A well-known brainteaser concerning statistical probability was created in the 1970s, generating a lot of controversy. You don’t hear a lot about it these days. It is relevant to trading, so I thought I’d being it up in case you have never heard of it. It is called “The Monty Hall Problem” and is based on a real game show that used to run on American TV. In the show, a contestant would be shown three doors. Behind one door, they were told (honestly), was a valuable item such as a car; behind the other two doors, comparatively worthless items. The contestant would then be invited to choose one of the three doors and could keep whatever was behind the door he or she chose. The choice at this stage was obviously a random gamble, with a 1 in 3 chance of winning the most valuable prize.
The “problem” imagines the game at this stage. The contestant has selected a door. The game’s host then intervenes, opening one of the other two doors to show there is something worthless behind it. We now have two mysterious doors, one of which the contestant has selected already. The contestant is offered the chance to switch to the other door instead. The “problem” asks, is it a good idea to make the switch, or should the contestant stick with their original choice. The intuitive answer is no. Yet the true answer is yes. This is because the host’s action is new information which increases the probability of the car or other most valuable item being behind the door which has not already been chosen.
The solution to the “problem” is hard to understand. It is something worth exploring because in trading, you will enter a trade with a certain probability of a positive result. As the trade remains open and the market price gives new information, does that change the odds? Or should you just stick with the trade because the odds were good enough in the beginning?
Later this week I will explore the various answers to the question as to why the contestant should switch. It can be proven mathematically that switching increases the positive expectancy, yet the answers as to why this is so remain controversial.