Games of Skill.A considerable time after the translation of Menabrea’s memoir had been published, and after I had made many drawings of the Analytical Engine and all its parts, I began to meditate upon the intellectual means by which I had reached to such advanced and even to such unexpected results. I reviewed in my mind the various principles which I had touched upon in my published and unpublished papers, and dwelt with satisfaction upon the power which I possessed over mechanism through the aid of the Mechanical Notation. I felt, however, that it would be more satisfactory to the minds of others, and even in some measure to my own, that I should try the power of such principles as I had laid down, by assuming some question of an entirely new kind, and endeavouring to solve it by the aid of those principles which had so successfully guided me in other cases.〈GAMES OF SKILL CAN BE PLAYED BY AN AUTOMATON.〉After much consideration I selected for my test the contrivance of a machine that should be able to play a game of purely intellectual skill successfully; such as tit-tat-to, drafts, chess, &c.I endeavoured to ascertain the opinions of persons in every class of life and of all ages, whether they thought it required human reason to play games of skill. The almost constant{466}answer was in the affirmative. Some supported this view of the case by observing, that if it were otherwise, then an automaton could play such games. A few of those who had considerable acquaintance with mathematical science allowed the possibility of machinery being capable of such work; but they most stoutly denied the possibility of contriving such machinery on account of the myriads of combinations which even the simplest games included.On the first part of my inquiry I soon arrived at a demonstration that every game of skill is susceptible of being played by an automaton.Further consideration showed that ifany positionof the men upon the board were assumed (whether that position were possible or impossible), then if the automaton could make the first move rightly, he must be able to win the game, always supposing that, under the given position of the men, that conclusion were possible.Whatever move the automaton made, another move would be made by his adversary. Now this altered state of the board isoneamongst themany positionsof the men in which, by the previous paragraph, the automaton was supposed capable of acting.Hence the question is reduced to that of making the best move under any possible combinations of positions of the men.Now the several questions the automaton has to consider are of thisnature:—1. Is the position of the men, as placed before him on the board, a possible position? that is, one which is consistent with the rules of the game?2. If so, has Automaton himself already lost the game?3. If not, then has Automaton won the game?{467}4. If not, can he win it at the next move? If so, make that move.5. If not, could his adversary, if he had the move, win the game.6. If so, Automaton must prevent him if possible.7. If his adversary cannot win the game at his next move, Automaton must examine whether he can make such a move that, if he were allowed to have two moves in succession, he could at the second move havetwodifferent ways of winning the game;and each of these cases failing, Automaton must look forward to three or more successive moves.Now I have already stated that in the Analytical Engine I had devised mechanical means equivalent to memory, also that I had provided other means equivalent to foresight, and that the Engine itself could act on this foresight.〈NUMBER OF THE COMBINATIONS.〉In consequence of this the whole question of making an automaton play any game depended upon the possibility of the machine being able to represent all the myriads of combinations relating to it. Allowing one hundred moves on each side for the longest game at chess, I found that the combinations involved in the Analytical Engine enormously surpassed any required, even by the game of chess.〈GAME OF TIT-TAT-TO.〉As soon as I had arrived at this conclusion I commenced an examination of a game called “tit-tat-to,” usually played by little children. It is the simplest game with which I am acquainted. Each player has five counters, one set marked with a+, the other set with an 0. The board consists of a square divided into nine smaller squares, and the object of each player is to get three of his own men in a straight{468}line. One man is put on the board by each player alternately. In practice no board is used, but the children draw upon a bit of paper, or on their slate, a figure like any of the following.The successive moves of the two players may be represented asfollow:—In this case + wins at the seventh move.The next step I made was to ascertain what number of combinations were required for all the possible variety of moves and situations. I found this to be comparatively insignificant.I therefore easily sketched out mechanism by which such an automaton might be guided. Hitherto I had considered only the philosophical view of the subject, but a new idea now entered my head which seemed to offer some chance of enabling me to acquire the funds necessary to complete the Analytical Engine.It occurred to me that if an automaton were made to play this game, it might be surrounded with such attractive circumstances that a very popular and profitable exhibition might be produced. I imagined that the machine might consist of the figures of two children playing against each other, accompanied by a lamb and a cock. That the child who won the game might clap his hands whilst the cock was crowing, after which, that the child who was beaten might cry and wring his hands whilst the lamb began bleating.I then proceeded to sketch various mechanical means by which every action could be produced. These, when compared with those I had employed for the Analytical Engine,{469}were remarkably simple. A difficulty, however, arose of a novel kind. It will have been observed, in the explanation I gave of the Analytical Engine, that cases arose in which it became necessary, on the occurrence of certain conditions, that the machine itself should select one out of two or more distinct modes of calculation. The particular one to be adopted could only be known when those calculations on which the selection depended had been already made.〈DIFFICULTY ARISING FROM CHOICE.〉The new difficulty consisted in this, that when the automaton had to move, it might occur that there were two different moves, each equally conducive to his winning the game. In this case no reason existed within the machine to direct his choice: unless, also, some provision were made, the machine would attempt two contradictory motions.The first remedy I devised for this defect was to make the machine keep a record of the number of games it had won from the commencement of its existence. Whenever two moves, which we may call A and B, were equally conducive to winning the game, the automaton was made to consult the record of the number of the games he had won. If that number happened to be even, he was directed to take the course A; if it were odd, he was to take the course B.If there were three moves equally possible, the automaton was directed to divide the number of games he had won by three. In this case the numbers 0, 1, or 2 might be the remainder, and the machine was directed to take the course A, B, or C accordingly.It is obvious that any number of conditions might be thus provided for. An inquiring spectator, who observed the games played by the automaton, might watch a long time before he discovered the principle upon which it acted. It is also worthy of remark how admirably this illustrates{470}the best definitions of chance by the philosopher and thepoet:—“Chance is but the expression of man’s ignorance.”—LAPLACE.“All chance, design ill understood.”—POPE.〈EXHIBITION OF AUTOMATON.〉Having fully satisfied myself of the power of making such an automaton, the next step was to ascertain whether there was any probability, if it were exhibited to the public, of its producing, in a moderate time, such a sum of money as would enable me to construct the Analytical Engine. A friend, to whom I had at an early period communicated the idea, entertained great hopes of its pecuniary success. When it became known that an automaton could beat not merely children but even papa and mamma at a child’s game, it seemed not unreasonable to expect that every child who heard of it would ask mamma to see it. On the other hand, every mamma, and some few papas, who heard of it would doubtless take their children to so singular and interesting a sight. I resolved, on my return to London, to make inquiries as to the relative productiveness of the various exhibitions of recent years, and also to obtain some rough estimate of the probable time it would take to construct the automaton, as well as some approximation to the expense.It occurred to me that if half a dozen were made, they might be exhibited in three different places at the same time. Each exhibitor might then have an automaton in reserve in case of accidental injury. On my return to town I made the inquiries I alluded to, and found that the English machine for making Latin verses, the German talking-machine, as well as several others, were entire failures in a pecuniary point of view. I also found that the most profitable exhibition which had occurred for many years was that of the little dwarf, General Tom Thumb.{471}On considering the whole question, I arrived at the conclusion, that to conduct the affair to a successful issue it would occupy so much of my own time to contrive and execute the machinery, and then to superintend the working out of the plan, that even if successful in point of pecuniary profit, it would be too late to avail myself of the money thus acquired to complete the Analytical Engine.
A considerable time after the translation of Menabrea’s memoir had been published, and after I had made many drawings of the Analytical Engine and all its parts, I began to meditate upon the intellectual means by which I had reached to such advanced and even to such unexpected results. I reviewed in my mind the various principles which I had touched upon in my published and unpublished papers, and dwelt with satisfaction upon the power which I possessed over mechanism through the aid of the Mechanical Notation. I felt, however, that it would be more satisfactory to the minds of others, and even in some measure to my own, that I should try the power of such principles as I had laid down, by assuming some question of an entirely new kind, and endeavouring to solve it by the aid of those principles which had so successfully guided me in other cases.
〈GAMES OF SKILL CAN BE PLAYED BY AN AUTOMATON.〉
After much consideration I selected for my test the contrivance of a machine that should be able to play a game of purely intellectual skill successfully; such as tit-tat-to, drafts, chess, &c.
I endeavoured to ascertain the opinions of persons in every class of life and of all ages, whether they thought it required human reason to play games of skill. The almost constant{466}answer was in the affirmative. Some supported this view of the case by observing, that if it were otherwise, then an automaton could play such games. A few of those who had considerable acquaintance with mathematical science allowed the possibility of machinery being capable of such work; but they most stoutly denied the possibility of contriving such machinery on account of the myriads of combinations which even the simplest games included.
On the first part of my inquiry I soon arrived at a demonstration that every game of skill is susceptible of being played by an automaton.
Further consideration showed that ifany positionof the men upon the board were assumed (whether that position were possible or impossible), then if the automaton could make the first move rightly, he must be able to win the game, always supposing that, under the given position of the men, that conclusion were possible.
Whatever move the automaton made, another move would be made by his adversary. Now this altered state of the board isoneamongst themany positionsof the men in which, by the previous paragraph, the automaton was supposed capable of acting.
Hence the question is reduced to that of making the best move under any possible combinations of positions of the men.
Now the several questions the automaton has to consider are of thisnature:—
and each of these cases failing, Automaton must look forward to three or more successive moves.
Now I have already stated that in the Analytical Engine I had devised mechanical means equivalent to memory, also that I had provided other means equivalent to foresight, and that the Engine itself could act on this foresight.
〈NUMBER OF THE COMBINATIONS.〉
In consequence of this the whole question of making an automaton play any game depended upon the possibility of the machine being able to represent all the myriads of combinations relating to it. Allowing one hundred moves on each side for the longest game at chess, I found that the combinations involved in the Analytical Engine enormously surpassed any required, even by the game of chess.
〈GAME OF TIT-TAT-TO.〉
As soon as I had arrived at this conclusion I commenced an examination of a game called “tit-tat-to,” usually played by little children. It is the simplest game with which I am acquainted. Each player has five counters, one set marked with a+, the other set with an 0. The board consists of a square divided into nine smaller squares, and the object of each player is to get three of his own men in a straight{468}line. One man is put on the board by each player alternately. In practice no board is used, but the children draw upon a bit of paper, or on their slate, a figure like any of the following.
The successive moves of the two players may be represented asfollow:—
In this case + wins at the seventh move.
The next step I made was to ascertain what number of combinations were required for all the possible variety of moves and situations. I found this to be comparatively insignificant.
I therefore easily sketched out mechanism by which such an automaton might be guided. Hitherto I had considered only the philosophical view of the subject, but a new idea now entered my head which seemed to offer some chance of enabling me to acquire the funds necessary to complete the Analytical Engine.
It occurred to me that if an automaton were made to play this game, it might be surrounded with such attractive circumstances that a very popular and profitable exhibition might be produced. I imagined that the machine might consist of the figures of two children playing against each other, accompanied by a lamb and a cock. That the child who won the game might clap his hands whilst the cock was crowing, after which, that the child who was beaten might cry and wring his hands whilst the lamb began bleating.
I then proceeded to sketch various mechanical means by which every action could be produced. These, when compared with those I had employed for the Analytical Engine,{469}were remarkably simple. A difficulty, however, arose of a novel kind. It will have been observed, in the explanation I gave of the Analytical Engine, that cases arose in which it became necessary, on the occurrence of certain conditions, that the machine itself should select one out of two or more distinct modes of calculation. The particular one to be adopted could only be known when those calculations on which the selection depended had been already made.
〈DIFFICULTY ARISING FROM CHOICE.〉
The new difficulty consisted in this, that when the automaton had to move, it might occur that there were two different moves, each equally conducive to his winning the game. In this case no reason existed within the machine to direct his choice: unless, also, some provision were made, the machine would attempt two contradictory motions.
The first remedy I devised for this defect was to make the machine keep a record of the number of games it had won from the commencement of its existence. Whenever two moves, which we may call A and B, were equally conducive to winning the game, the automaton was made to consult the record of the number of the games he had won. If that number happened to be even, he was directed to take the course A; if it were odd, he was to take the course B.
If there were three moves equally possible, the automaton was directed to divide the number of games he had won by three. In this case the numbers 0, 1, or 2 might be the remainder, and the machine was directed to take the course A, B, or C accordingly.
It is obvious that any number of conditions might be thus provided for. An inquiring spectator, who observed the games played by the automaton, might watch a long time before he discovered the principle upon which it acted. It is also worthy of remark how admirably this illustrates{470}the best definitions of chance by the philosopher and thepoet:—
“Chance is but the expression of man’s ignorance.”—LAPLACE.“All chance, design ill understood.”—POPE.
“Chance is but the expression of man’s ignorance.”—LAPLACE.
“All chance, design ill understood.”—POPE.
〈EXHIBITION OF AUTOMATON.〉
Having fully satisfied myself of the power of making such an automaton, the next step was to ascertain whether there was any probability, if it were exhibited to the public, of its producing, in a moderate time, such a sum of money as would enable me to construct the Analytical Engine. A friend, to whom I had at an early period communicated the idea, entertained great hopes of its pecuniary success. When it became known that an automaton could beat not merely children but even papa and mamma at a child’s game, it seemed not unreasonable to expect that every child who heard of it would ask mamma to see it. On the other hand, every mamma, and some few papas, who heard of it would doubtless take their children to so singular and interesting a sight. I resolved, on my return to London, to make inquiries as to the relative productiveness of the various exhibitions of recent years, and also to obtain some rough estimate of the probable time it would take to construct the automaton, as well as some approximation to the expense.
It occurred to me that if half a dozen were made, they might be exhibited in three different places at the same time. Each exhibitor might then have an automaton in reserve in case of accidental injury. On my return to town I made the inquiries I alluded to, and found that the English machine for making Latin verses, the German talking-machine, as well as several others, were entire failures in a pecuniary point of view. I also found that the most profitable exhibition which had occurred for many years was that of the little dwarf, General Tom Thumb.{471}
On considering the whole question, I arrived at the conclusion, that to conduct the affair to a successful issue it would occupy so much of my own time to contrive and execute the machinery, and then to superintend the working out of the plan, that even if successful in point of pecuniary profit, it would be too late to avail myself of the money thus acquired to complete the Analytical Engine.