Economy in the hands of gamblers

In a post last week I suggested that engineers and physicists might be better stewards of the economy than are politicians and economists. In an article in Slate, Jordan Ellenberg, an associate professor of mathematics at the University of Wisconsin, suggests the economy is actually in the hands of not-too-smart gamblers.

In his post, titled “We’re Down $700 Billion. Let’s Go Double or Nothing!” Ellenberg likens the “complex derivatives behind the current financial havoc” to the martingale game—a “sure fire” way to make, for example, a hundred dollars on a coin-toss game. You bet $100 on heads—if heads come up, you win $100; if tails comes up, you lose $100. But all you need to do is double-down: bet $200 on the next toss; should you lose again, bet $400 on the next toss, and so on until heads inevitably comes up.

Of course, it’s not inevitable that heads will come up before you are wiped out. It takes only 10 tails in a row to set you back $102,300, and you’ll need $102,400 to stay in the game.

If you don’t have that, surely you can find an investor. As Ellenberg puts it, “If people keep staking you money, you can just keep betting until, eventually, you win big time.”*

He adds: “See where I’m going with this? The carefully synthesized financial instruments now seeping toxically from the hulls of Lehman Bros. and Washington Mutual are vastly more complicated than the martingale. But they suffer the same fundamental flaw: They claim to create returns out of nothing, with no attendant risk. That’s not just suspicious. In many cases, it’s mathematically impossible.”

Ellenberg uses the concept of expected value to show that “the martingale strategy doesn’t eliminate risk—it just takes your risk and squeezes it all into one improbable but hideous scenario. The expected value computation is unforgiving. No matter what ultrasophisticated betting strategy you adopt, you can’t expect to make money in the long run by flipping a fair coin.” One hideous scenario, of course, is having 10 tosses in a row go against you and not have the hundred-grand-plus needed to stay in the game.

Ellenberg acknowledges that complex derivatives aren’t literally martingales, but he argues, citing John Quiggin, an economist at the University of Queensland, that the derivatives, like martingales, shift risk into low-probability, high-consequence events. With the banks out of money, the taxpayers are being required to double-down. Let’s hope the next throw is heads.