A strategy in game theory (called the Martingale System in gambling circles) that, in its simplest form, reads like this:
Assume that there is an infinite row of individual games. In each game, you bet the amount n (the size of which you can choose). With a probability of 50%, you lose your bet and your capital decreases by n, but if you win, you get back twice your bet., so your capital increases by n.

Now, the doubling strategy says that you start by betting a certain amount. If you win, you repeat. But if you lose, you double your bet in the next game!

Naively, this means that you can never lose - see St. Petersburg Paradox for an example of this naive treatment and my explanation why it's wrong. Basically, it fails to take into account two key factors that are easy to forget.
  • The fact that bets are paid from the limited capital of the player. If the doubling exceeds the player's remaining assets, the game ends with a huge loss. Temporarily increasing your assets through loans may seem to counter this, but in reality there are always limits, the eventual loss just becomes bigger (see the example below).
  • The fact that in reality, no game continues indefinitely and that it can be stopped for a variety of reasons - such as a player betting obscene amounts based on loans (i.e. other people's money).
For a real life example, look at Nick Leeson who was called a Wunderkind of the stock market until it turned out that he had (against rules) followed a doubling strategy using stock options and amassed debts of over one billion pounds, causing his employer, the Barings bank to collapse.

In game theory, doubling strategies are well-known for being disruptive, because they are deceptively successful for a long time, creating false confidence in their users, but eventually leading to cathastrophic losses with the potential to harm not only the player who used them but also the entire system. Thus, it is important for the health of the overall system that there are systematic safeguards against doubling strategies so that people cannot use them.

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