A little riddle to test your understanding of logic and probability...

Imagine three ring boxes; in one you can see a very expensive ring and the other two empty. Now the boxes are closed and mixed up, you have no way of knowing which one contains the ring. If you select the box that contains the ring, you get to keep it.

Before opening your selected box, one of the remaining two boxes is opened to reveal it is empty. Now you get another choice; do you switch to the remaining unopened box on the table or to stick with your original choice?

Please - decide now - before reading on to find the solution if you truly want to test your understanding of probability and logic.


Most people stick with their original choice. They trust their gut instinct and also have the fear of missing out or being wrong switching to later find out that they had the ring in their hands would be devastating ("Dammit I knew I was right!"). But what does probability say you should do?

You should switch! Switch every single time and you will win 2/3 of the time. Stick and you have just 1/3 chance of being correct. Do you prefer a 33 per cent chance of winning? If so then stick with your original choice. If however like me, you prefer to stack the odds in your favour then switch and you have just given yourself a 67 per cent chance of success.

I can hear the screams and feel the frustration from some of you already "It's 50:50" you say, "there are two boxes left, I have one and there is one on the table so the odds of success are 50:50 and switching provides me no benefit". I am sorry to say that is wrong. Switching increases your odds dramatically and most people don't even realise it. This scenario is in fact quite famous and is known as the 'Monty Hall Problem'. Google it and you will not be disappointed, many very smart people including mathematicians and PHDs get this wrong and refuse to believe they should switch until shown the solution.

Let's work through it briefly and if you still disagree with the logic (I use this on my seminars and know some people never give in) then google is there to assist.

For arguments sake, let's say you always choose box A. There are three boxes on the table and they all have 33 per cent odds of containing the ring so A is as good as any.

One third of the time you will be right and you will have the ring in your hand. If you agree so far, then you must also agree that there is a 2/3 chance the ring remains on the table. So two out three times, the ring is on the table and one out of three times it is in your hand. If it is in your hand then I as the host, can open either of the boxes on the table to show you it is empty. One third of the time if you switch, you will lose.

However, 2/3 times the ring remains on the table, leaving me no choice as to which box I open since I have agreed to open and reveal an empty box. That means two thirds of the time, the box containing the ring remains on the table unopened. Two out of three times if you switch, you will win.

Get it? It takes a while sometimes... I did not get it myself, in fact I was in the club initially of those who argued black and blue that the odds were 50:50 and I therefore might as well stick with my original choice. I was wrong and once I realised just how wrong I was, I must admit I was slightly embarrassed to be so easily tricked. There is a good lesson in there for those who want to learn it and not let a misunderstanding of probabilities trick them so easily in the future.

How does this relate to trading financial markets?

New traders have an unwavering reliance on their gut instinct. They buy and sell randomly (they just don't know or admit it is random) and then stick with that trade regardless of the result. When they are wrong they feel robbed, like the market has taken something from them.

They buy because of something they read in the paper today without logically realising that people already profited yesterday from the news they are now reading today. They buy and sell based on the recommendation of some analyst without realising that analyst probably does not have a single cent of his own money invested, he is simply paid to have an opinion.

They trade because they heard of a famous market player such as Warren Buffet buying a certain stock. What they don't realise is Buffet has been buying that stock for the past decade and plans to hold it for 30 years more, beyond the likely lifetime of the man himself. Their strategy is likely very different to Buffets, if they have one at all.

In short, they have little to no strategy, they have the odds stacked against them, they misunderstand the probabilities of their success and yet they refuse to believe any of this. They become married to their positions, take big losses and fail as traders or investors.

Another way it relates to traders is the failure to see opportunities where the odds are stacked in their favour. Imagine playing the ring game 1000 times without ever understanding the true odds of success. You will stick with your choice, lose 67 per cent of the time, feel frustrated and wonder why you are so unlucky.

Traders experience these exact same emotions for the exact same reasons they miss the opportunities right in front of them that can stack probabilities in their favour just because the misunderstand the game they are playing and the probabilities of winning in the first place. They need a simple strategy, like switching boxes, that when flawlessly executed over a large sample set of trades, shows the probabilities in their favour.

My next column will begin to show you how a trading strategy, when executed flawlessly, can put the probabilities in the favour of a trader. Some will passionately disagree with me, that's fine and completely expected. Some passionately disagree with the solution to the Monty Hall Problem and they are wrong about that too!