Quick quiz.
Give me the first answer that comes into your mind.
What are the chances that a coin lands on tails five times in a row?
If there were 100 coin flips, how often would you expect to see five tails?
The movie titled A Series of Unfortunate Events, starring Jim Carrey, released in 2004, was about the Baudelaire children orphaned after their parent’s mysterious death and faced one unfortunate event after another.
What bad luck.
While that was just a darkly comedic fictional story, unfortunate events do occur in real life, and sometimes they happen all at once, in what we call “a perfect storm.”
We, as humans, have a poor notion of probability and statistics.
Therefore, when a series of unfortunate events occur in clumps, we say we must be the most unlucky person in the world.
A cluster of unfortunate events occur, and they occur more frequently than most people would expect, with the possible exception of those who are permanent pessimists.
Contents
Probability of Five Consecutive Tails
Statistically, there is a 3% chance that you will see five tails in a row.
It is calculated like this:
The probability of getting tails on one flip is one out of two or 1/2.
Since coin flips are independent events, we multiply probabilities.
The probabilities of five tails in a row is = ½ * ½ * ½ * ½ * ½ = 1 / 32 = 3%
There is one out of 32 chance you will get five tails in a row.
Flipping 32 times, you would likely see one instance of five tails in a row.
Flipping 100 times, you likely see three instances.
Did that match your answer?
Or did you think five tails would occur more?
Or less?
Roulette Wheel
A roulette wheel has equal numbers of red and black squares.
So, you would think that red and black outcomes would alternate fairly regularly.
Using an online roulette wheel, I spun the wheel one hundred times, and these were the results (excluding the results of green):
See the cluster of reds.
I saw ten reds in a row.
We also see clusters of blacks too.
In this example, I got 58 reds and 42 blacks.
If I had more time to continue spinning, there would be about the same number of reds and black numbers.
However, they can occur in clumps and may not be as evenly distributed as we would like or expect.
Really Bad Luck
Do you think a roulette wheel can get 26 blacks in a row?
What are the chances?
The probability is one in 66.6 million.
But it happened.
It happened on August 18, 1913, at the Monte Carlo Casino in Monaco, which gave rise to the concept of gambler’s fallacy.
Gamblers who keep betting on the opposite color – not believing that this can happen – lose a lot of money.
What Does That Have To Do With Trading?
Traders trying out a new strategy for the first time may encounter five losing trades in a row and claim that the strategy does not work.
They go to the next strategy and see the same thing happen.
And the next strategy.
And the next.
Now, they are not able to stick with a strategy long enough to see it profitable.
By understanding that bad things can happen, we don’t throw out a perfectly good strategy.
It is possible for a strategy to have a statistical edge with a positive expectancy and still get five losing trades in a row.
Drawdowns will happen.
Then again, it could also be that the strategy is no good.
It is difficult to tell unless you give the strategy a long run.
If you don’t want to lose money while trying out a new strategy, backtest it or paper trade it first.
If it is possible that you can get five losing trades in a row, then you better size your trades properly with appropriate stop loss so that five losing trades in a row do not wipe out the account.
Just as unfortunate events may occur more frequently than one might expect, fortunate events can also occur more frequently than one might expect.
However, we are likely to remember the unfortunate events more because they are more painful than the fortunate events are pleasurable.
A trader’s loss is more painful than the pleasure of a win of the same amount.
This leads to the psychological effect of risk aversion.
Final Thoughts
It’s been a long time since I saw the movie A Series of Unfortunate Events.
I recall it was a good movie, and I’ll make a mental note to watch it again.
We hope you enjoyed this article about probability in options trading.
If you have any questions, please send an email or leave a comment below.
Trade safe!
Disclaimer: The information above is for educational purposes only and should not be treated as investment advice. The strategy presented would not be suitable for investors who are not familiar with exchange traded options. Any readers interested in this strategy should do their own research and seek advice from a licensed financial adviser.
Great article.
Would you say it’s better to earn little amounts with almost “guaranteed” methods(like bull put spreads that can turn into covered calls), or instead to have bigger winnings but have to deal with the pain of losing sometimes? I am doing the first one and find it hard to do trades that I know might cause me to loose money say every 3rd trade or so.
I prefer small, consistent winning trades while avoiding big losses. Aiming for base hits rather than home runs.