Calling the Race

November 15, 2012

The big winner from the US Presidential election has been Nate Silver and his 538 blog. On the eve of the election, Silver had calculated the following probabilities from polling data:

Silver also has a fascinating analysis of which polls were accurate, and which weren’t. In particular, polls based on calling landline telephones tended to seriously underestimate the Democrat vote. Voters without landlines are more likely to be young, urban, Black, Hispanic, strapped for cash, or some combination of the five, and all five categories are more likely to vote Democrat. There are lessons here for pollsters in other countries.

The following simple NetLogo simulation model (click on the image to run it) re-rolls Silver’s electoral dice, giving alternative outcomes – exactly the kind of simulation Silver actually did to support his 90% prediction of an Obama win:

Silver appears to take a Bayesian approach to statistics. A Bayesian has been described as “one who, vaguely expecting a horse, and catching a glimpse of a donkey, strongly believes he has seen a mule.” The legendary XKCD summarises the perspective quite elegantly:

– Tony

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