Risk in the real world.
We do not come into this world with an innate sense of how the random part of our world works. We talk about probabilities casually and think we understand. When the weatherman forecasts 60% chance of rain today we do not have a precise definition of what that means. In reality we mostly have unreliable notions, and perhaps some wrong conclusions, when it comes to randomness in our lives.
Matching Birthdays
For instance, few of us know that if a group of 25 randomly selected people are asked their birthday that the chance of at least two of them having a birthday on the same day of the year is better than 50%. I met a man who knew all the odds of drawing various hands in poker. When I told him this little known fact he was in disbelief and gave me 2 to 1 odds on a bet. The 14th person he queried for a birth date matched one of the previous ones. He declined to repeat the bet. (More on how to calculate this probability)
Gamblers Fallacy
There are beliefs held by some traders that are likely wrong. Some say that after a string of losing trades success on the next trade is more likely, so position size on the next trade should be increased. According to Larry Williams: "After you have had 3 or 4 losing trades in a row, the probability of the next trade being not only a winner but a substantial winner is way in your favor." This may or may not be true in trading, but for most random events like flipping coins, it is definitely not true.
A common belief is that after suffering a series of loses, the odds of winning on the next trade are higher. This is known as the gambler's fallacy. What this implies is that the probability of winning each trade is somehow influenced by the result of the previous trades. This is not true for coin tossing - the coin has no memory of what side came up last. Each toss is totally independent of the previous one.
It may be argued that in real trading that each trade may not be independent of the previous trade. For instance if we are trying to use a breakout system it may be that after several failures success will follow. The problem is that we don't know in advance which trial will benefit from increased size so increasing position size may leave us with a large loss. Those who try to pick bottoms may sooner or later succeed - if they still have any capital left.
Doubles in dice
In the casino, rolling a particular double pays 30 to one odds. One line of reasoning says that since there is a 1/36 chance of rolling a particular double, simply watch for a long string of rolls without a particular double occurring and then bet $1 on each subsequent roll. For instance if double 2's have not occurred for the last 30 rolls, is it more likely that double 2's will occur in the next few rolls? No it is not true. Assuming fair dice, the odds of a particular double are totally uninfluenced by the past history of rolls. Just like the coin, the dice have no memory. The expectancy for betting $1 on double 2's is 30/36 = 0.833. The casino will be happy to keep 16 2/3 cents out of each dollar bet.
Copyright 2002, Larry Sanders