Monday, April 22, 2019

Wargame Design: In Defense of the Humble D6


Many budding war game designers spend a great deal of time talking about mechanics, especially using dice.  It is only natural since dice mechanics are the “crunchy” part of war game design.  The only other topic that can compare in the “crunch” department are points cost or balancing mechanics.  Therefore, it is an easy topic to discuss.  This is not the first time I have tackled it on the blog.

The “Best Type of Dice” to use is a frequent conversation piece.  Lately, the humble d6 has fallen out of favor with many designers.  The main reason is the available range of numbers that a d6 can generate, and the probabilities it can simulate are limited.  Keep in mind as we proceed that I am not a mathematical genius or expert on probability.  In fact, I am just a humble war game blogger….. pretty unexciting expertise. 



Cons
So, let’s start by talking about the Cons of the d6.  As mentioned it can generate only 6 actual results.  This is much lower than a d10 or a d12, or even a d20.  Therefore, there is a much smaller range of numbers to work with and this makes differentiating of success and failure much harder. 

Essentially, you have a 16.67% chance of getting any individual result.  Therefore, if you need a 6 to do something, you will only score that 6 16.67% of the time.  If you need a 4, 5, or 6 you have a 50.01% probability.  16.67% is not very fun to calculate with, but 50% is fine.  What about 5+ then?  33.34%.  Compared to the d10 and their 10% increments, the d6 is far inferior for calculating outcomes and running the numbers quickly.  The same can also be said about a d20 AND it adds more possible outcomes.

Every modifier of + or – 1 adds a 16.67% variability in the outcome.  That is a big swing between potential outcomes made by relatively simple modifiers.  This means a -1 penalty is a big reduction in efficiency for a dice roll and a +1 is a huge gain.  Those large swings can be hard to moderate for. 



Pros
With those clear deficiencies, why would anyone want to continue using a d6 as their primary dice?  Are they insane or just stupid?  Neither, as the humble d6 also has its benefits. 

The first is that they are common and easy to get.  Custom dice or other polyhedron dice raise the barrier of entry for a game.  Granted, if your core audience is “experienced” gamers only then this does not matter.  However, most games are trying to appeal to the widest audience possible to garner use.  Everyone can get or has access to the humble d6.  I see that for sale in packs of 5 at the local gas station for less than $1 USD.  They are ubiquitous and have been in use for centuries. 

Once you start adding multiple d6 together, you have a very nice and simple bell curve of likely results.  Rolling two single pips has only a 2.78% chance, while rolling a combination that adds up to 7 is a 16.67% chance.  16.67% is actually the highest result you can get on 2d6 so you are statistically most likely to roll a 7.  This bell curve allows a designer to accurately predict outcomes than any single dice. 

Combined 2d6 also gives you same amount of potential results as a d10, without the “randomness” of any 10% option coming up.  You know a 7+ combination will come up more often than a 10+ combination on 2d6.  7+ is 58.34% on a 2d6, while 10+ is 16.67%   Meanwhile, on a d10 a 7+ is ~40% and a 10 is 10%.  Curves provide more predictability than a straight line chance, which allows a designer to “stack the deck” with modifiers to create tactical play in a more meaningful way. 

What happens when you start adding multiple dice to d10’s or d20”?  The more numbers you add, the flatter the curve, and you the less predictability it adds to the curve.  For example, 2d10’s most common result is an 11 at 10% and the equivalent roll on a 2d6 is 16.67%.  2d20 is 21 at only 5% which is the same as a single d20 result, so why roll 2 d20?  2d6 gives you the most “dramatic” bell curve. 

There is a reason d6 have been the most common types of dice for centuries.  They provide a dramatic and interesting probability curve that other dice can not match in groups.  The closest is the d12, and I can only think of one designer who really stresses the use of a d12.  Even that is just a derivative of a d6. 


Why So Many Single D6 Games Then?
Okay, so maybe I have convinced you that 2d6 is the ultimate dice to roll for your mechanics.  Then why do so many games use a single d6 resolution mechanic?  I would argue that very few of them actually do use a single d6 resolution mechanic.  They almost all temper it with some sort of multiplier….. let’s take a closer look at some mechanics in games. 

Arguably, the most familiar of the game systems that is based on a single d6.  However, to determine a hit from shooting you take a model’s shooting skill and subtract it from 7 to get the target number needed to hit.  If you have a shooting skill of 4, you need a 3+ to hit.  If you have a shooting skill of 3 you need a 4+ to hit.  Therefore, a shooting skill of 4 vs. 3 is 16.67% better and more “lethal”. 

However, you will notice that it takes more to incapacitate your target in Warhammer 40K than a shooting roll.  They mitigate the odds by adding two additional rolls for wounding and a potential saving throw made by the defender.  Therefore, to remove a single model, you are really rolling 3d6 looking for a series of target numbers.  It is not resolved by a simple d6 roll at all.  AS the probability for each roll result is added in, the likely outcome from the series is reduced. 


In Lion Rampant, they use a single d6 per model compared to a stat to determine if a “hit” is caused.  Therefore, a model with a shoot skill of 5+ will “hit” a target with a 33.34% likelihood of causing a hit.  However, when you look closely at the rules, you will see you roll a d6 per model so you are typically rolling multiple dice at a time.  In addition, the number of hits are compared against a units’ armor to remove targets.  Armor can be modified by range and terrain.  Therefore, the key arbiter of lethality is armor rating and not just a single d6 roll.



This game also only uses the humble d6.  However, it uses them in opposed dice pools.  The target number is always 4+ on a dice to get a success and then you compare successes to determine opposed tests.  In addition, the game has no negative modifiers.  Instead, extra dice are added as a bonus. 

For example, if a hero is behind a wall, their is no reduction in dice for the villain shooting at them.  Instead, the hero gets extra dice to resist or dodge the attack.  The probabilities come from the number of d6 rolled against each other, minimizing unknown outcomes with the more dice that are rolled.  However, the small element of chance is still in play.    


Final Thoughts
The humble d6 has been the dice of choice for centuries because it offers the most dramatic, yet predictable probability curves for game designers to play with.  Combine various mechanics to group dice and combine probability curves from a d6 results allows for a wide variety of game play options. 

Ultimately, very few people play a game because of its dice mechanics.  Instead, they play games that set out to model or do certain things that the players find appealing.  As a designer, the dice mechanics are simply a tool to try and reflect the “reality” of your game and accomplish the goals you have set out for the game itself.  The specifics of the dice mechanics are secondary to that goal.  As a designer, you need to use the tool that meets the games goals whether that be d6, d10, d12, or d20s.  Mechanics for the sake of mechanics are an empty and hollow exercise.          

1 comment:

  1. I rather like the limited range of the D6. The big jumps in probability between the numbers provide clear & simple outcomes where differences actually matter. At least if you stick to 1 to or 2 D6 per roll. And it doesn't have to mean your game is simplistic. You just have to be more creative elsewhere in your rules. The sophisticated action & counter-action system of Rogue Planet (which uses 2D6 and limits modifiers to +3 & -3 maximum) would be a nice example.

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