The Ludic Fallacy

I have grandchildren who bring me pleasure in many and diverse ways.

The oldest of them is a smart guy, who has good analytic skills and curiosity.  As a student, if you can have only two skills, they will do.

A couple of years ago he was taking probability theory in mathematics class.

Being a grandfather has many advantages, not the least of which is permission to appear eccentric.  I said, “Suppose I have tossed a coin and it has appeared as heads twenty consecutive times.  What is the probability for the next toss?”

He, of course, answered “50-50.” and I of course said “No!”

He argued that the previous events had no relationship to the current case and therefore 50-50 was the right answer.

I had to point out that he had just seen something unusual happen and that had to be considered.  In this case, the odds of it happening were 1,048,576 to 1 against.  How can you ignore that?

“It doesn’t matter.  It is still 50-50.,” says he.

“Wrong”

The probability is that you should examine the coin.

I know people who would have been examining the coin by the time it came up heads four times, never mind twenty.  They are the ones who ask, “Am I being paranoid enough?”

If an observed event is so improbable that it casts the validity of the system into doubt, you will usually do better by checking the system than by blindly following theory.  It is what Nassim Nicholas Taleb calls “The Ludic Fallacy.”  Essentially, statistics that are artificially confined or confined by specific rules.  Game-like statistics.  The real world does not have these limits.

If you have not read “The Black Swan” do so immediately.  The new edition has some material on fragility.  Worth the price.

It is far from well-written but the ideas within it overshadow that defect.  You can also learn a lot by looking at edge.org.  Particularly this essay.  http://www.edge.org/3rd_culture/taleb08/taleb08_index.html

Try and explain 19 October 1987 when the market fell 22.61% in the day.  Using the conventional approach to market statistics, that is a 20.98 sigma event.  The biggest up tick occurred 13 October 2008 at +11.82 sigma.

The odds of a 10 sigma event are roughly 1 in 100,000,000,000,000,000,000,000.   A 20 sigma event cannot happen.  Not ever!  Well, maybe if the universe was a billion times older than it is and the stock market had been open every day since it began.  Even then it would be improbable.

It can however happen if the system you are using to create your idea of reality is flawed.  Truth is stranger than fiction because fiction has to be plausible.  The moral here, in the same way, is real world statistics are stranger than academic constructs because academic constructs have to make sense.

Pay attention to the system for analyzing portfolios.  There are other opinions out there as to how you should do it.  If the system in use is not right all the time, then you have the the problem that you will do worse by knowing methods that are wrong than you will do by knowing nothing.  If you know nothing, you can still be right by accident.

I know the grandson is catching on to how numbers work.

Shortly after the probability episode, he asked if I would help him design a campaign for class president.  Being cynical, I suggested he just behave like other politicians and bribe the folks.

His reply, “Actually, I would only need to bribe half of them.”

One Comment on “The Ludic Fallacy

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