It Doesn't Take a Lot

The year was 1650.

As the beating heart of France, Paris was blossoming into a major metropolitan area. The narrow streets were crowded and noisy. It was an age of scientific awakening and civil unrest.

Among the residents of Paris was a man named Antoine Gombaud, better known as the Chevalier de Méré. Gombaud was an amateur mathematician, a wannabe philosopher, and what historians have called a “gentleman gambler.”

By his early 40s, he also inadvertently sparked the birth of modern probability theory, and helped Blaise Pascal cement his legacy as a brilliant mathematician.

It all started with dice.

Gombaud had stumbled into the realization that he could tilt the odds in his favor during dice games. He went around Paris to places were noblemen gathered and tossed dice for money. His bets were always small, to avoid suspicion, but he figured a large volume of tries would still net him a tidy sum.

Armed with a fair, six-sided die, his wager to the noblemen was simple. If he rolled a six within four tosses, he would receive a small payout. If he failed, he would pay the same amount to his challenger.

With the help of modern mathematics, we know today that Gombaud’s bet had a probability of winning 51.77% of the time, just better than 50-50 odds. That was good enough to accumulate a surprising amount of wealth over time.

But eventually, the party trick got old. Gombaud likely had a difficult time finding new takers for his wager. Inspired by his success, though, he devised a new scheme. Brimming with confidence, he began offering a new wager, more complex than the first.

Gombaud bet his opponents that he could roll double-sixes with a pair of dice within 24 tosses.

Gombaud believed he had used his mathematical prowess to his advantage again. But as he implemented this new system, he unsuspectingly lost more and more money as he played. His overconfidence overshadowed his judgment and soon Gombaud was nearly broke.

Not knowing what else to do, Gombaud asked his friend Blaise Pascal for help. Pascal immediately deployed his brilliant mind to study why Gombaud’s latest bet tossed him into financial ruin.

In computing the odds, Pascal eventually determined that rolling double-sixes with a pair dice within 24 tries had a probability of 49.14%. In other words, just shy of 50-50 odds. That meant the more Gombaud played the game, the more likely he was to lose.

51.77% was sufficient to make Gombaud wealthy. 49.17% was enough to make him nearly broke.

A slight advantage over time is all it takes to do well.

Going back nearly 100 years, the U.S. stock market exhibits a similar edge. On days when the market ends higher than the day prior, the average gain is 0.75%. On days when the market ends lower than the day prior, the loss is 0.78%. This doesn’t look good at first blush. However, the market has more “up” days then “down” days.

If you look at all days, the market is up 0.03% on average. Barely positive.

And yet, that was sufficient for the U.S. stock market to rise 40,000% in value during those nearly 100 years. Enough to make long-term investors incredibly wealthy along the way. It doesn’t take a lot to make all the difference.

Whether you know it or not, you have an edge in investing. You just have to play it to your advantage.