Chance and Wargames

One of the features of Bonaparte at Marengo that has excited the most comment is the chance-free method of resolving combat. Although it is not the first game to resolve combat without dice, cards or other randomizers, it is certainly one of a very small group of wargames to do so, which is why this aspect of the game has attracted so much attention.

It is not the point of this essay to defend the game against accusations that it doesn’t work: there is in fact a general consensus among players of the game that it does work, rendering such a defense redundant. It is also not the point of this essay to attack other games that use chance elements; although some games that use chance may not work well, so many do (and some work very well indeed) that a general attack on the practice would have to be considered absurd.

Rather than make a general attack or defense of the use of chance in wargames, the intent of this essay is to explore its role where it is used, the class of problems it is invoked to handle, and specifically, since wargames are simulations as well as games, what it is called upon to simulate.

Chance and Combat Resolution

The prototypical use of chance in wargames is as the final arbiter for resolving combat between opposing forces, and so it is here that the consideration of the problem will begin. There are two common types of combat methods used in wargames: the first is the “gang-bang” method, whereby multiple attacking pieces can combine their strengths against one or more defending pieces, with the relative strengths expressed as a ratio. In this method, the results of combat generally affect both sides. The second is the “roll-to-hit” method, whereby pieces make their attacks individually against (usually) a single defending piece and the results only affect the defending piece (in order to inflict losses on the attacker, the defender becomes the attacker in turn and carries out his own roll-to-hit attacks). As the summary of both would suggest, roll-to-hit is prone to substantially more die rolls to resolve a fight between some set of attacking and defending pieces than the gang-bang method. Interestingly, the fact that more die rolls are used represents not a greater role of chance in the design but a lesser role – the more statistically independent random events are generated, the more likely they are to average out (in statistics, this phenomenon is known as the regression to the mean). For this reason, it is a perverse truth that a game with a huge number of random events to resolve any particular question would be almost identical to a game with none at all.

The fact that all other things being equal, the amount of chance in wargames varies with the number of die rolls (the smaller the number of die rolls, the more probable that the result will differ from the statistical average) is itself interesting, particularly when considering that because larger scale games tend to have more pieces and more die rolls, they have less chance in them than smaller scale games with fewer pieces and fewer die rolls. The difficulty smaller games have with regard to their play balance being affected by a few lucky die rolls has long been noted (Avalon Hill’s old Africa Corps was infamous for the entire game tending to come down to a single die roll on a 2:1 attack on Tobruk), but the question about chance in combat being raised is not from a game balance but from a simulation perspective: just what is it that chance in combat resolution is simulating?

Chance and Simulation

It is singularly unhelpful to say that chance is used to simulate “chance”. While chance is currently recognized as part of modern physics at the level of quantum mechanics, it is probable that none of the wargames that have ever used chance have done so to simulate phenomena at that level. Above that level “chance” in wargames doesn’t simulate “chance” in the real world at all, but something else that is obscured rather than revealed by calling it “chance”.

To understand better what sort of answer is sought, let us imagine a game in which an “attack” represents a single shot fired by one man from one weapon against a “defense” consisting of a specific targeted location. In such a game, chance might be called on to represent to represent the state of the specific weapon (clean or dirty, close or far from the manufacturer’s specs, hot or cold, etc.), or the state of mind of the man firing the weapon, or wind conditions, or visibility. One interesting point is that all of the things on the above list might be simulated by chance in the game, but they might also be simulated by actual game mechanics: the game might have rules covering the state of the individual weapon, or the state of mind of the man firing the weapon, or wind, or visibility. In short chance can be seen as often nothing more than a catch-all for things that the game does not otherwise simulate: “chance” in the game represents not “chance” in some sense in the real world, but instead marks the limits of the simulation: the presence of chance may thus be a sign-post in the game that says “Simulation Stops Here”.

With this realization, it may seem that the search for what chance simulates is at a dead-end. Game designers have great freedom as to what they do and do not simulate, which seems to leave the question of what chance simulates as something that can only be reasonably considered on a game-by-game basis. What’s more, there is an even more profound reason for thinking that this might be the final answer: in representing the limits of what the designer chooses to simulate, it may also represent the limits of the designer’s knowledge; that it is a double-dead-end in that it represents not just what the designer knew about but chose to leave out, but what he didn’t even know about in the first place, and if the designer himself didn’t know what he (so to speak) left to chance, what hope do we have of figuring it out?

Both of these concerns, however, seem to be overly pessimistic. Game designers may have great freedom, but they are often attempting to do very similar things, under very similar constraints, and are often heavily influenced by what each other has done. The fact that we can make so many generalities about wargames that, if not completely true of all wargames, are nevertheless true for large numbers of them, speaks to this point. Further, even if the designers themselves are unaware of exactly what they are leaving out, that doesn’t mean that we necessarily have to give up hope of finding it, certainly in a generic if not specific sense. With these encouraging thoughts in mind, let us proceed to seek such insights as we can find while acknowledging in advance they will not be perfect. Having asserted that chance represents the limits of simulation, for example, we can proceed by consideration of what different types of limits may exist: the classification of different types of limits can also serve as a classification of different types of the use of chance.

Chance and Limits of Scale

We can observe that one limit that all wargames have in common is one of scale: each game represents both an analysis and a synthesis of its subject. As an analytic tool, it breaks it subject down into a number of smaller elements (converting an army into multiple pieces is an analysis of that army, for example), but it does not keep breaking down forever: eventually it stops breaking its subject down and by virtue of halting its analysis it instead performs acts of synthesis (for example, converting many individuals and items of equipment into a single piece). Thus, a game that can be said to analyze an army into regiment-level pieces can also be said to synthesize men into regiment-level pieces. With this in mind, we can see that chance can be used to represent a synthesis of elements below the game’s level of analysis in terms of scale. For example, in simulating an an artillery bombardment, a game may analyze that bombardment down to 15-minute blocks of time that an individual artillery battery spends firing, and use chance as part of simulating the synthesis of all the variations affecting individual guns firing individual rounds. From this, it can be seen that the previous conclusion that chance represents the limit of simulation is not true from the perspective of the designer: the categories of events which the designer assigns to chance and the possible outcomes and their probabilities are in fact a form of simulation, but they are synthetic rather than analytic simulation. The prior conclusion, however, remains true from the perspective of the player: he only participates in a simulation where it is analytic; in a synthetic simulation he is reduced to the level of observer.

Chance and Limits of Scope

Wargames, however, are not only limited in scale. Another important limit is one of scope. In one sense, the limit of scope is inverse of the limit of scale: the problem being the treatment of things that are above, as distinct from below, the game’s scale. For example, a game may simulate a battle analytically, but the battle has limits in terms of space, time, forces involved, and objectives. Many things are left unsimulated not because they are too small for the game but because they are too big: the world does not really stop at the edge of the battlefield. In some games, scope issues may directly affect the outcome even at the level of resolving individual attacks (air support may or may not show up, off-board artillery may or may not fire, etc.), but this is not the only (or even most common) way chance can be used to reflect limits of scope. One common use of chance as a scope limit is with regard to the natural world, particularly weather (weather can be simulated deterministically as well, but the advantages and disadvantages of such an approach is an interesting question that will be taken up later, in a different context). Another possible use of chance is with regard to force availability: what forces the players have available, both initially and during the game, may depend on chance as part of the game’s simulation of decisions and events outside the limits of the game (for example, an off-map battle may affect what reinforcements players receive and when they receive them). Still another possible use of chance is in terms of objectives: what the players are trying to achieve may depend on decision-makers above the player’s level or by events beyond the battlefield.

Chance and Limits of Control

Not all limits in wargames are limits of scale and scope. Another more subtle limit is the replacement of a multitude of decision makers in the real world (all with different goals, abilities, and knowledge) with a single decision maker in the game (the player). Below the game scale limit, simulation of this tends to fall into the general synthesis of individual attacks. Above the game scope, it can be represented by the methods described above. This problem, however, also exists within the game’s scale and scope limits. In the real world, the actions represented by fifty game pieces might be controlled by fifty different decision makers (even setting aside the even more numerous lower-level decision makers represented in the game by synthesis). Many games of course simply do not simulate this (particularly simple games) others simulate it through various restrictions but do not use chance methods, and still others include chance as part of the simulation. (As an aside, it is interesting to note that, the larger – and more “realistic” a game – is, the more grave this problem becomes: the game with 1000 pieces has replaced 1000 decision-makers with 1, whereas the game with 20 pieces has replaced only 20 decision-makers with 1.) The general effect of command-and-control rules (as rules dealing with this problem are known) is to reduce the control players have over their own pieces. The role of chance, where it is used, is part of this general reduction of control (for example, forcing a player to roll a die before he can carry out some action).

Chance and Limits of Knowledge

Still another simulation limit is the limit of knowledge. Interestingly, here the problem for simulations is that they do too much rather than too little: the problem isn’t the simulation of knowledge per se, but the simulation of the limits of knowledge. The most obvious form of this limit is knowledge of the opposing forces (the problem of limited intelligence), but the problem domain also embraces limits on knowledge of future events and even friendly forces. Limits on knowledge of friendly forces have only occasionally been implemented (typically through “green unit” rules where the strength of a piece is unknown to the player controlling it), but limits on knowledge of future events are implemented pervasively: explicitly in cases such as weather, where the goal is not to simulate historical weather, but to simulate the real-world lack of foreknowledge of weather, and implicitly in areas like combat, where chance (whatever synthetic simulation purpose it may also serve) keeps players from knowing in advance how attacks will come out. There is an interesting tension in historical games between the goal of simulating uncertainty and the goal of simulating history: in the area of weather, for example, some games will deterministically reproduce the historical weather while others have random weather; both are trying to be good simulations, but they are each forced to be a bad simulation of one thing in order to be a good simulation of the other.

An interesting aspect of the simulation of the limits of knowledge pertains to the choices available to achieve it. Regardless of the type of knowledge being limited, the simulation choices are the same: complexity (where knowledge is limited by the ability to understand), secrecy (where one player has knowledge that the other does not), and chance (where neither player has knowledge). Complexity as a factor in limiting knowledge is not the same as complexity in terms of rules but in terms of how easy it is to understand a situation and to know the consequences that an action might entail. However complex wargames may be in terms of their rules, they usually are not very complex in terms of the situations they present (it is generally much easier to understand the consequences of a move in a typical wargame than in a game like Chess or Go). Because of this, wargames have a surprisingly difficult time simulating limited knowledge through complexity alone, which leads to the next choice, secrecy. Secrecy is minimally present in all wargames in that each player has no knowledge of what the other player is thinking, although often that is the only way it is present. Use of secrecy in the game mechanics themselves is atypical, even though a substantial minority of wargames have used secrecy for decades (there are many reasons for this, but one common to wargames is the need to have different rules for different kinds of pieces, and those rules cause trust issues if the relevant information about the pieces is secret). Finally, we come to chance. While chance is sometimes used for no other purpose than to impose limits on knowledge, it more often is used for that purpose in combination with other purposes: for example, chance can be used in combat not only as part of the simulation of limits of scale but also for limits of knowledge is well: it is important that not only the chance results simulate the range of outcomes that a given event could produce, but that neither player knows those outcomes in advance.

Chance and Replay Value

Before concluding, it is well worth noting that there is another reason why chance is used in wargames that has nothing to do with simulation per se, and that is to increase the replay value of a game by using chance as an engine for increasing the variability of game play. In one sense, increasing the variability of game play is an end itself towards increasing the entertainment value of a game: the greater the variety of situations a game can present players, the more fresh challenges it can present to their skill. Beyond this, games face an additional special challenge as a form of entertainment: that of not being solvable, that is, of not devolving into puzzles which the players solve and then discard. It is interesting to note that the term players use for a game which has been solved is that it has been “broken”, a term which no doubt owes something to code-breaking but also reflects what has happened to the game as a game. A game is broken when players discover a single plan for one side that the other side cannot prevent from being executed (even with foreknowledge of it) that will result in one side almost always winning the game. Chance has always been an aid in avoiding this, although the number of “perfect plans” and broken games in the history of wargaming attests to its imperfect effectiveness.

Chance in Bonaparte at Marengo

Because this essay began with a discussion of Bonaparte at Marengo, it seems appropriate to end it by evaluating chance as it is used (and not used) in that game according to the categories of limits developed above: