I have been reading Nicholas Nassim Taleb's The Black Swan: The Impact of the Highly Improbable. One of the main points Taleb makes is that the world that we live in is not governed by strict rules that allow for prediction. Taleb argues that the Gaussian bell curve does not reflect real life.
Note the central assumptions we made in the coin-flip game that led to the proto-Gaussian, or mild randomness.
First central assumption: the flips are independent of one another. The coin has no memory. The fact that you got heads or tails on the previous flip does not change the odds of your getting heads or tails on the next one. you do not become a "better" coin flipper over time. If you introduce memory, or skills in flipping, the entire Gaussian business becomes shaky.
Recall our discussions in Chapter 14 on preferential attachment and cumulative advantage. Both theories assert that winning today makes you more likely to win in the future. Therefore, probabilities are dependent on history, and the first central assumption leading to the Gaussian bell curve fails in reality. In games, of course, past winnings are not supposed to translate into an increased probability of future gains--but not so in real life, which is why I worry about teaching probability from games. But when winning leads to more winning, you are far more likely to see forty wins in a row than with a proto-Gaussian.
Second central asssumption:no "wild" jump. The step size in the building block of the basic random walk is always known, namely one step. There is no uncertainty as to the size of hte step. We did not encounter situations in which the move varied wildly.
Remember that if eithe rof these two central assumptions is not met, your moves (or coin tosses) will not cumulatively lead to the bell curve. Depending on what happens, they can lead to the wild Mandelbrotian style scale-invariant randomness.
After reading the above passage (my apologies for the length of the quote, but it beats reading the entirety of the book, right?) I thought about how some games, even those with strict rules, the first assumption is almost never right. Consider card games. Even though with every new hand (assuming the dealer is not cheating, which, as Taleb and reality will tell you is not always a reasonable assumption) each player has the same chance at getting a "good" hand or a "bad" hand, and because there are only 52 cards and they always have the same thing printed on them each time, the chances of someone getting an incredibly good hand (e.g., a hand that would be impossible to beat, no matter how you laid down the cards -- such as getting all 13 spades in a four-person game of Spades) are slim to none. Yet, really good card players (who are either born with incredible abilities or who have gotten better by playing the game) may be able to win consistently with average or even slightly bad hands. Thus, the first central assumption is not met because the players (or at least some players) will likely become better over time.
Now to my discussion of how Call of Duty: Modern Warfare 2 (hereinafter "CoD") approximates real life even more so than the card game because the game itself enhances the abilities of the skilled players.
In CoD, when you begin the game you have an avatar with a certain limited skill set: the avatar can only run so fast and so far, he changes weapons at a slow speed, and his aim is only so-so. In addition, the player has a limited choice of weapons and those weapons have no enhancements (such as a scope, silencer, or laser-sight). In the multiplayer online version of the game this beginning player gets thrown into a game with other players who not only would likely be able to defeat this newcomer (aka "nube" in gamer-talk) even if their avatar had the same slow running-speed, sighting-the-gun speed, etc. because the experienced player (1) knows the map, (2) has played the game and is more familiar and skilled with the controls, etc., but the changes of the experienced player defeating the nube is increased because the experienced player has things such as (a) a broader selection of weapons (some of which are 'better' because they are more accurate, fire faster, cause more damage) (b) weapons attachments that make it easier to kill other players (e.g., a thermal scope that makes it easier to spot and kill opponents), and (c) enhanced abilities such as running speed, speed in changing weapons, etc. Therefore, at least to some extent, the past winnings of the experienced players gives them an increased probability of future wins.
I was, at first, a little frustrated with the game because I felt that the natural advantages of having played the game for long periods of time (e.g., map knowledge, familiarity with controls, etc.) were sufficient to make the players better without giving them exceptional weapons or skills that the beginning players don't have (perhaps the game should give the beginners the "cool" weapons and make experienced players fight with "lesser" weapons to make the players more evenly matched, I thought). I felt like the game was not really fair in that respect. After reading Taleb's work, however, I realize that CoD is more a reflection of real life in that the winners get better: and the game actually enhances their ability to get better as time passes.
Beyond games, I tried to think about how this concept applies in real life. I thought about professions where relationships play a big part in success. Here I'll talk about stock brokers/financial advisors (hereinafter "FA's"). Taleb talks about "cumulative advantage" as the concept that those who have initial success tend to continue to have more success because the early success builds and creates future success. The examples he gives in The Black Swan are of academic authors: once a person gets published and cited by other authors, they are more likely to get cited more and hence, more likely to have their works more readily published when they submit new publicaitons (because journals value authors who are 'recognized' and cited frequently by others). Taleb argues that the initial publication and/or citations by others is due, frequently, to randomness rather than purely on skill. I think you can see the same thing in successful FAs.
Imagine two FAs starting out. They work at the same firm and receive the same training and they both have exactly the same opportunity for success. If FA1 lands a large account in his first week on the job and that client with the large account is well connected and really likes FA1, FA1 will likely add clients from the friends of this client. FA1s success will build the more clients he adds because his network (through those clients) will grow with each new client. The successful FAs become more successful through networking in addition to (we hope) picking up skills along the way, both in salesmanship and (maybe) in advising clients. FA2 might be smarter and better at giving financial advice, and FA2 might even be good at networking and good with people, but if FA2 does not "land a big fish" early in his career he may not make it through the training program and the firm may terminate him.
I hope to write more about this concept in future posts.
In regard to whether or not to read Taleb's The Black Swan: The Impact of the Highly Improbable, I think it is a must read for everyone. The book challenges the thinking we've been fed in psychology and statistics classes about bell curves and unlikely events. Taleb's book seems to give a practical and real description of randomness, and the book may provide some insight both into how "the real world" works as well as ways to find success in the real world that exists outside the bell curve. The Black Swan does tend to jump around a bit and I think Taleb could both pare down the book and make it more readable (he tends to go on unrelated tangents, or, at least fails to connect the anecdotes or thoughts to the point he's trying to get across). The concepts are too valuable to miss, though, and it's worth reading for the thought stimulation alone.