Operational Design in Wargaming Chapter 3 - What's in a roll?

“Circumstances vary so enormously in war, and are so indefinable, that a vast array of factors has to be appreciated in the light of probabilities alone. The man responsible for evaluating the whole must bring to task the quality of intuition that perceives the truth at every point. Otherwise a chaos of opinions and consideration would arise, and fatally entangle judgment.” -Clauswitz

This is either really good or really bad, depending on your rules.

The one unifying feature of wargames is the need to manage uncertainty.  At the end of the day, we want a method to inject random probability in order to validate our tactical decisions and interpretations of historical events.  (If we are honest with ourselves we must admit that the primary purpose of that roll is to provide the kinesthetic feedback and dopamine rush that adds excitement to the game.) As such most rule systems can be broken down into two categories:  Fist full of dice or single roll results.   But what do these die rolls really mean?

I think many rule systems run into trouble from the outset because they approach the design mechanism from the wrong angle.  Instead of  form follows function, (i.e. how do I want to break down probabilities?), they start at which die should I use?  The invariable answer always seems to be the D6. (Würfel Uber Alles!)  We seem obsessed with cubes and the outcomes they provide.  I have met many gamers who simply don't trust or like games that use alternative polyhedrons.  In this case we have to admit that we are letting personal preference for dice influence the entire game and settle for outcomes accordingly.

I have seen many clever rules mechanics, but they all tend to center around manipulating cubes.  For example, the designers of Warhammer wanted to incorporate the D20 mechanic from D&D, but stick with D6s.  This resulted in a system where a models throws a D6 to hit, followed by a D6 to wound, ending with the opponent throwing a D6 to save.  Thus the game manages the probabilities by adding or subtracting modifiers from each roll, rather than dealing with a cumulative effect. Allowing the opponent to make a saving throw gives them a way to interact in the event rather than sit a be a victim of another person's luck. The dice essentially bring a modicum of gambling into the game, and thus introduce three challenges common to gamblers into the design.
  • Availability heuristic -(the tendency of individuals to overestimate the probability of an occurrence simply because it comes readily to mind.)   We have all read about famous events in history that establish precedent for a necessary game mechanic or roll modifier.  However, I would argue that many of the events we read about were written down specifically because they were exceptional and thus worth reporting.   
  • Gambler’s fallacy -thinking that future events occurring in a random sequence will be influenced by past events.  I've rolled a lot of 6's, my luck is sure to change!
  • Illusion of controlAlthough directed by chance, we believe that we have some amount of control over the outcome.  Let's nudge the outcomes in a certain direction, so why not add a modifier here or there to do that?

It is on that last point, where I see the biggest challenge in rules design.  The desire to account for every possible variable creates unwieldy systems with pages of modifiers for every die roll.  I have vivid memories of games of Fire and Fury, for example, where my opponent stood with a hand up counting our modifiers as the GM read through the list, it seems we spent more time going through the QRS to determine the roll than actually playing the game.  And then there is Harpoon....


Having selected a D6 the game's author seems to follow a basic progression:

  1. Do I use a 1D6, 2D6 or 3D6 result?
  2. Is low good or bad?
  3. If 1D6, do I make 1 roll or throw many dice?
  4. Should successes be rolled again to determine level of success?
  5. Should the opponent have an opportunity to make a counter roll?

With the answer to five complete, the intrepid rules designer seems to progress on to modifiers.  It is here where I find most games bog down.  The desire to include many possible variations results in QRS's that are primarily lists of modifiers.  This is exacerbated by the desire to use random outcomes for multiple aspects of play: spotting, movement, shooting, closing to combat, reacting to combat results, command, morale, defense, reaction.  Each one of these concepts opens up to more modifiers.  The desire for granularity than drags to game out, or worse turns it into a dice contest with scenery and models in the background.  

So what is the answer?  
  1. The first step is to consider what is most important to you in your games.  Do you want to focus on establishing probabilistic outcomes or the hedonistic feedback loop of throwing the dice to get the results?  Many games focus on the die rolling aspect to ensure an engaging and exiting interaction and give short shrift to actual considerations of the effect of probability.  These games are fun, and can provide extreme outcomes.  On the opposite ends, games that focus on strict mathematical probabilities can satisfy the craving for historical simulation while still bogging down in the minutiae  
  2. Determine the level of game to represent.  If I am playing a division or corps commander, than why am I worried about a regiment forming square?  Rather than trying to account for the small details below my level, perhaps I can build those into the narrative of the roll:  The cavalry charged my infantry and they failed a response roll "They must have failed to get in formation in time"  or the cavalry rolls really well "They beat them to the punch" or "a dead horse broke the square."  The command level of the game is intended to limit the scope of the player as general.  Rules design than should ensure that the probabilities and modifiers are in line with the level of command represented.  
  3. Closely related to the above, consider the level of effect for an individual modifier.  An individual D6 solution means that each pip represents a 17% change in the likely outcome.  Does the issue being modeled really have that much influence on the outcome?  If not consider omitting it as a consideration or lumping it in with similar considerations.  Otherwise D6 may not be the best choice as dice like D10 or D20 allow for 10% and 5% increments.  There is a tendency to avoid this through alternate means like 2D6 or roll 2 dice and choose the highest/lowest, but they also present challenges in probability.  The distribution curve in 2D6 for example means that +/- 1 to a die roll can have a significant difference to the outcome as you move away from a '7"  
  4. Determine the maximum difference in allowable power level.  How far apart should the best and worst units in the game be in order to keep it playable?  My goto example of this was one of the first games of Modern Spearhead I played.  It was a convention scenario where I had a battalion each of T-55s and BTR 60s attacking a mixed battalion of M1s and Bradleys.  I was informed that in order to suppress a target I needed to roll '6' and then roll the die again to get a 4+.  My opponent could suppress me with on a 2 or kill outright on a 3+.  What was the point in the game?  The power differences resulted in a less than compelling narrative.  I tend to favor a D10 for Modern Spearhead because it allows for more graduations in power level which makes games between different generations of tanks more playable on the table.  
  5. Determine the level of influence by both players on a given outcome.  The attack role/defense roll mechanism works well when you want both players to feel they can influence the outcome. This is most important in the IGO/YOUGO style where one player has to wait for the other to execute his entire turn.  This can get rather boring or disheartening if you have to spend 20 min watching him tear apart your force while all you can do is watch.  This is less of an issue in games like Lion Rampant where there is a more dynamic play as initiative passes back and forth.  
  6. Consider where you are willing to accept determinism as well as probability.  Limit the aspects of the game that require random inputs.  

The end state for all of these considerations is to make an enjoyable game that gives satisfying and timely results.  I have found that my own tastes have evolved to favor rules that reduce the complexity to keep my focus on the level of the game.  I have found that I am more apt to abstract the results of a die roll to consider an overall effect rather than specific damage.  I like Spearhead, for example, as it uses the concept of suppression and destruction of a platoon more in terms of dispersion than outright elimination. Battleground WWII was once my favorite skirmish game, but today I admit that the level of detail required for die rolls really bogs down anything larger than a few squads.  I tend to prefer games that 'front load' modifiers like command, morale and experience into a unit stat rather than try to stack them onto the die roll later.  

Comments

  1. I remember that dice roll and it was BAD for me! I will return with more thoughts after having cogitated on your treatise for a awhile.

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    1. I figured there was a reason I had it in my catalog. I seem to have a small collection of photographs of particularly august and tragic rolls.

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  2. Jake, your thoughts are all well presented and very interesting. Your point regarding abstracting decisions below a commander's level of command is a good one and a point that should be well noted.

    Perhaps, we have gamed (amicably) together all of these years in part because we tend to see wargame design similarly? While I enjoy a good "game," my preference is for historical "simulations." That preference likely drives much of my design philosophy.

    In either game design or selecting a commercial game to study, the most important decision as you state is to establish what type of game is desired. Without laying that foundation early on, the design can quickly become muddled. Most games have resolution mechanisms consisting of both fixed and random components. If a more deterministic model is desired then the range of the die (dice) randomizer(s) ought to be less than the aggregation of defined and fixed die roll modifiers, column shifts, odds ratios , etc.. If a more chaotic model is the goal then allow the range of the die (dice) randomizers to dominate the possible aggregations of the fixed components. In this latter situation, the tail (of the distribution) really can wag the dog...

    I say, model what you can; abstract what you must.

    As for your example of counting modifiers with upheld hands during Fire & Fury games, well that still continues to this day!

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    1. The example of Fire and Fury is somewhat muddled by the fact that we were playing with a modified version that included combat resolution from JRIII, so it was a mess. I think the basic point remains. If can play a regimental game in two hours or six hours based on the granularity of the rules and still achieve a comparable result what am I getting out of the six hour game?

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