Fifty-Three and the Deep Blue Sea

A few years back an Italian woman from Tuscany leaped into the ocean and drowned herself after betting and losing her family’s life savings on the number fifty-three in the Italian lottery. The Italian lottery offers bets on numbers between 1 and 90 in its twice-weekly drawings. Fifty numbers are pulled in each drawing, so the odds of the elusive fifty-three appearing seemed quite good. But number fifty-three had not been drawn for over two years. Wagering on it had become a national obsession as bettors with a skewed view of probability theory wagered, and lost, more than $3.5 billion Euros chasing the scarce number. A few lost much more.

The law of probability essentially states that if the probability of a given outcome to an event is “P” and the event is repeated “N” times, then the larger “N” becomes, the greater the likelihood that the proportional outcome of the occurrence will equal the outcome of “N*P.
Before your eyes glaze over, let’s look at an example based on something we all understand. The probability of throwing a twelve with two dice is 1/36. Someone may toss the dice a hundred times and not toss a twelve. But the more times we throw the dice the closer the results will eventually come to 1/36. Closer – but not equal to.

Let’s look at the old familiar coin-flip as another example. If you flip a coin 100 times and it lands on heads 60 times and tails 40 times tails, many gamblers believe that tails is now “due” to get even. Most gamblers call this the Due Number Theory. Mathematicians know it as the Maturity of Chances Theory. The gambler’s much-anticipated “streak” of tails is known as a “corrective.” Gamblers expect the corrective to bring the total number of tails tossed equal to the number of heads. The belief is that the “law of averages” really is a law, which states that in the longest of long runs the totals of both heads and tails will eventually become equal. This belief is, of course, wrong.

When dealing with number of tosses as opposed to percentages, it is easy to become confused. Sometimes what you believe is a logical outcome is completely opposite of statistical reality. For example, in the above example it is true that as the number of tosses gets larger, it is more likely that the percentage of heads and tails thrown will approach 50% each. But the difference between the actual number of heads or tails thrown will probably get larger.

Say what?

Okay, let’s take another look at our example of 60 heads and 40 tails in 100 coin tosses, and imagine that the next 100 tosses result in 56 heads and 44 tails. The ‘corrective’ has set in, as the percentage of heads has now dropped from 60 per cent to 58 per cent. But there are now 32 more heads than tails, where there were only 20 before. The ‘law of averages’ follower who backed tails is 12 more tosses to the bad. If the third hundred tosses result in 52 heads and 48 tails, the ‘corrective’ is still proceeding, as there are now 168 heads in 300 tosses. 56% of the tosses resulted in heads, down from 58% after the last set of tosses. But the tails backer is now 36 tosses behind. In each case, the percentage difference got smaller, but the number of heads tossed versus tails continued to increase.

You’ve all heard the old saying, “the dice have no memory.” In fact, chance events are not influenced by the events that have gone before. If a true die has not shown the 6 for 36 throws, the probability of a 6 is still 1/6 on the 37th throw. This offends the gambler’s instinct in a lot of us, but it is still true. The ability to recognize and capitalize on this over the long run is what separates gamblers and advantage players. The gambler’s mind has difficulty coping with the seemingly contradictory laws of probability. The advantage player looks at the statistical proof, plans his play and plays his plan. To the guy who stands at the dice table, waits for eighteen consecutive rolls without a twelve, and then plays a midnight martingale it all makes perfect sense. The lady in Tuscany believed in the Due Number Theory so strongly that it ultimately cost her everything, including her life. Sadly, she was not the first person on record who took her life after losing everything. Nor will she be the last.

The real question boils down to this. Do you want to gamble or do you want to win?