Dario De Toffoli - Blackjack: A Champions Guide

There are those who interpret games of chance as pure escapism, something to get a buzz. In some ways, studying probabilities, seeking to control chance and adopting the most rational behaviour at all times detracts from their legitimate amusement. This book is not for them, reading it would only spoil their fun.

We, however, believe, just as the great Pierre Simon de Laplace taught us in his unparalleled A Philosophical Essay on Probabilities, that probability is a tool that can bring us closer to the objective reality, where this is too complicated to be reconstructed and anticipated in rational terms.

Two centuries have passed since the first edition of the Essay was published (1812), but the power of his thought is still not common knowledge, newspapers still print criminal features recommending lottery numbers to unwary readers and there are still people who believe the Roulette ball has a memory of its own.

Laplace warns that we ought always in the conduct of life to make the product of the benefit hoped for, by its probability, at least equal to the similar product relative to the loss. But it is necessary, in order to attain this, to appreciate exactly the advantages, the losses and their respective probabilities. For this a great accuracy of mind, a delicate judgement, and a great experience in affairs is necessary; it is necessary to know how to guard ones self against prejudices, illusions of fear and hope, and erroneous ideas, ideas of fortune and happiness, with which the majority of people feed their self-love.

Well, its not always easy to follow Laplaces suggestions in real life; in fact its far too difficult to consistently make the best decisions without a general understanding of what is happening, why it is happening and what might happen. But in games of chance we can indeed get an idea of where were coming from, what were doing and even where we might go, that is, all the final situations in which we might find ourselves, each with its very own set of probabilities.

I certainly would not want to deny the ever decisive role of Lady Luck, but awareness of your behaviour leads to statistically better results, the pleasure of using reason and, whats more, protection from compulsivity.

Once upon a time, a friend of mine was playing Blackjack. And I was watching him. I noticed that on several occasions he did not follow the well-known tables that show the best way to behave in every game situation and I tactfully enquired why not. He was gobsmacked that I believed in those tables. According to him they were only distributed to condition players into playing to the dealers favour. No, no, much better to trust your instinct!

His reasoning is easily refuted on the basis that it certainly was not the casinos that distributed the tables, but whatever makes him happy.

Nevertheless, to better counter his argument, I began to consult publications on Blackjack. Dozens of them showed these mythical tables, but not a single one took the trouble to explain them. Sooner or later, I thought, Ill have to calculate them myself!

And the perfect opportunity arose a few years later, in the guise of Margherita Bonaldi, grappling with choosing a topic for a mathematics thesis on games of chance.

Can you suggest anything?

Yes absolutely! The tables for the Blackjack basic strategy need to be demonstrated. They need to be recalculated whilst clearly explaining how to proceed.

Ok, it sounds interesting.

Deal done. The professor accepted and thus the thesis Modelli probabilistici e strategie di comportamento nel gioco del blackjack (Probabilistic models and behaviour strategies in the game of Blackjack) was born. The language is for beginners as strictly demanded by the academic world but it had substance. At this point I had an idea, why not transform these preliminary calculations into an actual essay on Blackjack? There was no doubt that we had the opportunity to create an entirely new product, despite there already being a vast amount of material on the topic.

And that is precisely what we did. We analysed every game situation in detail and recalculated all the tables, explaining them every step of the way.

And dont panic, theyre all correct!

But for us the recalculations themselves were a fascinating mathematical adventure, a pleasure of the intellect.

What is more, we introduced the concept of the mathematical hope of every possible game situation; to borrow from Laplace, it is the product of the sum hoped for by the probability of obtaining it.