dissection

Attempting a taxonomy of negotiation:

Open Negotiation

Free-form done through conversation and persuasion. Open Negotiation is unbounded/unconstrained and is frequently only incidentally related to direct/current in-game concerns (what tokens are where, what permissions are granted etc) and is generally much more interested in establishing consensus on mutual policies and long-term collusive patterns. Diplomacy is perhaps the titular grandfather of Open Negotiation in game design. The key elements are primary focus of the negotiation is to persuade another player to pro-actively collude (Will you do XYZ for me?), and while the focus of the negotiation is informed by the game, the majority of the negotiation content is meta to the game details.

Simple Negotiation

Frequently tactical and usually directly informed by and concerning current game specifics and the disposition of specific game tokens. The most common forms are simple requests for permission or abeyance. May I do QRS? or If I do ABC will you not attack me? The key element is direct focus on and discussion of game particulars (and thus a rather tactical focus). Questions of policy and long-term collusive patterns are not part of Simple Negotiation.

Implicit Negotiation

In short, where moves are offers. Moves, independently arrived at by the players, without discussion, for negotiative patterns due to common understandings of collusive self-interest which emerge from the game-play. Gun-boat1 no-press2 Diplomacy is the great-grand-daddy here. More recently Wabash Cannonball has epitomised this model3.

Personal views

I am generally not a fan of Open Negotiation in games, rather like Simple Negotiation as (exemplified by such games as Lords of the Spanish Main, Quo Vadis and Traders of Genoa) and adore Implicit Negotiation (eg Wabash Cannonball, Pampas Railroads, or King of Siam).

Footnotes
  1. Diplomacy where the identity of the players is known only to the GM/Judge.
  2. Players can’t communicate with each other, they can only write orders. Much negotiation still occurs, but via orders which suggest cooperation between players. The most frequent form of such a move-as-offer are support orders which suggest a future move or alliance to a potential ally. Support into/or around Switzerland are the most famous in this regard.
  3. eg Capitalisation actions are usually either (mute) requests for a partner or an attempt to sunder a too-successful partnership.

Existentially reliant parasites

A while back Jacob Butcher finally categorised me, You like negotiation games! He’s right of course and I especially like them when the negotiation is implicit instead of explicit, or to quote a more recent conversation with another friend, Where your moves are offers.

I love that idea. Moves are offers. Adorable. Juicy. It is likely that single characteristic, married tightly to a raw game theory core1, is what has so attracted me to Wabash Cannonball. Moves as offers.

So I’ve been thinking for about a week now, mulling around ideas surrounding moves as offers and trying to see what sort of game could be wrapped on that skein. The working concept, which is weak, is a game in which each player has 1/Nth of a limited resource in the game and every move they either offer (partial) access to their stock to one or more other players, or exploits the access that others have offered while also offering access in return. All terribly vague, but the core sense is a sort of dance of offers and engagement and commitment and perhaps even betrayal. The obvious comparables are So Long Sucker and Intrige, but I’d like something far more implicit than those fine stalwarts, as well as far more implicit than explicit.

So far I’ve come up with…nothing. Which is fine for this stage as the thought toy has been delightful, but I’d would like to tangible realise this idea. Sadly inspiration has fled. Still, the thought toy is so charming, so very Mary Poppins in every possible very nearly perfect way.

Footnotes
  1. I introduced a new chap to the SVB gaming group on Tuesday, a rather RPGish sort. Mid-way through the chat he said, “Oh, you’re a game theory guy!” Uhh, yeah. So I taught him King of Siam and Wabash Cannonball.

Effusive incoherence

I’m not getting to play with Muck & Brass as much as I’d like lately — Lords of the Spanish Main is occupying too much of my attention — so a little disclosure seems in order: Rules for Muck & Brass!

I also give you the brief graphical evolution of Muck & Brass:

Scratch pasta and sauce

  • Pasta ([[penne|penne]] is more traditional but it really doesn’t matter)
  • Tomatoes (I use a 2:1 ratio of diced tomatoes and whole plum tomatoes)
  • Bacon or thin-sliced ham (I use bacon scraps and hand-remove all the fat to produce semi-ham)
  • Olives (I prefer oil-cured black kalamata olives but green also work)
  • Rosemary (a little goes a long way)
  • Garlic
  • Olive oil
  • Salt

Chop the meat into little bits and then heat until cooked but still limp (not crisp or chewy!). Drain the fat. Quickly chop and brown the rosemary in the bottom of a saucepan along with the garlic and a little olive oil. Chop or slice the olives and dump the meat, tomatoes, olives and rosemary into the pan with the rosemary and garlic, and stew until the diced tomatoes have lost most of their consistency. Salt to taste. When ready, dump over freshly cooked pasta (a little [[al dente|al dente]] is good — the chewiness adds structure and makes it easier to eat).

While great hot and fresh, the final dish also refrigerates well and improves in flavour over time as the flavours meld. If you’ve picky kids, lower the rosemary and olive proportions. If you’re like me, up the rosemary and olives. If you want to (deliciously) experiment, coarsely cube and brown some [[aubergine|aubergine]] on the side and dump into the mix right before the end.

A failure to communicate

The tool I’ve been using to footnote definitions of terms some readers may not know has a problem. It can result in broken RSS and Atom feeds which don’t validate, usually due to non-UTF8 characters in strings which are defined as UTF8 strings. In turn this causes various RSS readers and aggregators (eg Bloglines and Technorati) to fail to import the feed. Ooops.

For now I’ve removed the offending definition linkages ([[suet|suet]] and [[jocund|jocund]]) and am on the lookout for a replacement WordPress plugin, preferably one based on dict1.

Footnotes
  1. I’m a frequent, nay, near-constant user of dict.

The fabled return of the pastie

Tinners’ Trail, while otherwise an ignorable game, reminded me of the noble pastie and what a fine food it is.

Basic ingredients:

  • Pie dough (pre mixed sheets from the store or make your own with all-purpose flour, salt, water and a little lard or butter)
  • Rutabega (aka swedes — it isn’t a pastie if it doesn’t have rutabega)
  • Potato (I like small quartered reds with the skins on)
  • Onion (I prefer strong yellow but red will also work)
  • Meat (I opted for hamburger, but chopped steak, stew beef, chicken, turkey, ham or pretty much any other lumps of dead animal will work)
  • Fatty meat. (I used ground pork but sausage or [[suet|suet]] will work and many prefer the arguably more traditional suet)
  • Salt & pepper

Optional ingredients:

  • Lamb instead of or mixed with the beef
  • Beef stock (helps stick it together, adds salt and a little flavour)
  • Celery (leave the leaves on)
  • Parsley
  • Mushrooms
  • Most anything else that might be tasty. A little rosemary can go very well for instance.

Ratios are very flexible. Use suet instead of the pork if you want a more traditional (and tastier) pastie. I used roughly two parts beef to one part pork to five parts potatoes to two parts rutabega and one part celery. Next time I’ll probably decrease the total meat proportion as I’m a little tired of meat-heavy/centric meals. I might also throw in a few other vegetables like turnips or cabbage or anything else I can think of just for variation (ObNote: carrots are traditionally verboten).

Precision is not important in the world of pasties — variation is the spice of life. Chop or cube the vegetables. Don’t worry about keeping it small, just whack them about a bit with a knife. Mix everything except the dough into a gooey mass. Salt, pepper and other spices to taste. Parsley is good. Don’t bother with keeping the mix even as distribution variations are tasty. Roll the dough out into circles around 30cm or so in diameter (precision is not important), or use pie dough that has already been formed into circles. Don’t roll the dough too thin; 3mm or so is fine. The dough needs to be thick enough to solidly hold the final contents. Dump of big glob of goo-mix near the centre of a dough circle and fold it over to make a half-circle with the lump in the middle. Thickly fold over and crimp the edges. If needed (depends on the dough), brush the edges before and after with water or butter/lard to make them stick together better. Prick the top in several places to allow steam to escape. Bake for around an hour at around 180C (350F).

Pasties can be made very quickly. 30 minutes from ingredients to oven is reasonable. A quick google search will return scores of variations on the above base. Some of the vegetarian curry pasties are especially good.

Eat hot or cold. Some like them plain or with catsup or hot sauce; it is all good. Eat by hand like a slice of watermelon, holding onto the thick crimped edge and eating out the filled centre. I made a bunch on Sunday evening and ate them all week for lunch. They were great.

Winsome Games’ 2008 Essen Collection — Order Line

THE ORDER LINE IS NOW CLOSED.

John Bohrer has kindly consented to allow me to act as a broker for this year’s Winsome Games’ Essen Collection. The 2008 Essen Collection is only available as a set of 4 game titles. The games cannot be ordered individually. Quoting Winsome Game’s release materials:

  1. Eddie Robin’s “Gulf, Mobile & Ohio” is an innovative new boardgame with no luck factor. This game takes place in the Southern US 1830-1850 where many small and large railroads sprang up, starting in 1830. Players charter railroads, build track, sell common stock and vie for connections in cities with other railroads. This game is for 3-5 players for about 1 hour.

  2. Harry Wu’s “Preußische Ostbahn” introduces an innovative new Player Order mechanism. Preußische Ostbahn is set in old Germany, 1840-1870. Eight historic Railroads create the network that bound the Germanies together. Each has a special characteristic, based upon its history. This game is for 3-5 players for about 90 minutes.

  3. The Age of Steam: Texas, Oklahoma & New Mexico Expansion happens in the Wild West. This expansion introduces two new Actions: Ranching and Cattle Drive and it also includes 32 Cattle cubes. The expansion is for 3-6 players, for about 2 hours.

  4. Harry Wu’s Wabash Cannonball: Erie Railroad expansion adds another railroad to Harry’s original Wabash Cannonball game. The Erie Railroad had an important influence in the history of this period of American railroad expansion. The expansion uses the base Wabash Cannonball game and allows the same number of players; it takes about the same time as the base game, maybe a few minutes longer.

If you are local to San Jose California and can collect the game directly from me, please use the following payment button to order the 2008 Essen Collection (US$130 + $5 S&H):

If you are elsewhere in the continental USA or Canada, please select the following payment button to order the 2008 Essen Collection (US$130 + US$15 S&H):

For buyers in the rest of the world, please select the following payment button to order the 2008 Essen Collection (US$130 + US$25 S&H):

I only have access to 100 copies, total. It is likely they will sell out quickly. If you are going to order 3 or more copies and would like to save on S&H, please place multiple orders above and then contact me on BoardGameGeek (user: clearclaw) or via email at my PayPal account address so that I may calculate the correct S&H for you and refund the difference.

The games will be packed and shipped by the most economical methods available. Orders for foreign countries with known package/postal problems will be heavily taped. Customs forms will identify the contents as media. Please be aware that the clamshell polystyrene cases may be damaged in shipping. This is a risk of the economical shipping method used. I will be shipping the games in a padded envelope but some postal services can be surprisingly rough. Shipping in a more protective box would more than double the S&H costs and due to lack of interest in previous brokered orders, is not available for this collection. I will have a small number of replacement cases available for shipping damages. I will receive and ship the games some time after the Essen trade fair in October. Estimated shipping time from here to your door is 7-10 days within the continental USA and 2-3 weeks for international addresses. Progress and updates for the group order will be made as comments to this post. Please subscribe to the RSS feed linked in the bar to the right if you’d like to keep up to date.

THE ORDER LINE IS NOW CLOSED.

Recycled whirlpools

A thought model; just a skein of partial ideas to consider hanging a game from:

External markets phase

  • A graph, nodes connected by edges. Some nodes are identified as (potential) start nodes.
  • Nodes bear a die indicating the current market demand at that node. cf The future market die (central collumn) in Lokomotive Werks
    • The die or node may be coloured to indicate a specific transport type (passenger, freight etc)
  • Players may claim edges between start nodes and other nodes, or between nodes already connected and other nodes (connected or unconnected). In this manner the network grows and becomes incestuous
    • Possibly an auction of the nominated edge?
    • cf Dutch Intercity’s blind-bid edge within a very small graph
    • The Riding Series method of rotation auctions until at least one player has spent all their cash and all players have auctioned at least once may be interesting
    • Ordering by cash holdings, or inverse, may also be interesting. cf The Riding Series and Lokomotive Werks for value considerations
    • Possibly there are limitations on contiguous networks, costs for non-contiguous networks etc.
    • Should claimed edges be coloured by player and if so, what is the value?
  • By claiming a connection a player has acquired commits them to supply transport in that volume in N-turns (N = 3?)
    • The auction for the edge sets the price for that product-type ($/volume) and this is tracked/recorded
    • Future auctions produce new values, also tracked
    • Minimum bids may be set as a function of projected values from this history
  • As additional edges are claimed new markets enter the game with their own demands for volume
    • Represented by a new “line” of dice for that node, possibly in a different colour or a higher value of a current colour
    • Thus a thriving market for one sort of transport (eg freight) prompts a market for passengers etc etc and so forth (yay theme)
  • In a later phase players may sell the futures among each other
    • Again an auction, modifies the tracked price?

Production phase

  • Effectively Lokomotive Werks redressed
    • D4s? — lower variance
    • Number of dice in future orders column equal to total of all dice-values on nodes connected by claimed edges
  • Building new factories unchanged.
  • Building capacity unchanged
  • Players don’t claim dice, they auction them (and receive the money personally)
    • What is auctioned is a commitment to supply Q product of that type in N turned (N=3?)

Future fulfilment

  • The current turn’s contracts are resolved
  • Each buy must be matched with sells of the same type etc.
    • Open negotiation?
  • Unmatched buys are satisfied by the hidden market which operates at a cost of X% of a function of the tracked market prices and those funds are covered by the players
  • Unmatched sells force the market price down and penalise the holding player by n% of the then market value?
    • Simply losing the future may be enough penalty
  • What is resolution order of what buys and sells are matched and in what order?
  • Monies are paid from the bank to players holding satisfied buy futures (they ship the goods?)

Market maintenance phase

  • Each dice line on a node grows or shrinks by one die Lokomotive Werks-style
    • Possibly this is a global function across all nodes, a local function/property of the node, or a mix of both
    • Possibly a function of the properties/types of lines in neighbouring nodes (reflective/communicative/memetic markets)?
    • The dice are rolled, establishing total orders within the period (may be less or more than total futures)
  • Each player in rotation claims either auctions a die at a currently connected node (assumes uncoloured edges?), or auctions a new/additional edge
    • A new edge may connect a new node, in which case they automatically get that die/contract, or if between already-connected nodes, may affect market maturation patterns in those nodes (see above)
    • Not clear what auction value an edge between connected nodes has?
  • Limit to total growth of dice lines on nodes?

A fractured thought model to be sure, plangent and struck through with gaping flaws.

Returning to the future

After some odd thoughts about how the network growth potentials of ‘Ohana Proa could be mapped as a pseudo-futures market, i’ve been thinking about representing futures in games quite a bit lately and I’m having a really hard time of it.

The simplest way to present a future seems to be as a pair of contracts:

  1. The agreement to sell at time X for price Y
  2. The agreement to buy at time Q for price R

The two are of course reciprocals. There are more complex forms of futures, but they are just that, more complex. The basic form would have PlayerA selling a contract to PlayerB, PlayerB giving PlayerA money in return for the guaranteed market (to buy or sell). The complexity is that PlayerB has to have the money now to buy the contract, and depending on the type of the contract, will also either have to have the trade goods or the money to satisfy the contract when it comes due. The primary justification for futures is to guarantee both the pricing and the existence of the marketplace into the future against the vagaries of market dynamics. Thus a wheat producer can not only set his effective price for next year’s tonnage now, but can also guarantee that there is in fact a market to sell his wheat next year. A wheat buyer can do likewise, protecting themselves against price spikes due to bad weather and a reduced crop (for instance). But you know all this — I repeat myself, re-tracing the pattern in hope that repetition reveals something new and useful.

The challenge is to (literally?) transcribe this into a game. There must be risks sufficiently large that the inefficiencies of futures are worth it. The range of extent of the risks must also be knowable (supply may be high or low, prices may be high or low, demand may be high or low). Additionally, if a futures market is to be represented, the actual trade of futures and the tracking of futures prices as a discrete market entities, then fulfilment must be sufficiently postponed that the value of the future has the opportunity for multiple significant changes and can be reasonably traded multiple times.

This suggests a future length of between 3 and 5 rounds1. The future would be sold and there would then be 3-5 rounds of market evolutions and potential trading of a given future before it matures and is fulfilled. A good rule-of-thumb is that a game has 7-10 rounds, with each player making at least one strategically significant evolution per round. 7-10 rounds gives sufficient time for player investments to mature, carrying player commitment and value, and for game arc to develop. Given that futures must have a maturation time of 3-5 rounds and assuming that all the maturation periods will stack as densely as possible, that means a game duration of 10-15 rounds.

This of course assumes that the players start the game with positions which require the sort of risk abeyance that futures provide: another problem to resolve. But, so far so good. The remaining problems are to establish the risks and the market variance controls which can express reasonably in 10-15 rounds.

The future definition could also be simplified to :

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

In essence the transaction occurs now except the fulfilment, the actual movement of goods, happens later. The pattern is similar to the mail order market model (given guaranteed delivery times) except that fulfilment is delayed by more than the postal system2. This is almost the same kettle of fish except that all the capital is required up front for the purchaser to abey the risks.

If the simplified model is combined with a loans/temporary-liquidity system 3 it becomes remarkably similar to the more classical and complex split contract/fulfilment/payment futures model.

Now for the risk system, and this is where I’m running dry.

The system needs a market with the following properties:

  1. High potential price variance
  2. Increasingly difficult to predict the longer the prediction (early-, mid- or late-game), not exponentially, but probably worse than linearly
  3. Reasonably predictable market volume demands

That last is a doozie. If I simulate supply and demand then either the supply and demand is highly unpredictable, or there is another large random factor in addition to supply and demand which affects market prices. One appealing possibility is using Lokomotive Werks’ novel dice-based market system, as it does provide a highly dynamic market with high variance supply and demand relationships4.

Positing Modern Mogul as an extrapolation of Lokomotive Werks is appealing as Lokomotive Werks is a fine game (review). Lokomotive Werks internally simulates the demand side through a combination of the number of dice rolled (which is a function of competition), the values that are rolled on those dice and the individual player’s turn order but leaves the supply side for players to construct. Somehow this needs to be split so that players can occupy both the supply and demand sides of the equation.

Demands are supplies for the next stemp in the consumption pipeline. What if there were the equivalent of two Lokomotive Werk’s tracks, one of factories for production (much like the current game) and the other with second stage demand? Thus, keeping with the train/transport themeing, one system would generate erratically growing sequences of transport demands (passenger, livestock, freight, etc), perhaps using a very similar system to Lokomotive Werks, which the players would then attempt to fulfil by representing back to the train production market as demands in some value distribution. Thus on the one hand players would attempt to gauge their position against the variations in transport demand, and by reflection from that, against the variance in production vehicle demand.

Much as I like perfect and certain information games, the use of dice (as a stand-in for any random system) seems suitable. here. The requirement is to create a high-risk difficult to predict system. A random system obviously does that and has the advantage that the range and distribution can be relatively precisely tailored. Building the system from player-interactions is likely possible but seems a difficult butterfly effect challenge and runs the risk of being fragile/crackable.

Hurm. Back-to-back Lokomotive Werk’s-like systems with a full futures market (time-based contracts to buy-and sell, plus dynamic price tracking). This needs musing on.

Harrumph. I started writing this post indending to explain how impossible it was to reasonably represent a futures market in a game and I had a stack of good solid (swiss-cheese) reasons in-hand. However, as hoped, as I assembled and articulated the reasons they built something else.

Footnotes
  1. A round being defined as a well bounded set of player actions and decisions sufficient to cause a significant strategic position change for each player
  2. I’m purposefully going to ignore delivery location.
  3. cf Container or Wealth of Nations
  4. This is rather cute, as Lokomotive Werks effectively implies a futures market for the trains the players build while never actually implementing any portion of that market!

1 winner and the rest of you losers

Matthew Marquand has been following the boardgame T-shirt racket for a while, most recently with Uberbadger. I went so far as to propose a shirt:

I would like a shirt with a graphic something akin to a large digit ‘1’ above the word “winner”, and the words “and the rest of you losers” written in a circle about that.

A rapid exchange with Matthew lead to the following sequence of designs:

pic345555.jpg pic345704.jpg pic345724.jpg pic346152.jpg

Plus an external suggestion from Chad Krizan of:

pic345814_md.jpg

A quick conversation with Ariel Seoane (Seo) on BGDF’s chat then lead to these suggestions:

JC_t-shirt.jpg JC_t-shirt_2.jpg JC_t-shirt_2a.jpg

Variously capitalising on suggesting a poker chip or classical smilie face model. BTW: The typo is known — the image is a quick sketch, not a final product.

The question is now which image is more interesting to buyers?

Bitticus

Seth Jaffee has made images for the tokens in Ohana Proa and graciously allowed me to make them generally available.

Reflections on an atoll

In a recent comment Ben Keightly argued that Ohana Proa both is and should be a resource management game, and to an extent he’s right. And wrong — well, if not-what-I-want can be accounted as incorrect then he’s wrong. Ultimately all games are resource management games: players have a variety of fungible resources, abilities and opportunities to exercise them during the game and the player that manages the use of their resources, abilities (really just another resource) and opportunities (yet another resource) most effectively will (should) win. Ergo all games are resource management games and it is thus a uselessly global and tautological definition.

At a lower and more useful altitude I define resource management games as games in which the resources in question are (generally) enumerable, limited, and usually highly granular. At heart resource management games are exercises in scarcity. At a crude character level players must mete and dole and shave their pennies while still accomplishing the victory conditions. However, that’s not my interest or goal for Ohana Proa. I’m not interested in Ohana Proa being a game of managing scarcity, rather it is intended to be (and is) a game of [[jocund|jocund]] excess. The resources I’m interested in players managing are not discrete enumerable elements of fish and shells and VPs and kula, but of opportunities and mutual player (dis)incentives and posture. Any reasonable player in Ohana Proa will have more fish and shells and kula etc than they necessarily know what to do with, they are going to be fundamentally rich and they are going to stay rich if they pay even marginal attention.1

Being rich is not the problem. Spending the wealth is not the problem (there’s always the turn order auction for that). The problem is simple: prestige. To get prestige the players must individually create and sustain situations in which the other players consistently give them disproportionately more than they give each other. It really is that simple. You have, more or less, all the wealth of the world, you are rich, but there’s a strict protocol for prestige-generating gifts and you need to manipulate the system so that you get to give more, more efficiently, than the other players. There’s a big machinery behind that prestige-giving protocol. There’s routes and auctions and fish and shells and kula and rot and a whole mess of details, all of which, Ben is quite right here, are almost busywork details.

There’s a common (and false) stereotype of rich people’s visiting gifts being things like a small pot of hand-made jam or the like (recently reiterated in Six Degrees of Separation, a wonderful movie BTW). Ohana Proa perpetuates this sorry model except that now the players have to grow their own berries, pick their own fruit (for themselves or each other), boil their own mixtures and in general go through a whole big and somewhat extraneous ritual just to get the little jar of hand-made jam to give their friends when they visit. But they have lots of friends and managing (there’s that word again) both the production pipeline of jam (kula) and the rate of opportunities to deliver (density of deliveries to islands connected by multiple players) as a set is difficult and the heart of the game.

Ahh, so there are resources to manage: the kula production pipeline and deliveries to multiply connected islands! Too true! Those are the primary resource challenges of the game, which makes it kinda sorta a resource management game except that the primary resources are:

  1. Opportunities to make deliveries to islands which are connected by multiple other players
  2. Network meshes that generate sufficient resource flow to afford those opportunities

And those things are not generally enumerable, particularly limited (scarce) or granular. They are more akin to diffusive field effects. Yeah, at a grand-level it is all busywork. All the little fish and shell etc stuff is noise, but it is important noise. It is busywork that builds the stuff that starts the multi-step inferential pipeline that establishes the incentives for the players to emergently create those opportunities and network-properties for your personal victory.

Quoting Ben again:

The way markets and kahunas interacted with the network is so interesting. It reminded me very strongly of the illustrations you sometimes see depicting gravity, with large planets sagging the 2D space-time grid. The way these interactions worked was clear as day. Unfortunately we were watching them happen from behind a pane of glass, and not consciously participating in the process.

Again, he’s right. My challenge is to diffusively but yet tangibly connect the players with that rubber sheet. I think, hope, that the recent rules changes, especially finishing splitting kula and damping the effect of kahuna will help make that diffuse connection more tangible.

Footnotes
  1. The concept of continual affluence is, in part, a deliberate swimming-upstream against the flood of managing-scarcity games. There are a great many games which manage scarcity in variously interesting ways. I don’t know of any other games which require the players to manage largesse without also drowning them in micro-management.

Decomposing: Wealth of Nations

The original content of this article was posted on here on BoardGameGeek and in the resulting thread.

After 5 plays and observing about a half-dozen more games we’re now mostly convinced that the game in Wealth of Nations is mostly absent. More simply it is grossly under-developed. The thought process runs something as follows.

Players will either take loans or not in the first round. If they don’t and another player does, the loan taking players benefit significantly from the lower market prices and extra operational time for their buildings. Ergo, players should automatically take loans to maximise their building. There’s simply no choice here.

If all players take loans, then the question becomes how many loans? In yesterday’s game but for a small artifact of placement the game could have ended in the fourth round. In that case I would have come second by a few points due to my unpaid loans. As the game ran longer my banks were able to pay for themselves and more. Thus taking quite as many loans as I did had some risk. I took 11 loans. 8 or so loans however would have been completely risk-free (and has been risk-free in prior games). I’m not about to define what that number should be, but clearly a reasonable number could be picked.

Why not then just start all players with 8 loans or their equivalent? Why bother having each player go through the rigamarole of taking loans and calculating prices and sequencing etc? There’s really no actual point to the loan taking process in the first Round in Wealth of Nations. It is automatic — they can’t afford to NOT take loans. Just start every player off with 10 or so loans and their equivalent in cash.

Similarly the cube-buying process in the first round is also almost perfectly scripted. There are only a few cube-based directions to head in and several of them are near identical. Why not simply gut the first trading round, start the players with say 8 loans, no cash and increase the money/cube draught pools correspondingly? That would easily cut almost an hour from the game and lose almost nothing in the way of interesting game decisions.

The markets almost work. Yeah there are efficiencies of scale and there is a modestly interesting under-/over-served-market pattern but it is shallow. Trading is again near automatic. Each player will have cubes they want, cubes they don’t want and a cube set they want to enter the Development phase with. Turning unwanted cubes plus cash plus loans into wanted cubes is purely mechanical and near decision-free. Almost any trade which moves them toward their desired cube-set should be rotely accepted. The only significant decision point is time ordering the trades based on opportunity cost against other desired trades. Very rarely there’s a decision about giving a specific player N-colour cubes at a cheaper trade cost or forcing them to buy at market cost, but those decisions are marginal as the penalty for them buying from the market is also marginal and they’re just going to get those cubes anyway.

In short the economic game seems like it is there, but the more I look at it the less and less there is actually there. Yeah, it seems muscular and aggressive and difficult and so forth and I have no doubt that non-analytical players can have a great time there. However once you catch on to the efficiencies that the game is built on, all the economy questions/decisions fall out to the simple: I want to build XYZ tiles, buy/trade for those cubes efficiently. Worse, the penalties for inefficiency (loans) are minor at worst — the odd dollar here and there really doesn’t matter that much. The value-differential of electively trading with players versus the bank/market is simply too small. Yeah, trading with player is more efficient, but the penalty of not-trading is marginal as versus say Settler of Catan’s or Bohnanza’s much steeper cliff providing both an interesting incentive and safety catch.

What’s left that is actually interesting is the board play: the tesselation patterns of the tiles, the control of area, the fight for space, the control of placement cost, etc. There’s actually a modestly interesting game there. I have a particular fondness for such games and am possibly rather good at them and that skill combined with my aggressive play-style has aided my success. However that interesting geometrical game is surrounded by a huge umbra of economy management which pretty much boils down to busy work.

Another problem, and I’ll discuss this more elsewhere/elsewhen, is the lack of butterfly effect in the game. The only significant source of variance is the draught and the initial tile placement locations. Outside of the geometry I really don’t see much interesting here. Oh, it is certainly possible during the initial tile placement phase to elect a player to lose the game, and I’ve done that and it can be modestly interesting for you if not for them, but that’s about it.

My other suspicion is that the game is mostly decided by the end of the first Development phase, outside of teleporting tile effects. In my last three games I’ve managed to secure the area and resources on the first turn to effectively guarantee my eventual success. 4 player games and teleporting tiles. Both those caveats are large. I see no reason to think that the game is nearly so deterministic with 5 players and see considerable reason to think that the spatial aspects in 5 player games will be much more interesting. The question is then whether that geometry game is sufficiently interesting to support the needless economic burden.

Update: After further thought this game-determination is bound fairly tightly to turn order. There is a severe advantage to placing later in the turn order in a 4 player game with 3rd probably being the sweetspot, as they (largely) get to control where the 4th player places. This, combined with the already present double-tile-set for the 3rd and 4th players in a 4 player game, is an impressive turn-order advantage.

I’m going to give up on 4 player games of Wealth of Nations except as teaching exercises. I’m not sure the game can be rescued with that player count without gross surgery. If I were to house rule the 4 player game I’d probably consider removing the black tile set from the draught and replacing it with another money/cube permutation set. I might also remove the second yellow tile set and sweeten the remaining yellow tileset with cubes/money. The first of or both of those changes should resolve a bit of the gross predictability of the 4 player game.

I will be pursuing 5 player games over the next weeks (we’ve played 4 four player games of WoN in a couple weeks, getting a few more 5 player games in shouldn’t be too hard). I’ll report back on my conclusions with that player count after that.

ObNote: The above comments are mostly specific to the 4 player game. I have yet to play with 5. Many of the points visibly remain with 5 players (loans, money, markets, cubes etc) but the decisions around board/area control and the choice and placement of each player’s second industry are clearly more subtle than they are in 4 player games.

Curmudgeon rescinds generosity

New rules.

New player aid.

The really short version is that my response to recent playtester feedback was overly generous and enthusiastic. The correct response is more conservative and curmudgeonly. I’m keeping the response to Slow Start, albeit slightly muted. That’s fine and even admirable. Automatic proa upgrades is not such a good idea. I considered that model extensively in the early development of the game and threw it out then, which I then forgot more recently. The game needs an additional drain on fish/shells for the first few rounds while the players build their networks. The drain doesn’t have to be big, but it has to be non-negligible. This prevents a too-early and crippling kula rush before the route-network can support it. I tossed out the ability to cash in kula for VPs immediately upon receipt as it destabilised the kula and VP markets in oddly feed-back-prone ways. The split kula remains as a fine way of maintaining off-turn player involvement while also adding pleasantly collusive elements, but the prestige and VP allocation is heavily adjusted with an eye to reducing the total number of manual transactions per turn and per gift.

Note: The kula/prestige/VP values are not final — I’ve not quite finished running models.

I also threw out the redundant About Fish & Shells section of the rules, which saved half a page. The only original material there was the statement that VPs could be discarded for fish and shells, which has been moved further up the document.

In summary two changes remain in the offing:

  1. Adjusting kula/prestige/VP values
  2. Pull in the end-game prestige line a bit (~27?) while also shortening the prestige multiplier brackets.

When in doubt, sink the battleship

Kublacon saw another Ohana Proa playtest with a response ranging from I want to play this again, I want to play it on Monday, bring it with you on Monday! to This is good but these bits need fixing. Happily all the complaints aligned with the extant problem list. Against my better and more generous nature the current idea is to make the following sweeping changes. They analyse Okay but I’m not sure I like the resulting picture, but suspect parental bonding for this latter.

  1. Tone down kahuna:
    • 1.5x production rather than 2x.
    • When a market is delivered to an island over a player’s route that also has a kahuna on that island, the kahuna-owning player earns VPs for the delivery in addition to the moving player. This may allow VP doubling for one’s own kahuna. not sure yet (ie the models haven’t finished running)
    • Building a kahuna once both have been built teleports one of the pre-existent kahuna to the new location
  2. Rejigger kula:
    • Rework all cost relations
    • Kula do not reward VPs upon receipt, but may be immediately discarded upon receipt for VPs or fish & shells
  3. Gut proas.. Players proas increase by one every turn unless their proas are already larger than the turn count. Automatic proa increase may be refused in return for resources and players may buy ahead for standard cost. If they buy-ahead then the next free proa doesn’t affect them. This is a standard tide-that-floats-all-boats

The most interesting change here is gutting the proas. Automatic increment removes a primary concern from the game, but also adds a potentially interesting decision without affecting any of the other base structures of the game: buy ahead for this-turn advantage or hang back for this-turn resource advantage? Removal of VPs from kula receipt is a little less interesting as the primary effect is to make kula dumping (stale kula gifts to players earlier in the turn order in the second delivery round) less significant. The second order effect of adding a thin kula management layer to the kula dumpee is mostly uninteresting.

New rules and player aids are on the slip.

Updated: Pampas Railroads income/action/valuation/etc chart

I’ve updated the income/action/etc sheets I posted a while back to version 1.3 to correct the mis-labelling of the action tracks and a few other typoes. Thanks go to James Ludlow (jdludlow) and Mark Hamzy (hamzy) for catching the errors — predictably I’ve yet to be able to play with my own aid! I also posted the files to BoardGameGeek in the Pampas Railroads area as version 1.3, but they are pending approval. Meanwhile the PDF and PNG versions may be found in the normal place.

Compressed freckled waves

A productive evening:

  • Put in a double switchback exploration round for the start
  • All players start with 2 explorers and 2 proas (need more resources too! forgot that)
  • Advanced Game has been made default, Beginner’s Game added for the kahuna-less game
  • Reciprocal kula implemented.
  • First pass at new kula value/pricing done

So far the models look Okay, but I’ll probably need to adjust the Prestige Track end-point upward a bit to 37, 39 or 42 or so.

The new kula language:

There are (blue) fish and (red) shell kula items, each available in two values. Small value kula items may be enhanced to larger value kula items.

Kula token costs:

(Table here of values. In short, fish kula are 3 or 7 VPs, shell kula are 5 or 11 VPs and costs are 7 or 5 resources for low value kula (basic/beginner’s game), 17 resources for big kula, and 11 for upgrades.)

Players may only spend resources on kula if that kula item is immediately given to another player as part of a delivery (see Deliver). Enhancing a stale kula item (face down) to a larger value creates a higher value stale kula item (face down).

When a market is delivered to an island containing a market of the same colour, the moving player may give a kula item to each player with a route connected to the destination island. The kula item given may be newly purchased with fish and shells, or may be an item previously received from another player (optionally enhanced). The gifting player receives all the following:

  • 1 point on the Prestige Track for giving the kula item
  • 1 point on the Prestige Track if it was a large kula item
  • 1 point on the Prestige Track if the kula item was just bought with fish and shells for this gift
  • 1 point on the Prestige Track if giving the kula item to a player with a kahuna on the destination island

The player receiving the kula item receives half the value of the kula item as victory points rounded down, or full value if their kahuna was present on the destination island. They also receive one victory point for each kula item they already possess.

Upon receipt of a kula item, the recipient may immediately give a kula of the opposite type in return to the giver and may spend fish and shells to buy a kula for this purpose. In this case the player reciprocally giving the kula receives:

  • 1 point on the Prestige Track for giving the kula item
  • 1 point on the Prestige Track if their gift was more valuable than the gift they were given
  • 1 point on the Prestige Track if the kula item was just bought with fish and shells for this gift
  • 1 point on the Prestige Track if giving the kula item to a player with a kahuna on the destination island

and the new recipient receives:

  • 1 point on the Prestige Track for receiving a kula in response to their gift
  • 1 point on the Prestige Track if it was a large kula item
  • half the value of the kula item as victory points rounded down, or full value if their kahuna was present on the destination island

At the end of each turn old face down kula items are discarded back to the supply and new kula items rot and are turned face down (see Rot).

Crushed origami cuts

  • Dividends are always truncated (this got lost somewhere).
  • The moving company always merges away and pays the special dividend
  • Clarified already-connected merger case
  • Double builds are only available to the clear plurality share holder
  • Clarified mergers and new shares
  • Removed the artistic extra dividend markers from the map
  • Added income markers to the manifest
  • Simplified London development to must always be the most valuable city
  • Reduced double development cost to $3
  • Cleaned up language in definitions
  • Extended setup section to be more explicit
  • Clarified that inactive company treasuries are not paid to shareholders
  • Simplified and clarified game ending language
  • Clarified that build expenses are always paid from company treasuries
  • Clarified port expenses
  • Added Dieter Danziger and Lokomotive Werks as inspirational
  • etc

A few things I like here:

  • The forced directionality plus the limitation on double builds of mergers makes poaching a bir more constrained and I think interesting. It also makes foreign ports a little more interesting as well as posing the nominal director’s interests in opposition with the minor shareholders.
  • The simplified London value ruling makes London far touchier in the early game, triggering an explosion of development if it is developed. Nice.
  • Inactive treasuries not paying out makes the first share of a secondary company pleasantly risky and asymmetric