Die of the Week: Sharpshooter – A Second Look

After Steve’s initial post on the Sharpshooter, which can be found here, I decided to continue focusing on it for my inaugural blog post (You can leave tips in the jar by the door).

While it’s interesting to look at the statistics of individual dice, at some point we need to look at how it performs in an army, as this is the most common situation the die will find itself in. This can help answer some important strategic questions, such as: Is the possibility of a Bullseye worth a 3-health spot in my force composition? Should I throw in multiples of this die? What are is the risk/reward trade-off? What is the average airspeed velocity of an unladen swallow, and can I shoot it down reliably? (Okay, maybe not that last one.)

The short answer is (of course): it depends. On how your armies are currently grouped, on terrain numbers, what your opponent is doing, and a hundred other considerations.

However, I think it’s helpful to see likely outcomes against some useful benchmark to get an idea of what the army is capable of, which can help inform our strategic, and sometimes tactical, decision-making. The benchmark army I have chosen is 12-health worth of that most ubiquitous of villains, the Zombie.

Why 12-health of zombies? Why not Unseelie Fairies, or Dragonlords, or <insert die here>?

Because A) Zombies are commons, which when in force are some of the most consistent result-generators around, B) They’re specialists in melee and saves; they’re quite dangerous in melee, having a 67% (or favorable 2 to 1 odds) of generating melee results, which is useful when we test their attack vs our army’s defenses, and they save very well, having a 50% (1 to 1) chance to generate a save on any roll, which is important to resisting the effect of Bullseyes and our missile results, C) 12-health is a convenient number, allowing us to test 12 common, 6 uncommon, 4 rare, 3 monster, or a wide variety of mixed dice combinations for our army, and D) Everyone likes beating up zombie hordes.

The Setup

I’m looking at two armies today to fight against our zombie horde, representing extreme decisions. The first army is 12-health worth of Bowman dice (12 dice total), the second army is 12-health worth of Sharpshooters (4 dice total). My measurements of choice: How many zombies do we kill? And how many losses do we suffer from them?

I programmed a simulator with both test armies and the zombies, and then rolled all armies 5,000 times (any Bullseye results were applied, and then the generating die re-rolled until there was a non-Bullseye result generated). I then looked at how many health-worth of dice were sent to the DUA on each roll, and created probability distributions based on those results. We’ll start with zombies killed by missile actions:

Also, some tasty statistics:

There’s a lot to digest here, but the major takeaways for me are:

• The commons have about a 50% chance to kill between 2 and 5 zombies; for the rares, it’s 50% for between 2 and 7.
• The rares have a better chance of killing nothing; it is their most frequent result (around 1/6), HOWEVER! their second-most frequent result is completely wiping out the zombie infestation! (It’s about a 10% chance – or 9 to 1 against)
• The commons are more likely to do some damage, but overall kill fewer zombies per action, while the rares are more likely to devastate the enemy army. The Sharpshooters have about a 17% chance (1 in 6) to kill 10-12 zombies with a single action, while the Bowmen only have about a 3% chance of doing that.

Notice if you count Bullseye as just a “missile result”, you end up with the same average results for both armies. But this is a bit deceptive; Bullseye is really, incredibly powerful. Think of it as a Lightning Strike that you don’t have to pay for, and can strike twice (or more!) – plus it gets around those annoying defensive spells like Open Grave and Ash Storm, while the standard Bowman army does not. The fact that the Sharpshooters can wipe out the zombies in a single action is a testament to its power.

The rare dice can certainly shake up a game – so why wouldn’t you use them? Consistency is a big factor – rares boom or bust more often than commons; the Sharpshooter army has a higher standard deviation than the Bowman army. Strategically, rares are high-priority targets for enemy armies; they’ll get Lightning Struck, Slayed, Plagued, Bullseyed, Finger of Death’d 68 times, and otherwise be murdered in unpleasant ways more frequently than commons. They’re also more expensive to bring back with magic. Which brings us to the other part of the coin: If the zombies get to swing first – how much health do we expect to lose?

Important note: this chart is assuming the Coral Elves are able to count their maneuvers as saves.

Both armies save about the same, which is to say, not very well (archers are fragile things). The median of 6 indicates 50% of the time, the armies will lose 0 to 6 health, but the other 50%, they’ll lose 7 to 12 health. The rares are again booming and busting harder; they have a 1/6 chance of taking no casualties, or taking 9 casualties (3 dice). A well-timed Palsy spell by the undead would compound this even further. Would you rather lose 6 commons or 2 rares to an attack?

Final Thoughts

Now that I’ve (hopefully) whetted your appetite a bit, the next entry will look at the all-common Bowman army, vs 9 Bowman and a single Sharpshooter, so that we can directly gauge the impact of a Sharpshooter (and, thus, Bullseye) over vs. another 3 Bowman.