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Review of Power-Up by Matthew Lane

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Title: Power-Up

Author: Matthew Lane

Publisher: Princeton University Press

Copyright: 2017

ISBN13: 978-0-691-16151-8

Length: 264

Price: $29.95

Rating: 94%

I purchased a copy of this book for personal use.

I enjoy creative takes on technical subjects that reveal the mechanics behind familar objects. Video games provide hours of entertainment and challenge. Beyond the need for attractive graphics and effective user interfaces, each game designer must decide how to award points, measure the effect of player choices within the game, and provide a balanced environment that maintains game play without sacrificing challenge. In Power-Up: Unlocking the Hidden Mathematics in Video Games, Matthew Lane describes how math enters into video game design. His book is an enjoyable read that taught me a lot about the math behind game design.

From Physics to Friendship

It would be difficult to find an example of a video game that doesn’t use math in some way. Some games allow exploration without awarding points, for example, but the player must still move around the game world to discover what’s next and every new discovery is an implied “score”. As Lane notes, math provides the foundation for almost every game out there. In Power-Up, he divides his coverage into nine chapters:

  • Game physics
  • Repetition in quiz games
  • Voting
  • Keeping score
  • Chase games
  • Complexity
  • Friendship
  • Chaotic systems
  • Value of games

The first eight chapters center on a specific math topic, such as the use of equations to model the physics of a game world and the difficulties of assigning points in games such as recent versions of The Sims where friendship can matter as much as health and happiness. The final chapter discusses the value of games as a human activity, specifically mentioning games as educational tools and opportunities to gamble, with a mention of early probability calculations designed to divide the pot fairly in an unfinished game.

I have a bit of math background and have studied probability and statistics in some depth, so I was able to follow almost all of the formulas and related discussion fairly easily. Lane takes care to explain the equations’ inputs and, more importantly, meanings so the calculations’ roles within games can be understood without too much trouble. I’ve seen Arrow’s Impossibility Theorem, which proves that it’s impossible to design a voting system that can’t be manipulated through strategic voting, discussed in several publications; I believe Lane explains the phenomenon effectively and makes the logic behind the theorem clear.

Repetition and Scoring

While there’s too much material to discuss each chapter in depth, I did want to offer more details about the discussions of repetition and complexity in Power-Up. I played early versions of the quiz game You Don’t Know Jack! when I was young and, as Lane indicates, I started seeing repeat questions after a relatively short time. In Chapter 2, the author shows how having a relatively small question bank suffers in the face of frequent play. The radical solution, not repeating any questions until they have all been used, has its own issues. Various strategies for reducing the repeat rate have been tried, but most center on reducing the probability that a previously used question will be selected again.

For example, if you have a die with the numbers one through six and roll a one, you might want to make the probability of rolling a one again 1/12 instead of 1/6. The problem is that 5/6 + 1/12 = 11/12, which is less than one. As Lane points out, the actual probability of rolling a one again should be 1/11. If you add 1/11 + 10/11 (the probability of rolling any other number is 2/11, multiplied by five), you get 11/11 = 1. This calculation is interesting and a bit counterintuitive, which points out the creativity required to create fair games that are also fun to play.

Lane also goes into some detail on keeping score, describing several different systems for distance traveled games, tile matching games such as 2048, and puzzle games such as Angry Birds. The discussion of Angry Birds was quite interesting for me because it overlapped with a friend’s personal experience. My friend Bill had one of the top scores in the world on the original Angry Birds, but he was frustrated that some of the reported scores above him on the leaderboard were impossible to achieve. Not because the point counts were too high, but because there was literally no way to accumulate a specific total. Lane discusses this phenomenon, where it’s possible to prove that some totals can’t be reached within a game’s scoring system, in some depth. I enjoyed the discussion and plan to share it with my friend.


In Power-Up, Matthew Lane describes many of the ways that math powers video games. Similar books and articles have provided in-depth coverage of a specific subject, such as physics models, but his is the first to go into detail on such a wide variety of subjects in the same book. I love his choice of topics and believe the depth of each chapter strikes an excellent balance between detail and length. Highly recommended.

Written by curtisfrye

October 4, 2017 at 1:45 am

Book Review: The Gamble, from Princeton University Press

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Cover graphic for The Gamble

Title: The Gamble

Authors: John Sides and Lynn Vavreck

Publisher: Princeton University Press

Copyright: 2013

ISBN13: 978-0-691-15688-0

Length: 322

Price: $29.95

Rating: 93%

I received access to a preview copy of this book via the NetGalley site.

The popular media covers U.S. presidential campaigns like announcers calling a horse race, highlighting every move, nuance, and setback as if it could determine the winner. Why? Because not doing so would give viewers tacit permission to watch something else, drive down the networks’ ratings, and cost them advertising dollars. One journalist from Mother Jones identified 68 unique events the press labeled “game changers.” Were they, or was it just meaningless hype?


In The Gamble: Choice and Chance in the 2012 Presidential Election, authors John Sides and Lynn Vavreck analyze the race’s twists and turns in measured tones, emphasizing the role “the fundamentals” (especially the economy) play in presidential elections. Sides is associate professor of political science at George Washington University and the coauthor of Campaigns and Elections. He cofounded and contributes to The Monkey Cage, a politics blog. Vavreck is associate professor of political science and communications at UCLA. As academics, they had to strike a balance between writing for a general audience versus writing for an academic audience.

Books without sufficient analytical rigor might not be considered during tenure evaluations, so the authors took a bit of a risk by writing mainly for laymen. I thought they struck a clever and useful balance by dividing the book into two sections: commentary text, where the authors summarize their findings in the main body of the book; and appendixes that present their data and analyses in more depth. The main text contains plenty of facts and figures, but the appendices extend the analysis by including summary statistics (such as standard deviation and standard error) and other measures of interest to professional academics.


So, did the various campaign gaffes, missteps, blunders, and revelations make a difference? Sides and Vavreck conclude that, in the long run, they did not. The American electorate is more or less evenly divided between Democrats and Republicans with only a small percentage of persuadable voters for each election. Seemingly substantial missteps such as Mitt Romney’s statement about the (alleged) 47% of Americans who pay no income tax and Barack Obama’s (real) horrific performance in the first debate caused a momentary blip in the polls, but the candidates’ results settled back to the predicted norm within a few days.

The Republican primary season provides an even starker example of how Mitt Romney kept his forward momentum as challengers such as Rick Perry, Herman Cain, and Rick Santorum were “discovered” by the media but ran off the road due to policy mismatches with the electorate, poor debate performance, or personal issues the press uncovered. The fundamentals of Romney’s campaign didn’t guarantee him the nomination, but the odds were ever in his favor.

So too with Obama, who could rely on an (albeit slowly) improving economy to lift his campaign. Sides and Vavreck point out that even a general sense that things are getting better makes the incumbent very hard to overcome. Just as most Vegas odds makers give NFL teams a three-point edge for home field advantage, improving economic times provide a lift to sitting presidents.

Of course, campaigns and independent organizations do their best to overcome these limitations through voter outreach (aka the vaunted Obama “ground game”) and advertising. The authors’ analysis confirms previous work that ads shift opinions for a short time after viewing, but the effect fades quickly. The Romney campaign tried to leverage that fact by buying a lot of advertising in the days just before the election, but the Obama campaign had done a good job of maintaining their candidate’s presence and prevented the Romney campaign from succeeding.

The Gamble also addresses what the Obama win implies for American politics. Did his win, which was by a reasonably substantial margin, constitute a mandate and indicate a liberal trend in the polity? Recent votes in favor of legalizing gay marriage and marijuana seem to argue in favor of that interpretation, but Sides and Vavreck found that the electorate tends to equilibrate by moving in opposition to the winning candidate’s views. In other words, a liberal candidate’s win results in a more conservative electorate and vice-versa.


When it comes to U.S. presidential elections, the percentage of the electorate that will vote for their preferred party’s candidate regardless of attempted persuasion is so large as to render most campaigning moot. The campaign machines are so well-tuned, the authors argue, they cancel each other out over the long run. The fundamental elements, especially the economy, are far more relevant. I find that aspect of The Gamble comforting.

Before I close, I’d like to give a quick shout-out to the cover designer. I didn’t see the designer’s name in my preview copy of the book, but the cover image uses the point of the “A” in “Gamble” as the fulcrum of a dynamic balance between red and blue, which is a terrific touch. It makes a good book that much better.


Curtis Frye is the editor of Technology and Society Book Reviews. He is the author of more than 30 books, including Improspectives, his look at applying the principles of improv comedy to business and life. His list includes more than 20 books for Microsoft Press and O’Reilly Media; he has also created over a dozen online training courses for In addition to his writing, Curt is a keynote speaker and entertainer. You can find more information about him at