The Book on Games of Chance: The 16th-Century Treatise on Probability

by Gerolamo Cardano, Samuel S. Wilks (Foreword), Sydney Henry Gould (Translator)

Mathematics was only one area of interest for Gerolamo Cardano ― the sixteenth-century astrologer, philosopher, and physician was also a prolific author and inveterate gambler. Gambling led Cardano to the study of probability, and he was the first writer to recognize that random events are governed by mathematical laws.
Published posthumously in 1663, Cardano's Liber de ludo aleae (Book on Games of Chance) is often considered the major starting point of the study of mathematical probability. The Italian scholar formulated some of the field's basic ideas more than a century before the better-known correspondence of Pascal and Fermat. Although his book had no direct influence on other early thinkers about probability, it remains an important antecedent to later expressions of the science's tenets.

Genres: Mathematics, History

64 pages, Paperback

First published December 16, 2015

About the author

He was born in Pavia, Lombardy, the illegitimate child of Fazio Cardano, a mathematically gifted lawyer, who was a friend of Leonardo da Vinci. In his autobiography, Cardano claimed that his mother had attempted to abort him. Shortly before his birth, his mother had to move from Milan to Pavia to escape the plague; her three other children died from the disease.
In 1520, he entered the University of Pavia and later in Padua studied medicine. His eccentric and confrontational style did not earn him many friends and he had a difficult time finding work after his studies had ended. In 1525, Cardano repeatedly applied to the College of Physicians in Milan, but was not admitted due to his reputation and illegitimate birth.
Eventually, he managed to develop a considerable reputation as a physician and his services were highly valued at the courts. He was the first to describe typhoid fever.
Today, he is best known for his achievements in algebra. He published the solutions to the cubic and quartic equations in his 1545 book Ars Magna. The solution to one particular case of the cubic, x3 + ax = b (in modern notation), was communicated to him by Niccolò Fontana Tartaglia (who later claimed that Cardano had sworn not to reveal it, and engaged Cardano in a decade-long fight), and the quartic was solved by Cardano's student Lodovico Ferrari. Both were acknowledged in the foreword of the book, as well as in several places within its body. In his exposition, he acknowledged the existence of what are now called imaginary numbers, although he did not understand their properties (Mathematical field theory was developed centuries later). In Opus novum de proportionibus he introduced the binomial coefficients and the binomial theorem.


Portrait of Cardano on display at the School of Mathematics and Statistics, University of St Andrews.
Cardano was notoriously short of money and kept himself solvent by being an accomplished gambler and chess player. His book about games of chance, Liber de ludo aleae ("Book on Games of Chance") , written in 1526, but not published until 1663, contains the first systematic treatment of probability, as well as a section on effective cheating methods. Cardano invented several mechanical devices including the combination lock, the gimbal consisting of three concentric rings allowing a supported compass or gyroscope to rotate freely, and the Cardan shaft with universal joints, which allows the transmission of rotary motion at various angles and is used in vehicles to this day. He studied hypocycloids, published in de proportionibus 1570. The generating circles of these hypocycloids were later named Cardano circles or cardanic circles and were used for the construction of the first high-speed printing presses.
He made several contributions to hydrodynamics and held that perpetual motion is impossible, except in celestial bodies. He published two encyclopedias of natural science which contain a wide variety of inventions, facts, and occult superstitions. He also introduced the Cardan grille, a cryptographic tool, in 1550.
Someone also assumed to Cardano the credit for the invention of the so called Cardano's Rings, also called Chinese Rings, but it is very probable that they are more ancient than Cardano.
Significantly, in the history of education of the deaf, he said that deaf people were capable of using their minds, argued for the importance of teaching them, and was one of the first to state that deaf people could learn to read and write without learning how to speak first. He was familiar with a report by Rudolph Agricola about a deaf mute who had learned to write.
Cardano's eldest and favorite son was executed in 1560 after he confessed to having poisoned his cuckolding wife. His other son was a gambler, who stole money from him. He allegedly cropped the ears of one of his sons. Cardano himself was accused of heresy in 1570 because he had computed and published the horoscope of Jesus in 1554. Apparen

Reviews

[Roberto Rigolin F Lopes · Rating 3 out of 5]

We are somewhere before 1578, Cardano is writing about his experiences with games of chance way before theory of probability was defined on rigorous terms. He was well read, aware of the perils of being a gambler even making references to Aristotle, Seneca and ancient games. But this is a short book where he lists the ratios for all probable outcomes with 2 and 3 dice. As a result, he concludes that the confidence one throws the dice has no influence on her/his luck. Dices are governed by pure chance but cards demand skills like memory and fast reasoning to predict future outcomes. But he doesn't go deep on card games. The fun here comes from his genuine struggle to understand chance. After reading this booklet, one should feel very lucky to be alive after clever people like Pascal, Fermat, Laplace and Kolmogorov.

[Peter Ypma · Rating 2 out of 5]

Een andere lezer zegt terecht "Na het lezen van dit boek ben je blij dat we geboren zijn nadat slimme mensen als Pascal, Fermat, Laplace en Kolmogorov geleefd hebben."
Qua wiskunde heb je dus weinig aan dit boek - al is het natuurlijk wel van historische waarde en grappig om te zien hoe moeilijk het kansbegrip voor een van de slimste 16de eeuwse wiskundigen te bevatten is.

[Kiril · Rating 3 out of 5]

Play is a very good test of a man’s patience or impatience. The greatest advantage in gambling comes from not playing at all. But there is very great utility in it as a test of patience, for a good man will refrain from anger even at the moment of rising from the game in defeat.

[Rick Sam · Rating 3 out of 5]

A short introduction to Gambling. I was more interested to know about Probabilities, it gives a basic introduction on gambling. He talks about dices and cards.

"Play is very good test of man's patience or impatience."

Deus Vult
-- Gottfried