Numbers Numbers

Mathematician vs. General

by Dana Lombardy

"Board wargames, for the most part, have beeb mathematical exercises in which the main point is to get more numbers against an opponent than he has. Terrain on the game board merely required more numbers to ouercome (or avoid). Objectives and conditions of victory were the end; the odds, the numbers versus numbers, the means to attaining them. Any theory of warfare, or combat, any evaluation of morale and weapons was reflected in numbers. "The best wargamers were not those who best understood warfare or combat, or who had the slightest idea what it was like to lead and direct men and material. Victory went to the best mathematician: he who had the patience and ability to apply the numbers he had so as to gain an adcantage ouer his opponent."

-- Dana Lombardy

This statement, though difficult to assess, was sent to several designers in the hope of inspiring comments. Below are some.

Michael McGuire of Simulation Design Group wrote:

I'd like to make one basic comment. Lombardy makes an accurate assessment of the state of board wargames. The games are mathematical exercises. Why? I think the reason can be traced back to one basic weakness in the board game concept. Seldom, if ever, do board games provide for "limited intelligence." In the normal play, player knows precisely where the enemy is and where the friendly forces are at all times. These games allow (unrealistically) 100 percent effectiveness in target acquisition and multiple-unit fire coordination. The vital areas of communication delays, morale, and "Acts of God" are not considered directly in the rules of play. The solution is simple. Players must be thrust into the darkness of the cloud of battle. Gamemasters or computers or both must be added to the foster the realism of uncertainty.

George Barna, one of our designers/playlesters, wrote:

In spite of what the "romantic" wargamer might feel, actual combat and board wargaming are related only in concept. To reduce the enemy and/or occupy key terrain by means of a strategic or tactical manoeuvre holds true on the battleffeld as well as on the battleboard, but dealing with human personalities, problems of the unknown, mass confusion, communication breakdowns and whatnot are nightmares only an actual commander can truly experience.

However, a good wargame is more than just an exercise in mathematics. Although numbers are the means by which an army is evaluated, it's up to the game designer to bring out with efficient design and pleasing aesthetic qualities a game that is not only playable, but one that reflects a "feel" of the actual battle or campaign being fought. I believe the most successful wargame, despite the use of numbers as an abstract means of evaluation, produced for the participants the feel of actually fighting the battle the game designer has set forth.

An interesting team present the following remarks. Leonard Kanterman and Douglas Bonforte, who will be publishing Cromwell for number 8 of Conflict, offered:

In order to render a situation suitable for re-creatlon on a map with cardboard units, quantification is necessary. The relative power of the units must be represented in some manner. We do face a major problem with quantification, however, and this is one we can attempt to correct. With the combat systems presently in use, quantification has resulted in excessive predictability of combat results. Too much information is available to a player; he knows too well how his units will perform in combat.

In our opinion, this is a direct consequence of reliance of most wargames on some sort of combat odds system. The biggest flaw of the odds system besides the laborious task of computing the odds and the unrealistic sharpness of the cutoff between the odds. 26 to 9 is only a 2/1, but add just one more factor and the attack becomes much more certain.Since a defender knows how strong his attacker can possibly be, by. ttacking rules, he can make his position "3/1 proof" in games like Stalingrad by placing a 7 instead of a 6 in a certain positions. Never in warfare were commanders able to place units with such certainty that one unit would hold while another would break, unless there was a gross difference in the quality of the units. The combat odds system, with its sharp distinctions, emphasizes and distorts differences between units.

.... The most obvious method to make battles less predictable is to conceal the strengths of the units before the battle occurs. In that way, an attacker cannot detail an absolutely predictable attack; rather, he must make "drives." This can be achieved by using inverted counters and dummy units, or a sort of matchbox system where a headquarters unit may conceal a certain limit of units. While this type of system does decrease the amount of information available to both sides to a more realistic level, it does not by itself eradicate the distortions of combat odds. The other problem with a system involving secrecy is that it eliminates solitaire play, which many wargamers rely on (due to isolation) or actually prefer (to emphasize the historical over the competitive aspects of the game)....

....In summary then, the mathematical aspects of wargames are necessary; but they don't have to rule the game. Under the combat odds system, it is true that the better mathematician will win; combat odds make situations too predictable, and predictability favors math. With a more detailed combat system -- especially one that involves choice on the tactical level -- certainty of information is removed, and tactical skill replaces math. A new dimension of suspense and excitement can be added to a game instead of tedious counting, multiplying, and dividing.

The final comments come from Professor C.L. Sayre, Jr. of the University of Maryland. Though by no means a "final conclusion" his remarks do shed some interesting light on the subject:

In all, I feel that game designers in the future will have to consider more than they have to date, new ideas and who will be playing their simulations. A combination of "thinking wild" and the "streamlining" of certain new ideas (e.g., the Combat Matrix, Atlanta command system, etc.) should help to get us out of our dependence upon numbers.

The question of whether a good game player learns to be a good strategist or tactician is largely philosophical and depends in a large measure on the motivation and attitude of the player. Hopefully, if the designer has done his homework (research and playtesting), the combat factors, movement factors, combat results tables and rules reflect hardware, organization, training, supply, morale, etc. Although it may be termed "wood pushing," the gamester is simply trying to improve upon history using the resources available to the original commander. He uses concentrations of troops and equipment (numbers), takes advantage of terrain (numbers), etc. in order to win. He may not recognize (or care to recognize) that, by trying to improve odds, he is doing those things which a good commander would try to do. Occasionally, a fluke occurs which permits some outrageous maneuver to win the game. I believe that this is due to faulty design, incomplete playtesting or because the designer had a preconceived notion of what should happen and failed to consider what could happen. Of course it can also be said that any game or any simulation is only an approximation to reality and must have some defects or shortcomings. In a well-conceived game the rules (and numbers) force the player into prudent and reasonable courses of action and prohibit or penalize stupid tactics. He may take chances, and he may have some luck with dice rolls; but a reckless disregard of probabilities will -- on the average -- end in disaster.

Certainly anyone who has played Afrika Korps recognizes the importance of supply to the Germans. Whether it is the gamester's desire to get those vital little pieces of cardboard or a lesson in military strategy is a matter of attitude. A player who wants to win (and knows when the game ends and what the victory conditions are) will play AK differently from a Rommel who has been abandoned by Hitler and has slim hope for reinforcement, withdrawal or survival.

I suspect that Grunt is unpopular, not because it is a bad game, but because of the frustration of the ARVN-US player slogging through jungle and rice paddies, turning up peasants and dummy counters, tense that the next discovery will be a booby trap or nest of VC. Whether USN teaches a strategic lesson about Guadalcanal or forces a game player to find a location to provide air cover for the eastern Coral Sea is a matter of interpretation.

There are some measures which can be taken to reduce the emphasis on numbers and numerical calculations. However, as long as the rules and victory conditions are unambiguous, as long as we quantify strength and movement, numbers will prevail -- on the average. We will be bound to numbers unless we shift to the "free kriegspiel" where we rely on the decisions of an umpire based on his judgment and experience (which is simply quantification of a different kind). One obvious way to divorce the gamester from his tedious calculations and comparisons is to place a time limit on the movement phase. We all recognize that two of the primary deficiencies of most games are unlimited intelligence and historical hindsight. Any game will take on new dimensions simply by fuming the counters upside down (Grunt, Franco-Prussian War, Wilderness, etc.). Reinforcement, replacement, and supply can be put on a probabilistic basis rather than a calendar schedule. This can be done so that each side knows his own schedule (but not the enemy) when the game begins, or one can let part or all of the schedule evolve a la Winter War and Verdun where events are triggered as the game progresses. The use of alternate scenarios requires the players to rely more on intuition and the general state of the situation rather than to concentrate on calculating every possible permutation and combination of movements and combats. The use of victory conditions which combine attrition and geographical (or other) objectives is more likely to promote good tactics or strategy than conditions which involve only one factor. The gamester is less likely to win on a fluke or technicality if he must attain different types of objectives.

Perhaps one of the most artificial ploys in many games is the use of the "soak off." Games which require combat by all adjacent units suffer the most. True, holding actions, rear guard actions, diversionary attacks and Banzai charges take place, but probably not in the numbers produced by the necessity to attack all adjacent units. Since most games permit the attacker to choose his attacks, it would require a complex set of rules to govern or limit his ability to "soak off."

One could also consider the effect that the soak off might have on the main troops and the performance of the unit which is sacrificed. In some cases the combat ability of the isolated unit might be enhanced, in other instances the morale would deteriorate. The main body might fight with increased vigor because of the sacrifice. The majority of troops might not know of the valiant effort and be unaffected. On the other hand, the van might only be contemplating that their turn would be next, and thus fight with less enthusiasm. Different commanders in different cultures or different eras would view the necessity of such sacrifices with a variety of attitudes.

One feature which is being proposed to improve realism which I feel adds complication without a concurrent improvement is simultaneous movement. Every combat or conflict situation is essentially action and reaction anyhow. The use of a mutual fire phase at the end of movement tends to minimize the "sitting duck" situation without overly complicating the mechanics.

In summary, if a "wood pusher" can win a well-designed, well-researched game without learning something about strategy or tactics, that is his fault, not a deficiency in the hobby. The hobby and the games mean different things to different people. Certainly there is no inherent stigma in considering the games as recreation and nothing else. No game (or even full scale troop maneuvers) can possibly encompass all the elements and aspects of command. Some games are better or more complete simulations than others. Just as the scientist may learn more from a laboratory experiment than from a textbook discussion of the same phenomenon, so can the game player and history buff recreate and relive (to some degree) conflicts in a more graphic way than from the pages of a book.


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© Copyright 1974 by Dana Lombardy
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