## Discussion on Dr. E. Slater's Paper on *Statistics for the Chess Computer and the Factor of Mobility*

DR. D. K. C. MACDONALD

In so far as a mental analysis of the feasibility of a machine to "play" Chess say assist us to decide more clearly what true constructive thought is and whether brains *in principle* are different from machines, I wholeheartedly support such work. I feel however that the actual construction of such a machine in all its relatively vast complexity ‑ apart from personal satisfaction which it may provide ‑ is of dubious value. To me, the purpose of Shannon's paper in Phil. Mag. was the analytical demonstration that a machine could simulate a process normally regarded as essential "brainy" ‑ not that one should therefore make one. I am reminded that Professor Simon once remarked to me that one could presumably make a machine that would smoke tobacco ‑ *cui bono*?

DR F. L. STUMPERS

I agree with Dr. MacDonald that the construction of a chess‑machine in itself is of doubtful value. I discussed Dr. Shannon's paper with Dr. Euwe, former world‑champion and mathematician and we thought that it was doubtful whether even this complicated machine would play a really good game of chess (better than an average club‑player). It is very difficult to see what inferences can be drawn from Dr. Slater's interesting statistical analysis. To stress the mobility too much would bring us back to the classical school in chess (Tarrasch). In the 1920's, e.g. Réti, Euwe, Alekhine have shown that mobility and space also give a great responsibility. The Indian games rose in popularity and Alekhine played his defence in which a knight moves over the board without any increase in mobility for his side. However, when many other things are taken into account, mobility is also of importance.

MR. A. M. TURING

I wish to make two points concerning Dr. Slater's paper. I was greatly interested by the statistics provided, but fear that some people might draw invalid conclusions from them. It might for instance be thought that a good way of playing is to maximise one's mobility at one's next move, or perhaps to minimise that of one's opponent at his next move but one. It is evidently not feasible to foresee mobilities many moves ahead. Although the immediate mobility is a useful measure of the relative advantage of the players in normal play it by no means follows that it is wise to direct one's play to maximising such a measure. To do so would be like taking a statistical analysis of the laundry of men in various positions and deciding, from the data collected, that an infallible method of getting ahead in life was to send a large number of shirts to the wash each week.

I wish also to put forward a plea for a more experimental approach to chess machines. A more raalistic attitude to these machines can be reached by making them than. by talking about them. There are three forms which a chess machine might take.

(a) Special machines built to play chess and for no other purpose.

(b) A digital computer programed as a chess machine

(c) Paper machines

The special machines I do not recommend. They would be too much trouble and Dr. MacDonald's comparison with a 'smoking machine' is very apt in connection with them. To programme a computer would be more rewarding, but not everyone has a computer. I wish however to recommend the 'per chess machines' to the symposium. By making such a machine I mean laying down a definite set of rules governing play and then obeying them, or in other words 'programming. oneself as a chess machine'. Anyone can do this; the only apparatus required is board and men, and perhaps pencil and paper. Both Dr. Shannon and I have many others. I recommend it as easy, instructive and entertaining. Similar experiments can be made with 'paper learning machines'.

DR I. J GOOD

I agree with Dr. Turing that mobility by itself is not enough. It seems not to take sufficiently into account the essential difference between strategy and tactics. I am reminded of the alleged motto of the Hampstead Chess Club: 'Never miss a check, ‑ it might be mate'. Mobility may be sufficient evaluation of a position for strategic purposes, but it does not allow sufficiently for tactics, i.e. combinational play or forced variations. A good chess machine would have to analyse all forceful variations, with a suitable definition of a forceful variation. This fact has almost certainly been recognised by Dr. Shannon and others. The definition of the forcefulness of a move would have topend partly on the difference between the strengths of an attacked piece and the attacking piece.

The analysis of the forceful variations in any given position would be a stochastic branching process, and the end‑points of the corresponding tree would be quiescent positions which would need strategic evaluation (e.g. by means of a measure of mobility). The total time taken to cope with such a tree would be roughly proportional to the number of individuals in this tree, and it is known that the probability distribution of this number is extremely skew. (See, for example, *Prop. Cam Phil Soc*. 45 (1949) 360‑3.). The time taken to analyse a position might be anything from 0.1 seconds to 100 years. There would therefore be a danger of the machine getting into time‑trouble. It would be advisable in fact for the machine to take into account the state of its chess clock. It would then modify its definition of the threshold forcefulness of a move. In other words the programme would contain a parameter, τ which would say how forceful a move must be in order to be examined as a sub‑variation i.e. it determines whether a position is quiescent; and τ would increase when the machine was short of time. Alternatively τ might be an increasing function of the number of moves 'deep' of any analysis (i.e. a function of the generation number in the tree mentioned before).

A really clever machine would also take into account the state of its opponent's clock. The machine might move faster when its opponent was in time trouble in order to give its opponent less time to think.

DR E. SLATER (in reply)

Dr. Good's remarks seemed to me important and wry much to the point. I am sorry if I gave the impression that tactical considerations were of little significance; they would have to be taken full account of in prograrrming the computer, and some method would have to be devised for making the machine sensitive to threats so that it would analyse forcing variations to a depth of five or six moves or more. The control of the time factor is a most interesting suggestion. Dr. Turing's argument by analogy from what a naive laundry worker might conclude about ways of becoming rich really amounts to the suggestion that strategic advantage is the cause rather than the product of an advantage in mobility. I do not think that this can be accepted. An advantage in mobility usually appears in a game a number of moves before strategic advantage is detectable in other ways; it seems to be an essential aspect of what chess-players understand by "development"; and it supplied the decisive criterion of winning or losing. The relegation of mobility to a place of almost trifling importance by the modern school of players, following the work of Réti, to which Dr. Stumpers has referred, has, of course, been an interesting evolutionary change in the style of the game; but one does not have to regard it as final. There are such things as fashions in chess as in other fields into which an element of intuitive appreciation enters. The final, or rather the first question, which is raised by Dr. MacDonald, namely whether this whole discussion is not so much beating of the air, is to some extent one to which there is no answer. In so far as a present answer can be given, that has already been done by Shannon in the introductory paragraphs of his paper. The real answer would appear only afters such a hypothetical chine had been built. To the general implication of Professor Simon's witticism one might reply with Faraday's classic retort: "What is the good of a new‑born baby?"