(continued from last month)  The hazards of the enterprise are that the convoy might be ambushed by the enemy, who is supposod to be so limited in strength that he could only afford to patrol one of the two roads. The officers planning the expedition have to recognise that on the good road there would be some chance of driving right through an ambush, and on the bad road the convoy might break down. Without mathematical analysis, the planning officers might easily fall into traps in this situation. For For example, they could quickly conclude that for the convoy the most threatening circumstances would be one in which both the convoy and the ambushing party had chosen the bad road, for then there would be an ambush and very little chance of escape. So, it might be argued, should we not send the convoy on the good road all the time, and hope for speed and good luck? A little reflection should show - perhaps even before the convoy had left - that this was a false position. For, the planning staff should recall, if the enemy has access to my informmion, surely he will realise that I will choose the good roads and surely he will send his ambush party there? So, perhaps, the convoy might be sent on the bad road at the last minute, and only after it had been the officers responsible be filled with doubts about their venture: might not the other fellow have banked on an attempt at bluff? On papar at least, games theory is well suited to analysis like these. In fact the idual solution is that the choice of road should be left to chance, with the only proviso that over a period of time (assuming that the convoy had to traval every night, for instance) that the number of times the good road is chosen should stand in a fixed ratio to the number of times the bad road is chosen, and that this ratio shoald be determined in a simple fashion by the estimates made of the chance of driving through a convoy, or the chance of a breakdown on the bad road. One of the important features of this analysis is that it provides a prescription for the strategy which ought to be adopted by both opponents. It turns out, for instance, that the ambusher should picket the two roads with different frequency. Another inference from this exampie is that it does not matter whether the opponents disclose their general strategic plans to each other, so long as they do not say just which road they plan to use or to picket on some particular night. Situations as simple as these can be analysed without difficulty: they are not, after all, more difficult than problems involving gambling and loaded dice. But from the anslysis of these and more complicated prblems, numbers of general propositions have by now emerged. We've been able to recognize those games whose rules permit one opponent to always force a draw, or to do so if he has the first move. In other games, the tsarting player can always win if he adopts the correct strategy. In still others, the rules of a game entail an oscillary phenomenom in which the tide of battle flows one way and then the other. In more general terms, games theory has turned up the common observation that in most ghames there are more different strategies than there are moves to be made. In numerical terms, it's calculated that there's roughly a million ways for a player to draw up a general plan of strategy to guide his play of noughts and crosses, even though there are merely 15,000 ways in whichi the game itself may be played. By the same test, the number of strategic plans upon which chess may be played is almost literally astronomical -- even though some of these plan would be bad. It is plain that the hearing of this type of analysis on the concept of political affairs must be, at bast, indirect. For example, the analysis of the problem of choosing a road for the military convoy, and of other similar problems, may demonstrate that no harm is done by letting the enemy know what general strategic plan may be. But in practice it is difficult to be sure that the same conclusions would be reached by a thorough - and impractical - analysis of any real world cituation. In these circumsytances, game thery can only be an unimportant guide to action. Indeed, one of the general conclusions of game theories seems to provide a hint of a more general importence, for the discovery that even artifically constructed gamos require a choice to be made between a very large number of alternative strategies is a warning that mathematical analysis properly applied will often only be able to emphasise the complexity of the situations. In practice this incapacity of games theory and its attendant skills to provide strategies for action in the real world is accentuated by the difficulty of assessing the psychological factors which help to determine the play even of the better games. Yet experience of such games as bridge suggests that the bidding temperment of partners and their opponents is at least as distinct a factor to be reckoned with as their skill with cards. It is of course no wonder that in real situations such factors as the temperment of the opposing nations should seem to be important. While mathematical analysis may provide valuable stimulation for people engaged in the detailed planning of military operations, it seems that it has very little to offer those whose concern is with the broad conduct of conflicts. Yet unfortunatoly it is in exactly this field that games theory has attracted most attention. A part of the reason for this is the notoriety received by such things as the Rand Corporation's study of the circumstunces in which surrender would be better than fighting. But if games theory can lead to such a study, may it also not to the study of circumstances in which war might be the best policy? This is the nub of complaints that have been made against games theorists. As it stands, it is an unrealistic charge, for there is no reason why abstract studies should not be made. The difficulty is that once caluclations have been made, there will be attempts to use them to guide real policy. Among recents attempts to do so should be included Dr. Herman Kahn's recent book called On Thermonuclear War which purports to be a reational policy to ensure the survival of at least some of the human race should there be a war. With this an other related pronouncements readers tend to think the author would wish to have his theories checked against facts. The games, it seems, are often too beguiling. Back to Table of Contents -- Wargamer's Newsletter # 25 To Wargamer's Newsletter List of Issues To MagWeb Master Magazine List © Copyright 1964 by Donald Featherstone. This article appears in MagWeb.com (Magazine Web) on the Internet World Wide Web. Other articles from military history and related magazines are available at http://www.magweb.com