Since you will win sooner or later, you are certain to come home with a small profit. Provided you are infinitely rich before you start. Otherwise, if you regularly engage in martingales, you will eventually go bankrupt – and the richer you are, the larger the scale of bankruptcy.
Since anyone who studies the problem knows that ruin is the outcome, your bank, or your bookmaker, will probably call a halt to the game while the shirt remains on your back. Such capitulation will leave you with a large loss, and an enduring grievance that others have deprived you of a great coup.
Martingales and related strategies are the familiar currency of financial markets. Risk managers struggle, not always successfully, to control the martingales of rogue traders. Loan covenants may specify that when your initial collateral becomes insufficient you must offer more. Governments have responded to each recent financial crisis by feeding enough money into the market to stave off immediate collapse.
Bold risk-taking has always been characteristic of the European Union. The architects of the European project believed that if the mechanics of integration were developed rapidly, the institutions and electorates of member states, and the degree of real economic integration across national boundaries, would eventually catch up. This approach has mostly worked. But as with most gaming systems, it works until it doesn’t.
Whenever European institutions have failed to end the current crisis, they have returned with a new, larger, commitment. “We will do what it takes”, “we will see it through”, is the strategy, if it can be called that. “Just in time, just enough”, is how my colleague Martin Wolf last week described the tactics. These are the key components of the martingale system. But debt markets illustrate a malevolent game. A player on the other side of the table – global financial markets – has very large resources, and can ensure that each round of the game can be played for very large stakes.
The wise person’s reaction to the casino is not to go there. The next best course is to plan an early night. Leave while you are ahead, and if you cannot do so, accept a small loss. If the eurozone had quickly recognised defeat in Greece, it would have suffered a manageable failure and learnt an important lesson for the future. Instead it has followed the martingale. As the size of the bet grows after a run of losses, the commitment to do what it takes becomes steadily less credible.
The gambler who is confident his system will work looks to rich friends. When the indulgence of Berlin was exhausted, a banker was dispatched to Beijing. Now the players look to the only remaining credible supporter. Surely the European Central Bank can enable them to see the night through. The ECB really does have infinite resources: if it runs out of money, it can print more.
Up to a point. Money created by a central bank is not free – if it were, we could all be as rich as Croesus. The resources of a monetary agency come either directly from taxpayers or indirectly from everyone through general inflation. To fund the bet the ECB would have to stand ready to buy, not just every eurozone government bond issued so far, but any that might be issued. And more. The subprime and Lehman failures demonstrated that the amounts of money that could be gambled on default were potentially far larger than the actual amounts at risk.
Of course, say the advocates of this course, if only the banker would promise to underwrite our losses he would not actually have to pay. If you will only lend me a bit more money, says the gambler, you will get it all back, and more. That is the seductive song of the martingale.