Pasquale Who?

Sometime back, I wrote a column about how my friend Grant Hiraoka and I worked out an underlying mathematical principle upon which to build our poker games. Back in Seattle, early in my poker career, over coffee after playing sessions, we combined Grant's knowledge of gambling, the computer programming logic I was learning in college, and our day-to-day trials at the table to establish the following principle: The product of net edge times volume equals expectation, which added into a recurring field will over time equal earn. To maximize poker winnings, you must maximize your edge, and when you have edge in your favor, you must maximize volume.

We were proud as puppies at figuring this out. What we didn't know then was that we were sort of reinventing the wheel. That column generated a slew of e-mail, snail mail, and Internet posts advising me that every graduate student in statistics knew this, and that I was a moron to think this was anything special.

The fact is that I am still pretty proud of figuring it out on my own, as opposed to having it taught to me in a classroom. And I think my application of the principle to modern poker in actual practice as opposed to in theory is indeed original. Almost every poker decision I have made since those days in that Seattle coffee shop has been based on the same premise: What action shall I take now, at this moment, that will maximize my edge? It is the principle that lies at the heart of my game, and it has served me well.

Among those who ribbed me over my ignorance was fellow Card Player columnist David Sklansky. "If Pascal doesn't mind, I don't, either," he said.

"Pasquale who?" I replied. The only Pasquale I knew was the collection guy for a Seattle bookie … not somebody you really wanted to ask any questions, and I was damn sure he hadn't developed any statistical theories.

"Blaise Pascal," David said. "He was a 17th-century French philosopher and mathematician. He laid out the basic principles of probability theory with Fermat."

I wanted to ask him Fermat who, but I figured I'd demonstrated enough ignorance for one day. So, I kept my mouth shut, and when I got home I fired up Google on the old PC and looked up Blaise Pascal. And I found one pretty cool dude.

Born in France in 1623, Pascal died at the age of 39. At age 12, he had worked out Euclid's principles of geometry on his own, having had no training of any kind whatsoever in math. (This was probably significantly harder than Grant and me working out the application of Pascal's work to poker on our own.) He invented a calculating machine, the barometer, the syringe, and the hydraulic press. He did some of the first experiments to prove that a vacuum could exist in nature. Pascal observed that the pressure of the atmosphere decreases with height, and deduced that a vacuum existed above the atmosphere. All modern hydraulic systems are based on Pascal's discovery that fluids transmit pressure equally in all directions.

In the philosophical world, Pascal was one of the first existentialists. Existentialism is a philosophy that emphasizes the uniqueness and freedom of the individual person against the herd, the crowd, or mass society. It emphasizes individual responsibility, individual personality, individual existence, and individual freedom and choice. Existentialists hold the belief that life's most important questions are not accessible to reason or science. The only certainty for existentialists is death. In the existentialist world, each person is born, lives, chooses his or her course, and creates the meaning of his or her own existence. Existentialism did not hold wide sway among philosophers until after World War II – Pascal was centuries ahead of his time. I rather consider myself something of an existentialist, so Pascal's thinking preceded my personal beliefs in more than the poker world.

One of Pascal's best known principles is the argument that belief in God is rational, often referred to as Pascal's Wager, and is expressed something along the lines of: If God does not exist, one will lose nothing by believing in him, while if he does exist, one will lose everything by not believing. Pascal proceeds to support this premise with mathematical and probabilistic reasoning.

Pascal explored the place where mathematics and philosophy meet, particularly with regard to the oh-so-human activity of decision-making. He sought to find ways that humans could apply reason to make the best possible decisions – a skill that is at the heart of any poker game.

In conjunction with the French mathematician Pierre de Fermat, Pascal formulated the mathematical theory of probability, which has become important in the actuarial, mathematical, and social statistics fields, and is a fundamental element in the calculations of modern theoretical physics – and, of course, poker.

From Calculus, Volume II by Tom M. Apostol (Second edition, John Wiley & Sons, 1969):

"A gambler's dispute in 1654 led to the creation of a mathematical theory of probability by two famous French mathematicians, Blaise Pascal and Pierre de Fermat. Antoine Gombaud, Chevalier de Mééréé, a French nobleman with an interest in gaming and gambling questions, called Pascal's attention to an apparent contradiction concerning a popular dice game. The game consisted in throwing a pair of dice 24 times; the problem was to decide whether or not to bet even money on the occurrence of at least one 'double six' during the 24 throws. A seemingly well-established gambling rule led de Mééréé to believe that betting on a double six in 24 throws would be profitable, but his own calculations indicated just the opposite."

Fermat himself had something of a gambling problem, and found himself often losing at dice games. He wrote to Pascal, seeking help. Pascal and Fermat exchanged substantial correspondence relating to the frequency of occurrence and developed the modern theory of probability. Although their work was principally founded on dice throws, it is most frequently expressed in the "coin toss" example: One can calculate the chances of anything happening by the number of possibilities present; for example, in the toss of a coin, the chance of its being a head or a tail on any toss is 50-50, because in the long run, with many tosses, that is how one should wager on the next toss, if we know that the coin being tossed is not affected by any extraneous factors.

The Pascal-Fermat correspondence resulted in, among other things, establishment of the concept of edge as a factor in decision-making, an idea that has passed down through the centuries to mathematicians, physicists, actuaries … and Roy and Grant in that Seattle coffee shop.

I am much obliged to David Sklansky for turning me on to Pascal, who in his short life had original thoughts beyond the wildest imaginations of most of us – and who definitely wasn't collecting for that bookie back in Seattle.

Now I gotta go look up this Fermat guy …

Roy Cooke played winning professional poker for more than 16 years. He is a successful real estate broker/salesperson in Las Vegas. If you would like to ask Roy poker-related questions, you may do so online at www.UnitedPokerForum.com.