One in 18 Septillion

A septillion is a very large number – 1 followed by 24 zeros!  That large number is the answer to, “what were the odds that one Joan Ginther would win the lottery four times; which indeed she did. Let’s set that aside for a moment.  Before we get too excited about learning her secret in beating the odds, let’s briefly look into the law of probabilities.  Like Lady Justice, Lady Luck also has blindfolds while holding up the scales of probability. Similarly. both can be skewed or tampered with. We know about how justice can be corrupted but the law of probabilities as well?  The third paragraph below explains. Meanwhile, statisticians and math mongers will tell us that had the question been re-phrased to, “what are the odds that a person, not a particular person such as you, or I, or Joan Ginther, will win the lottery four times, the odds are better than we think – 1 in 5 million.

Author David J. Hand in his book, “The Improbability Principle”, wrote that the number of lotteries going on around the world and the number of people playing it allows for winners because of the “Law of Truly Large Numbers”.  That is why when the Powerball prize money gets bigger there will ultimately be a winner(s) as more and more people participate. But the odds are still against you or me specifically winning.  That is the same as trying to guess at which particular blade of grass a grasshopper will land on a 10-acre meadow.  But if it does it will have picked one blade of grass but not the one that you or I chose – in all probability, so to speak.

 

Now, Joan Ginther’s “luck”, truth must be told, had to have an asterisk beside it.  Winning her first lottery was one thing but parlaying a lot of her initial winning into buying more tickets afterwards sort of “stacked the deck” in her favor; three winnings totaled $15 million in Texas. In reality she actually invested over 3 million dollars over the period of her next three wins.  And then she turned around and took tax deductions for her losing tickets. Some estimated that she may only have spent a net of just merely 1 million dollars after the deductions.  And get this, it turned out she had a PhD in statistics from Stanford.  According to an investigative journalist from the Daily Mail, she somehow “could have used publicly available information to look for patterns that could lead her to figuring out the pseudo-random computer algorithm that determines when and where the winning tickets in each packet would arrive”. And she would buy up a lot of the scratch off tickets from the stores in the area.  She was not picking numbers for the Powerball drawing but buying chunks of scratch-off tickets from particular sites that sell them.  By doing so she merely shrunk the 10-acre meadow to the size of an English garden.   

The odds of winning the Power Ball or any state lottery are definitely staggeringly low. Jeremy Elson wrote in a 2011 this analogy, “Keep in mind the probability of winning is, as always, fantastically low. Imagine someone was to lay down a strip of pennies along the road from Seattle to Miami, and put a secret "X" on just one of them. You are about as likely to find the "X" by randomly picking a single one of those pennies as you are to win the Powerball jackpot.”

With that, why do people still buy lottery tickets when the odds of, say, winning the Powerball jackpot are so indescribably, if not dauntingly, low?  We all “know” that but often the most used rationale (if you can call it that) is that $2, or even as much as $10, is actually cheap entertainment for a thrill lasting a few hours or more until the final ball is drawn and the ticket(s) we held so dearly became scraps of ordinary paper. Sadly for some, the hankering for the thrill is repeated time and time again when “cheap entertainment” becomes a habitual financial burden – mostly for the segment of the population that can ill afford it.

The science of probability is not the same as the phenomenon of coincidence.  The human mind expects the grasshopper’s choice of a blade of grass to coincide with our pick, for a number of different reasons – limited only by what can be imagined.  After all, someone won with the numbers he or she took from a fortune cookie, the combination of birthdays in the family, numbers that appeared in a dream, combination taken from someone’s driver’s license number, etc.  Undeniably lotteries have been won that way. The Law of the Truly Large Numbers made that possible.  Around the world there are millions of fortune cookies with lottery numbers sold every day, every body in a family has a birthday, billions of people dream every night, drivers’ licenses in the U.S. alone number no lesser than 200 million and their numbers can be combined in a staggering number of ways.  Believe it or not, one of those will match with one of the many lottery drawings somewhere. We just simply don’t hear about the millions of losing numbers fashioned in a similar manner. A blade of grass will have been randomly picked by the grasshopper.  (Note the future perfect tense of the statement as you read the next paragraph).

Probability and coincidence live separate lives. The former lives in the world of many possibilities in the future, while the latter dwells in both the certainty of the future perfect and past tense. All probable outcomes cease to exist (collapse into nothingness) once one (and only one) of its many faces becomes reality. Coincidence manifests itself after the fact - a sure thing; otherwise, why would it be a coincidence?   Yet, it is the intersection of two or more events or situations with one another without any apparent trigger to cause them to cross. We wish for one probability (our pick of numbers) to “coincide” with the drawing of a winning set of numbers. That’s asking for the two to meet – the Terminator finding John Connor at some point in time.  Coincidence and probability operate independently of each other. 

Probabilities can influence how we make decisions; coincidences just happen without anyone or anything causing them to occur. A blade of grass has no influence on the grasshopper. Actuaries utilize probabilities to assess insurance premiums.  Casino owners rely on it to calculate their returns on investment as well as to make the gaming interests high enough to entice gamblers to keep coming back.  Algorithms for the slot machines must allow for percentage payout within 82% to 98%.  It is called “return to player”, RTP for short.  Maintaining the RTP at those ranges does insure that the casino is guaranteed anywhere from 2 to 18 % rate of return. It does not seem like much but the Truly Large Numbers make that a steady sure thing of a cash cow.  The algorithm does not care who wins, how much and at what time but it makes sure that somebody does win from time to time. Undeniably, we know more people who lost at the slots than those who win.  If we were to conduct a survey by interviewing people coming out of the casino it is likely that we will find winners versus losers at the rate inversely proportional to the RTP.  The reason is that for every jackpot winner of say, $2000 and above, many other hapless folks had contributed their cash to make that possible, after the casino had taken their 2 to 18% cut, of course.  The rule of thumb, if I were to make one, is to stay within the “budget” you are prepared to lose. If you’re lucky to win 2 X or more of that budget before exhausting your capital, QUIT! Also, once you’ve reached your "limit", QUIT! How many people actually do that?  Unfortunately, the longer you keep on playing the more opportunity for probability to conspire against you. That is why there are no clocks anywhere within the casino.

The law of probability is interesting but the phenomenon of coincidences is eerily weird, if not insanely inexplicable. But statisticians will tell us differently.  First of all, there truly are many coincidences beyond the common “small world variety”.  Consider the following that happened to Jean Moisset in April 21, 1988:

“Although I now reside in the city of Nice, when I have a medical problem I prefer going to a hospital in Paris, the city where most of the members of my family reside. After having experienced some urinary problems, I consulted my family doctor who arranged for an x-ray to be taken at the Necker hospital in Paris.

My appointment was for 8:45. I arrived a half hour early, that is, at 8:15. The receptionist told me that I was a half hour late since my appointment was set for 7:45. I showed her my appointment paper which did indeed indicate 8:45. Just as we were discussing the error, a man of about the same age as mine approached the desk. He said that his name was Jean Moisset and that he was sorry he was late for his appointment which was set for 7:45 and was for an examination similar to mine.

The name Moisset is not a very common name. Moreover, having the same first name, having arrived at about the same time at the same desk and for the same type of examination makes it highly improbable that it was by pure chance. To me it was obviously another good example of coincidence (which I call synchronicity) several of which I have experienced over the past few months.”

Jean Moisset had since collected many more such stories.

Here is one I read about the 19th-century French poet Emile Deschamps. This is considered by some who look into the subject as one incredible story of coincidences over a prolonged period of intervals.

"As a teenager, Deschamps meets a man with a strange name, Monsieur de Fortgibu. De Fortgibu is an immigrant from England, and he introduces Deschamps to a very English dessert: plum pudding.

Ten years go by. One day, Deschamps passes a Paris restaurant that has plum pudding on the menu. He goes inside, only to be told the last of the plum pudding was just sold to a gentleman sitting in the back.

"And the waiter calls out loud, 'Mr. de Fortgibu, would you be willing to share your plum pudding with this gentleman?'  It was the same Monsieur de Fortgibu.

Years pass, and Deschamps is at a dinner party with some friends.

The host announces that an unusual dessert will be served. You guessed it — plum pudding. Deschamps jokingly says that one of the guests at the party must be Monsieur de Fortgibu.

"Well, soon the doorbell rings and Mr. de Fortgibu is announced. And he enters, he's an old man by now, but Deschamps recognizes him. And Mr. de Fortgibu looks around and he realizes that he's in the wrong apartment." He was invited to a dinner party next door.

We’re told by statisticians and mathematicians that the coincidences are really no big deal.  They’re weird, strange, or even magical perhaps, but that is because we try to explain them. I cannot explain that except to say that maybe we should just accept them for what they are - mere happenstances. The experts say that that is exactly why coincidences are more common than we think. In fact, our own lives are filled with many coincidences; some good, others not so good. One coincidence may be more spectacular than another but just the same, they’re just one of uncountable intersections that occur on a regular basis.  Oh, well.

A personal story gave me first look into the science of probability as an effective tool for decision making. I worked for a large oil company in the old country where one of my duties as a Supply Assistant (a logistics job) was to oversee the transportation of petroleum product from the refinery to the terminal by barge in open ocean.  Naturally, the product was insured.  The company paid an insurance premium equivalent to 10% of the value of the product for each trip. It seemed like a reasonable expense – 10% against a 100% total loss – and had gone on long before I took over the job.  One day I realized that after every ten trips we were paying for 100% of the value of the product (10% X 10 trips) in insurance premiums.  I figured we can afford to “sink” every 11^th barge worth of product and break even. (The barge carrier had insurance to cover for the loss of their vessel and environmental liabilities were under separate insurance). Convinced by the memo I wrote which begun with the 50-50 probability of a coin toss to the likelihood of a barge capsizing, the Operations Manager, though reluctant to embrace the radical idea, asked me to make the presentation to the Treasury Manager together with representatives from the insurance company in attendance. I was “junior enough” in the hierarchy to be “sacrificed” in case my argument was poked with holes and failed to sail, pun intended.  Not unexpectedly the insurance company representatives agreed with the argument. Paradoxically, however, they did not counter with a lower quote to keep the business. It was likely, we surmised, that they were not about to set a precedent of lower premiums for their other clients; besides they had other businesses with us. Up to that point in time not a single barge was lost.

Now here is the thing.  What if after we implemented foregoing with insurance one of the barges sunk? That would have been just coincidence although a tragic one for my career, even though it should have had no bearing on the idea to forego paying for insurance.  For years and years before that and until I left the company to immigrate to the U.S. no such event happened.  Probability dictates however that sooner or later it will, but by that time enough money will have been saved to cover the loss. I don’t know if that policy continues today. I left the country and the company over thirty years ago.

Fast forward to a few months later, after arriving in the U.S., when a providential coincidence had a role in how I ended up working for the one American corporation I wanted so much to join since arriving.  I must mention that the U.S. company and the one from the old country were both part of the same international group of companies, except that there was no correspondent relationship between the two; besides I did resign from the previous company. One day I sent my application.  Meanwhile, as I usually did whenever possible I would spend time at the Brooklyn Business Library in New York. A few days, maybe a little over a week, after I mailed my application, I chanced upon an article in the Oil & Gas Journal that featured the General Manager for Distribution of the same oil company I applied to. Somehow something prompted me to write to him directly, enclosing the very same resume in my first application. Within a couple of days after mailing the letter, I got a letter from the company – alas, it was a rejection letter, signed by an HR recruiter. It was obviously a rejection-form-letter to my first application but a real damper, nonetheless.  I was disappointed but what can I do?

A little over a week after that rejection letter, a telegram came (for some of you young folks, this was pre-e-mail era) that instructed me to call collect (there was no 1-800 number then either).  It was from the same HR recruiter who signed the rejection letter. Based on our opening conversation I sensed he was talking about my second letter, totally oblivious that his department had already sent me an auto-signed rejection earlier. Anyhow, that got my foot in the door, a chance for an interview, and the rest is history.  Now, had I received the rejection to my first letter before mailing the one addressed to the General Manager, I would not have sent it for the obvious reason.  What may have likely happened was that he probably just initialed my application and had his secretary forward it to HR – a scenario that bettered the odds that the letter was paid some attention at HR. Of course, had I not read the Oil & Gas Journal article about the General Manager in the first place, I would not have been prompted to do what I did. By the way, I never met him (I found he was quite high up in the totem pole) and by the time I had the courage to try to meet him, he had already retired. So, we can say, this was a case where a single coincidence bettered the odds favorably. My career lasted 27 years with the same company.

Guess what, my first job was coordinating barge product movement up and down the Mississippi River. I immediately realized that the company, like all other major oil companies in the U.S. had been self-insuring their products for years. I had no knowledge of it prior to coming over so it was just a coincidence I thought of it earlier as a Supply Assistant.

If we examine it closely, our individual lives are filled with coincidences: many are too subtle to be noticed.  Catching a smile from someone across a crowded room, a casual introduction, bumping into someone from childhood at an unlikely place, etc. while purely coincidental, had on more than one instance led to an enduring marriage.  It is not one spectacular coincidence but if it resulted in a lifelong commitment, the odds of that happening in this day and age has more significance than anyone can ever hope for.  Not exactly one in 18 septillion but it could very well be a huge win in the Powerball of life.