The Book on Games of Chance: The 16th-Century Treatise on Probability
64
The Book on Games of Chance: The 16th-Century Treatise on Probability
64Paperback
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Overview
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.
Product Details
| ISBN-13: | 9780486797939 |
|---|---|
| Publisher: | Dover Publications |
| Publication date: | 12/16/2015 |
| Series: | Dover Recreational Math |
| Pages: | 64 |
| Sales rank: | 1,148,365 |
| Product dimensions: | 6.00(w) x 8.90(h) x 0.40(d) |
About the Author
Sydney Henry Gould is a mathematician and author of Russian for the Mathematician.
Samuel S. Wilks (1906–64) was a mathematician who taught at Princeton and made significant contributions to the field of mathematical statistics.
Read an Excerpt
The Book on Games of Chance
The 16th-Century Treatise on Probability
By Gerolamo Cardano, Sydney Henry Gould
Dover Publications, Inc.
Copyright © 1961 Holt, Rinehart and Winston, Inc.All rights reserved.
ISBN: 978-0-486-80898-7
CHAPTER 1
On Kinds of Games
Games depend either on agility of body, as with a ball; or on strength, as with a discus and in wrestling; or on industriously acquired skill, as at chess; or on chance, as with dice and with knucklebones; or on both, as fritillus. Acquired ability may be of two kinds, as in games or in contests. Such a game is primero: for games of cards come under the same name as games of dice, since in ancient times cards were unknown, and for that matter, even the material they are made from. Evidence of this is the fact that men wrote on parchment hides, as of kids for example, and on Egyptian papyrus, on tablets, on wax, and on linden bark. The game is called primero because it holds a primary place among the games of chance, either because of its beauty or because it consists of four primary associations (as it were) which is the number of primary elements from which we (though not the whole world) are composed. Moreover, it has marvelous varieties.
CHAPTER 2On Conditions of Play
Attention must be given to the state of the player and of his opponent, and also to the conditions under which the game is played, such as the amount of money wagered, the place, and the occasion; for the latter is of such importance that permission has been given for gambling at funeral banquets. Thus there is a heading in the law books, "Funeral expenses and games of chance." At other times it has been condemned by the law, as in the Titian and Cornelian Laws.
But in times of great anxiety and grief, it is considered to be not only allowable, but even beneficial. Also, it is permitted to men in prison, to those condemned to death, and to the sick, and therefore the law also permits it in times of grief. For certainly, if any occasion will justify it, none is so worthy of excuse as this one. In my own case, when it seemed to me after a long illness that death was close at hand, I found no little solace in playing constantly at dice.
However, there must be moderation in the amount of money involved; otherwise, it is certain that no one should ever play. As for the excuse made by some that it relieves boredom, this would be better done by pleasant reading, or by narrating tales or stories, or by one of the beautiful but not laborious arts. Among these latter, playing the lute or the virginals, or singing, or composing poetry will be more useful, and for three reasons. First, because such a change from serious business is more praiseworthy than gambling, either since something is produced, as in the case of painting, or because it is according to nature, as in music, or because the man learns something, as in reading or hearing tales or stories. Second, it is not without its element of toil and so does not rob us, against our will, of more time than it should. And time, as Seneca has rightly said in his work on Length and Shortness of Life, is the most precious of all things. Third, such employment of leisure is more respectable and does not present a bad example, as gambling does, particularly to one's children and servants. To these facts must be added that gambling arouses anger and disturbs the mind, and that sometimes a quarrel flares up over money, a thing which is disgraceful, dangerous, and prohibited by law. Finally, one cannot gamble alone, whereas the above delights can be enjoyed even when we are by ourselves.
CHAPTER 3Who Should Play and When
So, if a person be renowned for wisdom, or if he be old and dignified by a magistracy or any other civil honor or by a priesthood, it is all the worse for him to play; on the other hand, gambling is proportionately less of a reproach to boys, young men, and soldiers. The greater the amount of money involved, the greater the disgrace; thus a certain holder of a very high priestly office (namely, a cardinal) was severely blamed because he played after dinner with the Duke of Milan for a stake of five thousand crowns.
This fault is particularly detestable in princes and is defended by no one except courtiers and flatterers of the prince, who do it either from fear or because they receive gifts if the prince is lucky. In the meantime his subjects are despoiled and the poor are deprived of the aid which has been assigned to them and which is their due. If a man is victorious, he wastes the money won by gambling, whereas if he suffers defeat, then either he is reduced to poverty, when he is honest and without resources, or else to robbery, if he is powerful and dishonest, or again to the gallows, if he is poor and dishonest. One's opponent, too, if he is a man of ill repute or of low station in life who is devoted to the game, is a source of disgrace, and of loss also. For if you play assiduously with men of this kind, you will come away a confirmed gambler; or otherwise you will be the loser because of their greater experience, trickery, and skill.
Your opponent should be of suitable station in life; you should play rarely and for short periods, in a suitable place, for small stakes, and on suitable occasions, as at a holiday banquet. Your opponent might be the king, or a prelate of outstanding character, or a relative by blood or by marriage. To play with professional gamblers is most disgraceful, and, as I have said, dangerous. The most respectable place is at home or at the house of a friend, where there can be no public scandal. Lawyers, doctors, and the like play at a disadvantage: for one thing, they appear to have too much leisure; for another, if they win, they seem to be gamblers, and if they lose, perhaps they may be taken to be as unskilful in their own art as in gaming. Men of these professions incur the same judgment if they wish to practice music.
CHAPTER 4The Utility of Play, and Losses
As advantages from well-managed play we obtain relaxation from anxiety and a pleasure from which we arise ready and eager for serious business; also knowledge of the character of our fellow-citizens for play is, as it were, a rack on which anger, greed, and honesty or dishonesty are made clear. For play both produces important evidence and is an actual torturer if the stakes are large. It is also a means of gaining friendship, and many have risen from obscurity because of the friendship of princes formed in play. This is what Cicero meant in his Philippic by the words "that fellow-player of yours, condemned for gambling."
But the losses incurred include lessening of reputation, especially if one has formerly enjoyed any considerable prestige; to this is added loss of time, vain words, including on occasion curses against the gods, the neglect of one's own business, the danger that it may become a settled habit, the time spent in planning after the game how one may recuperate, and in remembering how badly one has played. There are also disputes and often, which is worst of all, provocation to anger; for then a man is carried away into playing for high stakes and into feelings of enmity, so that he no longer has control of his own mind. As a result he throws out large sums of money and may be said to abandon them rather than play for them.
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.
CHAPTER 5Why I Have Dealt with Gambling
There are two reasons why I have considered it fitting for me to deal with gambling: first, on account of its useful features, for, since it is useful, there must also be need for giving a systematic account of that usefulness under various conditions, and pointing out exactly how great it is. Even if gambling were altogether an evil, still, on account of the very large number of people who play, it would seem to be a natural evil. For that very reason it ought to be discussed by a medical doctor like one of the incurable diseases; for in every evil there is a least evil, in every disgrace a least disgrace, in every infamy a least infamy, and similarly in loss of time and fortune. Second, it has been the custom of philosophers to deal with the vices in order that advantage might be drawn from them, as, for example, in the case of anger. Thus it is not absurd for me to discuss gambling, not in order to praise it (for I have known some writers to attempt this, but their efforts are vain and form a bad example; I have read books of this kind) but in order to point out the advantages in it, and, of course, also its disadvantages, in order that the latter may be reduced to a minimum.
CHAPTER 6The Fundamental Principle of Gambling
The most fundamental principle of all in gambling is simply equal conditions, e.g. of opponents, of bystanders, of money, of situation, of the dice box, and of the die itself. To the extent to which you depart from that equality, if it is in your opponent's favor, you are a fool, and if in your own, you are unjust. With respect to your opponent, if he is more powerful than you, or unscrupulous, or likely to be violent, or a man who hopes to win everything by creating sufficient delay, if he is given to complaint or litigation, or is clamorous, or deceitful, if he can disturb your equanimity by making you afraid or angry, then he is the worst man in the world for you; and to play with him is not to play but simply to lose your money.
And there is even greater danger to be feared from kibitzers, if they favor your opponent; and so it happens that, if you play in a large crowd of people, you can scarcely avoid folly if they are against you, or else injustice if they are for you. They can injure you in many ways: for example, by giving your opponent open advice and information, which is a twofold evil, since it not only helps their side but also provokes you to anger and disturbs you; for an angry man, as long as he is angry, is simply insane. Others will annoy you by their disorderly talk, even without giving definite information. Some will purposely consult you on serious business; some will even be so impudent as to provoke you to anger by quarreling with you; others will make fun of you in order to make you angry; others, more modest than these, will indicate to your opponent by foot or by hand that the decision he has made is not the right one; others again, a little farther off, will do this with a nod, perhaps with no other purpose, it may be, than to help him by filling your mind with suspicion. Still others will state falsely how the die has fallen; others again will worry you by accusing you of such things.
For all these reasons it is of the very greatest advantage to you to have your own supporters if you wish to win unjustly; and to play otherwise in the presence of a crowd is simply to waste your money, not to contend for it; for even if no trickery takes place, suspicion itself disturbs a man and makes him err, so that a suspicious man should not play. There is the same danger when your opponent seizes the die very quickly or moves his counters in such a way that you cannot see what he is doing or what the die has shown; and similarly if he plays with coins which are counterfeit, or debased, or excessively worn by water; or if the situation is one to cause fear, or if you are in a place of ill repute; and if the die is dishonest or if you are playing with a hanging dice box.
CHAPTER 7The Hanging Dice Box and Dishonest Dice
Set the round gaming boards in the middle; if they incline toward your opponent, then the dice box will incline in the opposite direction, and this is unfavorable to you. Similarly, if there is a slope toward you, then the box will be out of plumb in your favor; but if the dice box is not moved, then this does not matter. Similarly, if the board catches the light from the side opposite to you, then this is bad, since it disturbs your mind; on the other hand, it is to your advantage to have the board against a dark background. Again, they say it is of benefit to take up your position facing a rapidly rising moon.
As for the die itself, there are two sorts of danger. In the first place, every die, even if it is an acceptable one, has its favored side either because of its shape, or for some other reason, or by mere chance; and if in this way a large point is changed into a small one, or vice versa, you can readily understand how much of a difference it makes. In the second place, the die may be dishonest either because it has been rounded off, or because it is too narrow (a fault which is plainly visible), or because it has been extended in one direction by pressure on opposite faces. Consequently, it should receive a threefold testing, since there are three pairs of opposite faces which determine the surface to show uppermost. So these matters must be considered very carefully. There are even worse ways of being cheated at cards; these will be noted later on. In everything one must keep a watchful eye and take note of any disparity among the cards.
CHAPTER 8Conditions Under Which One Should Play
It is foolish to play even for small stakes for the mere purpose of being beaten because you do not notice what is going on; but it is also foolish to devote yourself entirely to gambling in order that you may win; for it is inevitable that he who plays more rarely should be less skilful. But should you therefore abandon all study of the arts in order that you may win at dice? And this only for small gain or even with the sole result of losing, and being angry at yourself and an object of scorn to others? And if you should lose a large amount, then certainly the gain to the victor is not so great as the loss to the loser; for usually he gives away a great deal; the man is wasteful and his time is lost; and when the die once falls unluckily for him, his loss may be greater than the net gain of many wins.
So you ought to be more skilful than your opponent, and more experienced, or else you ought to play in such a way that it does not matter how the die falls, as will be the case if you play for small stakes or with your loved ones for a short time after dinner. But if you are determined to play for large stakes, then play constantly with an opponent who is neither more experienced than yourself nor more fortunate, and let the conditions not be unlucky for you. For luck plays a very large part in these matters also.
CHAPTER 9On the Cast of One Die
The talus has four faces, and thus also four points. But the die has six; in six casts each point should turn up once; but since some will be repeated, it follows that others will not turn up. The talus is represented as having flat surfaces, on each one of which it lies on its back; it can be seen in this way and is therefore so depicted; in actual practice,however, it is not so, but boys spin it as though it were a spindle and it does not have the form of a die.
One-half of the total number of faces always represents equality; thus the chances are equal that a given point will turn up in three throws, for the total circuit is completed in six, or again that one of three given points will turn up in one throw. For example, I can as easily throw one, three, or five as two, four, or six. The wagers are therefore laid in accordance with this equality if the die is honest, and if not they are made so much the larger or smaller in proportion to the departure from true equality. But (as I have said) these facts contribute a great deal to understanding but hardly anything to practical play.
CHAPTER 10Why Gambling Was Condemned by Aristotle
But when we come to speak of the play itself and of actual gambling, which we will discuss below, I do not hold anyone blameless in this matter except those who play for money because of great grief of mind; and gambling is disgraceful because a man makes gain from his friend against that friend's will. For the case stands thus: gain from those who are both willing and aware is best; next best, is gain from those who are aware and unwilling. To the first class belong lawyers and doctors, and to the second merchants. The third kind is gain from those who, being aware but unwilling, are one's friends, as in gambling. The fourth kind is gain from those who are unwilling and unaware, as in gain by trickery. The fifth kind is gain from those who are unwilling and aware and not one's friends, as in robbery.
Aristotle gives another reason elsewhere when he says (4. Ethics,Chap. 1, in fin.) that gamblers, thieves, and robbers ply a sordid trade for they traffic in base gain; in fact they do everything for the sake of gain and thereby incur reproach. But thieves at least undergo great risks for their spoils, while gamblers gain from their friends to whom they ought rather to give. So both classes of men whose aim is to make gain where they ought not, traffic in base gain, and all such acquisitive acts are sordid. Moreover, a confirmed gambler is a perjurer and a blasphemer, and is at the same time prodigal and greedy; and if not so already by nature, he soon becomes irascible; he cherishes vain hopes in his idleness and he corrupts the youth.
(Continues...)
Excerpted from The Book on Games of Chance by Gerolamo Cardano, Sydney Henry Gould. Copyright © 1961 Holt, Rinehart and Winston, Inc.. Excerpted by permission of Dover Publications, Inc..
All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
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Table of Contents
Contents
Foreword,1 On kinds of games,
2 On conditions of play,
3 Who should play and when,
4 The utility of play, and losses,
5 Why I have dealt with gambling,
6 The fundamental principle of gambling,
7 The hanging dice box and dishonest dice,
8 Conditions under which one should play,
9 On the cast of one die,
10 Why gambling was condemned by Aristotle,
11 On the cast of two dice,
12 On the cast of three dice,
13 On composite numbers up to six and beyond and for two and three dice,
14 On combined points,
15 On an error which is made about this,
16 On card games,
17 On frauds in games of this kind,
18 Customary conventions in primero,
19 On the diversity of points or numbers in primero,
20 On luck in play,
21 On timidity in the throw,
22 On the twofold division of games,
23 On card games in which there is occasion for trained skill,
24 On the difference between play with cards and play with dice,
25 On card games,
26 Do those who teach also play well?,
27 Is there some element apart from skill which plays a role in the exercise of skill?,
28 On far-reaching plans, judgment, and procedure [in backgammon],
29 On the character of players,
30 On games of chance among the ancients,
31 On play with knucklebones,
32 Conclusion of the work,