The article presents an interesting analogy for the financial markets.

Unfortunately, it's *only* an analogy. And it breaks down in a couple of places.

1. Coin flipping is a random act easily described by probability theory. Markets are not random and are not nearly as easy to describe with probability theory. In markets, each transaction pits the knowledge and deception skills of two or more parties against each other. To game theorists, markets are more like wars than they are like coin-flipping, because players are struggling against each other. They employ tactics, use guile, attempt to create or discover weaknesses and exploit them, alter the odds in their favor.

To illustrate this idea: I sell you a derivative note backed by 100 junk-quality commercial mortgages for $5 million. I'm betting that taking your money will put me ahead; you're betting that taking the derivative note and giving up $5 million will put you ahead. I will attempt to know more about the transaction than you, and since I packaged the derivative note, I'm in a good position to succeed. You can, of course, attempt to beat me at my own game, and by agreeing to buy my derivative note, you are saying you think you can do exactly that.

Markets are battlegrounds on which a great many people are attempting to alter outcomes in their favor. Some of them are not above cheating. Packaging junk-quality mortgages as AAA-rated derivatives is cheating; it's cheating, not bad luck, that led us to this moment.

2. Unlike coin flipping, factors external to the transaction can alter the outcome. In a market where real estate prices are rising, the derivative transaction I just described can make us both winners. I slyly sold you a shaky investment. But market exuberance may make your purchase worth more than you paid anyway; you can unload it to people even less informed than you were about the underlying value of the note.

Conversely, if real estate values are falling, your ability to sell a shaky investment will fall, too. People will be walking away from no-equity mortgages. An already shaky investment becomes toxic.

Because of these external factors, the "=0" part of your equation is untrue for markets.

Mr. Ellenberg's article is an interesting thought-experiment, but it pays to keep in mind that classic probability theory offers, at best, an extremely limited source of insight into the behavior of markets.