Benefiting from Board Games

November 5, 2012

Playing the Ticket to Ride board game

I’m a big fan of board games, especially the newer German-style board games, which are far superior to the games of my youth. This book argues the benefit of modern board games for learning and teaching, highlighting some of my favourites.

Board games are more than just entertainment. According to a press release, a lecturer at the University of Tennessee has won an award for using the Ticket to Ride board game to teach operations research to students. This makes good sense, since German-style board games tend to involve complex optimisation decisions.


Some Dominion cards (photo: Shannon Prickett)

Consider a massively simplified version of the enjoyable game of Dominion, for example. There are six kinds of card: copper money (costs $0, worth $1), silver money (costs $3, worth $2), gold money (costs $6, worth $3), estates (cost $2, worth 1 point), duchies (cost $5, worth 3 points), and provinces (cost $8, worth 6 points). The real game has many other interesting cards, but even this simple parody is non-trivial.

At each turn, the player draws a hand of five cards (from a deck of initially ten), purchases a new card, and discards the hand. When the deck is empty, the discard pile is shuffled to form a new deck, so each purchased card will be “used” multiple times (which is why it’s sensible to spend $6 on a gold card worth $3). However, only the green cards are worth points – as with many German-style games, the money does not directly contribute to winning the game. On the other hand, purchasing many green cards reduces the chance of a five-card hand containing much money.

One strategy is to only purchase money or the valuable province cards. A simple simulation of the game shows that, after 50 turns, this results in an average score of 112 points. In contrast, a strategy of preferring to buy green cards gives an average score of only 39. However, “switching” from one strategy to the other does best of all, with an average score of 128 when the “switch” is made at turn 35 (and an average score of at least 120 when the “switch” is made somewhere between turns 25 and 45). In other words, winning requires optimising when the strategic “switch” is made.


Average scores, as a function of when the strategic “switch” is made. Switching at turn 35 is best.

For full-blown German-style games, the optimisation problems are more difficult. As this podcast argues, they are often in the difficult class of problem called NP-complete. These are hard enough to challenge both a human and a computer.

As I’ve said before, I also have a long-standing interest in collaborative board games, such as Arkham Horror, Pandemic, and Lord of the Rings (for fans of Arkham Horror, here is one of my custom characters, with back story and marker). Collaborative board games offer an excellent way of both exploring and teaching teamwork, and a 2006 paper by José Zagal and others explores Lord of the Rings in this context.


Reiner Knizia’s Lord of the Rings collaborative board game

Good board games generate the level of engagement that makes wargaming work. When the team is attempting to solve a difficult optimisation or decision problem (as in SCUDHunt), things can get very interesting indeed.

– Tony

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(Religion) Lost in Space

September 24, 2012
Luna 9 :*Denomination: 2 Forint

Luna 9 :*Denomination: 2 Forint (Photo credit: Wikipedia)

The concept that any future interstellar exploration be free of organised religion has recently been discussed.  Some have expressed the view that religion is toxic for human interaction and cooperation as is evidenced in many unsavoury incidents throughout history and is currently being witnessed with respect to the YouTube video denigrating the prophet Mohammed and subsequent reaction to it.

Humans have many attributes which may be positive or negative depending on the context.  Adaptability and imagination are very valuable human abilities, but these skills are not required nor perhaps desirable in a situation that requires heuristic thinking.  Conversely, applying a flawed or inappropriate heuristic can have disastrous consequences, or prevent a more appropriate paradigm from being developed.

A human will always be influenced in how they act and think by their prior experience. Even the application of the scientific method cannot eliminate these influences. The ability to assess complex data for example can be affected by education, training, aptitude and a host of other factors, which can vary according to the information being assessed.  It probably explains the range of specialities within a discipline, for example, in medicine, physics, chemistry, engineering and psychology.  With regard to future space exploration, the various TV program depictions such as Star Trek portray a range of specialists in the crew, making the assumption that all of these skills will be required to fully comprehend the magnitude and complexity of space.

Given that previous experience or belief systems are an inherent part of the human condition, it seems logical that a religious aspect will also then be represented within the crew of any intergalactic mission if it is to be truly representative of the human species.  And as bigoted or fundamentalist religious views are by definition extreme values within a normal population, it is highly unlikely that these would be represented to any significant statistical level.

With regard to positive and negative attributes, religion has been blamed for many ills, many of which can be justified.  However, religion should also be recognised for its many positive aspects, such as altruistic value systems, beneficence, the intrinsic value of individuals regardless of race, social standing or wealth, the existence and importance of a fundamental natural order and the concept of stewardship and responsible use of resources that then derive from it. Many advances in science were made possible by the religious systems of the time, such as astronomy and mathematics, although some of the authorities subsequently disputed the findings for whatever reason.  Is it so different to what is currently occurring where the evidence supporting climate change is disputed by certain sections within a secular society without any obvious underlying religious philosophical rationale?  It seems that belief systems generally, not just religious ones, are the root cause of disagreement.  This can be beneficial in the search for scientific truth and the progression of understanding – perhaps conflict is a positive human attribute as long as it is confined within an intellectual framework.So the discussion regarding the crew mix for future space exploration missions should expand to include all human experience and belief systems.  Perhaps religion can help unlock the mysteries of the human mind and the continuing quest of the species to explore and understand the universe.  All of which relates back to human science.


Games and teamwork

August 16, 2012
I Had Trouble in Getting to Solla Sollew

I Had Trouble in Getting to Solla Sollew (book cover)

One of my favourite children’s books is I Had Trouble in Getting to Solla Sollew by the great Dr Seuss. It contains that wonderful description of teamwork:

… ‘This is called teamwork. I furnish the brains.
You furnish the muscles, the aches, and the pains.
I’ll pick the best roads, tell you just where to go.
And we’ll find a good doctor more quickly, you know.’
Then he sat and he worked with his brain and his tongue
And he bossed me around just because I was young.
He told me go left. Then he told me go right.
And that’s what he told me all day and all night.

Is that really teamwork, though? There are requirements on true teamwork, and these requirements include processes that are (at least to some degree) democratic. But apart from that, what does a good team really look like?

In a 2006 paper in Simulation & Gaming, José P. Zagal, Jochen Rick, and Idris Hsi explore Reiner Knizia’s “Lord of the Rings” board game, in which a team of up to five people play the roles of hobbits intent on destroying Sauron’s ring.


Reiner Knizia’s “Lord of the Rings” board game

Zagal et al. find that this collaborative board game models four aspects of more realistic teams:

  1. There is a genuine tension between perceived individual utility and team utility.
  2. Players may, if they wish, take actions which go against group consensus.
  3. Players are able to trace outcomes (good or bad) back to player decisions.
  4. Players have varying strengths and weaknesses in the context of the game.

These characteristics make the “Lord of the Rings” board game, and similar collaborative board games, fascinating tools for exploring teamwork at its best (or at its worst), and for exploring strategies for improving team effectiveness. And they’re fun, too!

– Tony