# What’s the role for Math Hammer in Narrative Gaming?

This was inspired by a question from Cadian Shock, and was originally supposed to just be a snippet. But it’s gotten a bit past that, and I thought it would be nice to post up something, because it’s been quite some time. Stretch those hobby muscles a bit.

And I think it’s an interesting question – what role, if any, does math, theory and understanding probability have in narrative gaming?

First things first…

I’ve missed you all. As many of you know, my actual job is as an infectious disease epidemiologist. One of the things I work on is emerging infectious diseases. Needless to say, the last few months have been…busy. I’m just now coming up for air, and even that’s a dubious prospect. But I’ve loved seeing you all posting hobby-related work on various sites, and I hope you’re all doing well. Stay safe, stay home…it really is important. I’d really, really like this to be over sooner rather than later.

Anyway, onto the main show.

## Does Theory Have a Role in Narrative Gaming?

The instinctual answer to this is “No”.

Math Hammer is a tool of competitive gamers, a way to seek the best, the most optimal form of something. It’s there to let ITC types tune their lists, play out scenarios, and know how things will unfold when they go full-bore into each other. But I actually think things are considerable more complicated than that. I think that a good grasp of theory, and the application of the same techniques used in competitive gaming have two major roles to play in narrative gaming:

1. List building
2. Narrative design

Let’s look at both of them in turn.

## List Building

While it’s easy to view theory as primarily chasing the optimal result, it can also tell you about things that are less optimal. They can help you understand the full totality of your list, in whatever form that is. There’s an argument to be made that list building in narrative games shouldn’t have any aspect of understanding those elements. That you should follow your bliss, take what makes the most sense for your scenario, and go from there.

I disagree. For two reasons.

The first is that non-functional lists are no fun to play, even if they’re narrative. If we conceptualize narrative lists as being lists that should play in a way you picture in your mind, theory can help you make sure that your list will actually work that way. To use a much lamented (by me) example, theory can let you play out if a squadron of Leman Russ Vanquishers will work the way they feel like they should when they are described in the text, an absolute menace to any armor that finds itself on the wrong end of their sights. Theory will tell you that no, if you just go with that, without thinking about other ways to mitigate their weaknesses, improve their performance, etc. that you may very well be setting yourself up for a bad time. Having a decent expectation of what your units can and cannot do is still important, even if you’re not worried about tabling your opponent at the top of Turn 2. And it can, for example, tell you where you have room for…affectation units. If your list is strong enough that it can (or should) be diluted with some less functional, but narratively enjoyable units in your army.

The second, which is sort of an outgrowth of the first, is it can help you understand and identify your army in ways that are not just “Is this trash in a competitive setting?” There is a phalanx of under-appreciated units I refer to as “80% Units”. If we imagine that the optimal, “What you should take in your competitive army” unit is 100%, there are a number of units in the codex who can probably manage 80% of that (or more). But you won’t see them in the competitive scene, because not optimal is not optimal – there’s no use for “kinda optimal”. But in narrative gaming, there is. Can you drop a unit that doesn’t fit your army’s concept, but fills a critical role, because this unit will do an adequate job of it? Can you take the edge off a little bit, without tying one hand behind your back?

A good example of this is the 7th edition Tau Broadside with Railguns. Strictly speaking, it was just worse than the missile pod variety. But it wasn’t bad – it was just obviously the wrong choice for best. There are lots of examples like this – new Chapter Tactics, or Craftworld Aspects, etc. that aren’t the drop-in winner, but can serve their purpose, and accomplish what they set out to accomplish.

Essentially, a lot of narrative players get accused of just putting together garbage lists that fit a theme. I disagree with that characterization (indeed, my Eldar narrative list was hell on wheels for two editions). But theory will at least let you know if your list is garbage.

## Narrative Design

Theory also lets you test out missions before they see the light of day, to avoid the dreaded “Well, that sucked…” feeling of having a mission you though was really cool end up being unplayably bad. I’m going to talk a little bit about a mission that could have used this – it’s a game from the LVO Narrative, and they took feedback on this really well, so I don’t want to seem like I’m picking on them. But it is a good illustration.

See the buildings marked “1” and “2” (“3” is off to the right of the camera)? Those are our objectives, and they must be preserved. Which seems fine – the Eldar, especially a Wave Serpent heavy list, can play a decent durability game, and try to target the obvious heavy hitters. Except there was also a pre-game strategem that was in use.

This Stratagem is used after all units have been deployed, but before the game begins. Roll a d6 for each Objective Structure. On a 4+ that Objective Structure takes d3+1 Mortal Wounds and all units on it or within 3” of its perimeter suffer d3 Mortal Wounds. This Stratagem may be used no more than 4 times per game.

Note the “no more than four times per game” implicitly actually means “spammable up to four times before the game starts.” I don’t remember how many CPs it cost, but it wasn’t very much. I get what the authors of the mission were going for – that cool scene in basically any WWI or WWII movie, where there’s an infantry assault that’s following up right behind a rolling artillery bombardment.

Some easy probability will tell you that with four uses of that stratagem, each building should be hit twice, and each of those hits should do 2.5 mortal wounds on average, for a cool 5 mortal wounds in expectation. The buildings have twelve wounds, which means on average every single defender objective is half-destroyed at the top of Turn 1. And one doesn’t need to imagine all that absurd a streak of good rolls for one or more of the objectives to simply be gone that first turn. That is indeed what happened in our game. Let’s do some more simulation based work to look at just how often these feel-bad situations will come up.

Simulating this opening bombardment 10,000 times (as one does…) we get the following distribution for each building, with the two plots respectively showing the number of wounds done, and whether or not the building was destroyed (0 = No, 1 = Yes).

As you can see, there’s a lot of variability in the number of wounds caused, but pretty reliably the attackers can be expecting to see 6+ mortal wounds done to the objectives, and 9 mortal wounds is not an uncommon outcome. Importantly, the plot below shows that, for our 10,000 simulations, 4.7% of the time a building gets destroyed.

In fairness, that means 95.3% of the time, a building doesn’t. But remember, that’s per building, which means there’s only an 86.5% chance that no buildings are destroyed. And that’s the somewhat generous “Is this game just completely bonkers” outcome – some of those 86.5% games are with buildings limping along on two or three wounds, one lasgun shot away from collapsing completely.

Is this unbalanced? I’d suggest yes. But more than that, for narrative play, I’d suggest that it’s disempowering. It sets up a situation where there’s a decent chance that one player will already feel that they’re out of the game before it really starts – not because of anything they did, but because of dice rolls. And mathhammer – like the stuff above – could tell you that. Like maybe dialing it down to one-use, or coming up with some other mechanic. You can of course discover this during playtesting, but this is rare – it’s the kind of thing you might not encounter after just a try or two.

So there we are – a “brief” exploration of the role I think theory has in narrative gaming, and in making your narrative games better.

The added bonus is you can do math while sheltering in place.

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