Posts Tagged ‘game theory’
When You’re “Due” — The Gambler’s Fallacy
I travel to Las Vegas once or twice a year, both to play poker (where I convince myself I have an advantage) and to dabble in other games (where I definitely don’t). Since 1993, when I started playing while on the East Coast, I’ve seen thousands of players succumb to the insidious gambler’s fallacy.
Let’s say you’re playing roulette and notice, as posted on the so very helpful display by the wheel, that five red numbers have come up in a row. Is black due? What about green (0/00)? The answer is neither. Roulette wheels are well-balanced and the little obstacles spread around the wheel, called canoes in casino parlance, make outcomes random enough to be considered independent trials. If red numbers come up five times in a row, the next number will be red 18/38 of the time, black 18/38 of the time, and green 2/38 of the time. Ironically, it’s our human urge to discover patterns that makes the gambler’s fallacy work. The wheel has no memory, but we do.
The bottom line is that when you play roulette, the proportion of red, black, and green numbers will tend toward the target ratios over millions of spins and the weighted payoffs will ensure the house earns its profit over the long run. But what about games like poker? Poker is a skill game with a healthy dose of luck thrown in, so trials aren’t truly independent. Inferior players beat better players over the short term, but only because of luck. But what happens when equal players face off?
It’s hard to find players of the same skill level at a poker table, but I tested the theory by replicating an experiment described by poker author Lou Krieger. Like Lou, I set up ten identical players in Wilson Software’s Turbo Texas Hold’em simulation mode and let them play hundreds of millions of hands against each other. Six of the ten players were just above or below breaking even, but there were two big winners and two big losers. Remember that each player followed an identical strategy — the only factor controlling their fate was the luck of the draw.
As human beings trying to extract a living from an indifferent universe, we must realize that the odds are not always in our favor and that we will go through bad streaks we can’t seem to reverse. At these times it pays to strengthen your base by learning new skills or practicing old ones, reinforcing friendships, reaching out to others for help, and offering assistance where you can. Doing these things doesn’t constitute “good karma” or “putting things out into the universe”, both dubious concepts. What you are doing is improving the chances you’ll be ready to take advantage of opportunities that you and your contacts discover.
Clustering and Streaks — Real or Imagined?
The folk wisdom that “bad things come in threes” is still popular in the U.S. Whenever two celebrities die on the same day, for example, even the most hardened critical thinker feels the urge to look for the third.
Is clustering real? Do events happen in streaks, or are they just a product of our pattern-seeking brains? George Carlin made fun of the “bad things happen in threes” adage by stating that bad things actually happen in 27’s, noting that “it just takes longer to see the pattern.” You can always find instances of “bad things” in the world to fill out your sets of three, but what does the research say? There have been a lot of studies on the subject, including Koehler and Conley’s “The “Hot Hand” Myth In Professional Basketball”, published in 2003 in the Journal of Sport and Exercise Psychology. The authors examined the National Basketball Association’s long distance shooting contest and looked for statistical aberrations in the sequences of made and missed shots. As in all but a few other studies, they found no significant deviation from chance. When they took each player’s base shooting accuracy into account, the effect disappeared.
Sports are physical contests and even little variations in physical conditions can affect performance, but what about chess? Chess is a mental game played with perfect information. That is, you know everything there is to know about a position and there’s no hidden information, such as a player’s hole cards in poker. As of this writing, I have played 19,738 games of blitz chess (each player has 3 or 5 minutes to make all moves in a game) at the Internet Chess Club since June 27, 2001. As I watch my online chess rating fluctuate from embarrassing to “not bad for me”, I wonder how much the streaks of wins, losses, and draws reflect my abilities and how much is the “luck” of an opponent making some horrible mistake.
The three-year graph of my rating shows huge swings, but the average is right about where I perceive myself as a player. Perhaps my streaks are due to luck. After all, I don’t seriously study the game and play to take a break from other work. The big changes make a strong visual impression, but there are a lot of small shifts in there, too.
Improvisers can make a fun game out of looking for apparent patterns and justifying reasons for believing streaks exist. The lesson for analysts? Carefully examine whether a sequence of events is due to some underlying cause or is just a sequence of events that might be due to chance. That said, given the strength of our innate need to discover patterns, is there any way to dispel what appears to be the myth of the hot hand? In a 2006 review of the literature, Michael Bar-Elia, Simcha Avugosa, and Markus Raab summarized the situation in this way:
As Amos Tversky, who initiated the hot hand research, used to say (cited by Gilovich in an online chat, September, 2002), ‘‘I’ve been in a thousand arguments over this topic, won them all, but convinced no one’’.
Gamification: Game Design and Addiction
I’m the editor and chief reviewer of Technology and Society Book Reviews, a site I founded in February 1998. I recently reviewed Natasha Dow Schüll’s book Addiction by Design, which makes many points relevant to my post on the ethics of gamification. The full text of my review appears below.
Title: Addiction by Design
Author: Natasha Dow Schüll
Publisher: Princeton University Press
Copyright: 2012
ISBN13: 978-0-691-12755-2
Length: 444
Price: $35.00
Rating: 89%
I purchased this book for personal use.
Natasha Dow Schüll, an associate professor in MIT’s Program in Science, Technology, and Society, explored the allure of food in mass quantities in her documentary Buffet: All You Can Eat Las Vegas. In her new book Addiction by Design from Princeton University Press, she examines how machine and game design facilitate addictive behavior.
Human Side of the Equation
Schüll begins by describing the human cost of gambling addiction by profiling several individuals, all of whom have driven themselves and their families into difficult situations because of their gambling. One woman interviewed by the author has structured her daily routine to visit a circuit of gambling establishments, including casinos and grocery stores with video poker machines. The small footprint, low operating costs, and revenue generation capacity of machines means that table games such as blackjack and craps have been squeezed into increasingly smaller spaces. Mirroring this trend, the typical problem gambler has changed from a middle-aged man who bets on sports or blackjack and waits ten years to get help to a 35 year-old woman with two kids who plays video poker and seeks help after just two years.
The financial windfall generated by problem gamblers is staggering. One study by Tracy Shrans indicated that gamblers who follow the industry’s “responsible gaming rules of conduct” (e.g, setting time and money limits, understanding the odds of the games, and not gambling when you’re lonely, angry, or depressed) generate just 4% of gambling revenue. A slew of studies, notably work published in 1998 by Lesieur (cited p. 16), estimate that problem gamblers generate between 30-60% of casino revenue. Part of gambling’s attraction is the possibility, however remote, of winning a significant amount of money, but the varied reward schedule plays a significant role as well.
Entering the Machine Zone
The effectiveness of a varied reward schedule holds true across the animal kingdom. Rats that press a lever and receive a food pellet every time will press only when they’re hungry, but rats rewarded on an irregular schedule, where they have no idea when the next food pellet will drop, will press the lever until exhausted. When the rewards come not from food but from direct stimulation of the endogenous reward system, the effects are even more pronounced. In her Great Courses video series Understanding the Brain, Jeanette Norden notes that rats with wires inserted into their brains, allowing them to stimulate their pleasure centers by pressing a lever, will forgo all other activities — including but not limited to sleeping, eating, and sex — to press the lever. She described the scene of an exhausted, filthy rat collapsed on the floor of its cage, reaching with its last bit of strength to press the lever just one more time.
According to Schüll’s analysis, the analog for humans appears to be entering the “machine zone”, where the player is engrossed in the game and their interaction with the machine. Unlike poker and other table games that provide experiences mediated by other humans and offer occasional thrills, machine gamblers are able to maintain stimulation for as long as their bankroll allows. The rhythm of their interaction with the device induces comfort and, most importantly, lets the player escape from the world for a time. Game designers have capitalized on this trend by offering multi-line video slot machines with as many as 100 payouts. The result is that most spins pay something, but the majority of spins pay less than the player wagered. Rather than a singular win or loss, these fractional payouts provide a smoother ride down as the built-in house advantage grinds away at the player’s bankroll.
Nevada is arguably the most libertarian state in the U.S., so it’s no surprise the gaming industry bases its arguments against limiting game design and player tracking on the grounds of personal responsibility. Schüll implies, but never as far as I could tell directly states that the games’ design promotes addiction. She probably couldn’t do so because of legal concerns and the inherent difficulty in proving such a statement, which is fair enough. That said, if there ever is such proof, it’s likely that the self-exclusion policies in other gambling jurisdictions such as British Columbia, Canada, and Australia would be replaced by stricter rules.
Conclusions
Schüll goes beyond the basic “reward schedule” addiction analysis so common in the literature and casts the role of casinos and their visitors in terms of the social theories of Weber, Levi-Strauss, and Foucault, mirroring the theoretical underpinnings of MIT’s Program in Science, Technology, and Society. (Though this publication and the program have similar names, we are not affiliated.) I thought her analysis added value to the book, but the sections didn’t feel tightly integrated with the rest of the narrative. Schüll wrote the book over several years and the book’s cohesiveness might have suffered a bit because of it. Important life events take priority, of course, and despite some small shortcomings Addiction by Design is a detailed, useful, and readable analysis of machine gambling and the players on all sides of the game.
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 lynda.com. In addition to his writing, Curt is a keynote speaker and entertainer. You can find more information about him at www.curtisfrye.com.
My Experiences Thus Far with MOOCs
I’m an information forager, someone who wanders among topics picking up bits and pieces of knowledge as I go. If you offer me a good way to gain information and experience, you’ll get my attention.
I’ve sort of fallen in love with the Massive Open Online Course (MOOC) offerings from Coursera. I’ve successfully completed seven of the courses, ranging from an easy introductory course on geospatial information and mapping to a challenging course on machine learning. I bit off substantially more than I could chew when I signed up for a natural language processing class, but at least I had the good sense to pack it in when I saw I didn’t have the skills to complete the assignments.
One of my just-completed courses was Model Thinking, by Professor Scott Page from the University of Michigan and the Santa Fe Institute. This session was the second time the course was offered and, as it turned out, it was an exact repeat of the first session. Dr. Page and his assistants didn’t update any of the lectures (or even edit out coughs and other flubs from original recording), participate in the class’s discussion forums, tweet from the advertised Twitter account, or update the class’s Facebook page or blog. As befits a summer offering, the class ran entirely on autopilot.
We’re very early in the days of MOOC development, so there are a lot of experiments going on as professors and institutions determine how to present MOOCs and incorporate them into university curricula. One of the big problems MOOC providers have to face is the immense number of individuals who sign up for the class but never watch a single movie. In some cases, only a third of students who sign up for a MOOC watch even one lecture, and most courses have pass rates of less than 10% (7% is typical). Part of the problem is that there’s no real penalty for not finishing the course — you know you didn’t do the work, but there’s no social stigma attached to it. And besides, you can always download the movies and watch them at your leisure.
Dr. Page seemed to address this dropout issue by making the Model Thinking class very easy to pass. Grades were calculated by adding 50% of your quiz scores (dropping the lowest two) and 50% of your exam scores, with everyone who scored a total of 75% or higher receiving a certificate. But here’s the kicker: you got three attempts at each quiz and the system displayed the correct answers after you took the quiz for the first time. All students had to do was write down the answers and re-take the quiz to get a perfect score.
Like the quizzes, you got three shots at the mid-term and final, but the system didn’t display the correct answers. It did tell you where to find the information required to answer the question, but you had to figure out the answer for yourself. Even so, if you received a perfect score on the quizzes (hard not to), you only had to get half the exam questions right to pass. The only reason a mildly attentive student couldn’t pass the course would be a lack of time to take the quizzes and exams. You barely needed to watch the lecture movies.
Is this strategy a good way to improve MOOC completion rates? Yes, if that’s your only goal. I would be very interested to learn how this Model Thinking class session’s completion and engagement rates compare to those of other MOOCs, but I wonder how much material students who took the easy route retained. If there’s no significant marginal cost per technically passing but unengaged student, perhaps it’s OK if they take little or no knowledge from the course. At the very least, it’s a worthwhile experiment.
