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Friday, May 24, 2019

Is Heroic Strike good? (Part III: Dueling with Shields, Banners, and Mounts)





We're almost ready to analyze the merits of Heroic Strike, but before we get there, we have a few more pieces of wargear to sort out: shields, banners, and mounts. As a reminder, here's what we've discovered so far (in relation to small troop combats: 1-on-1, 2-on-1, and 2-on-2):
  • RULE #1: In an even duel, both sides have an even chance of winning.
  • RULE #2: Having higher fight value than our opponent helps us win the fight, but only if we have a drawn combat. 
  • RULE #3: Adding more dice (on its own) is more likely to help us win fights than improved Fight Value (on its own).
  • RULE #4: Flailing reduces our odds of winning the fight, unless we already have a lower fight value than our opponent.
  • RULE #5: Feinting reduces our odds of winning the fight, unless we have a fight value that is 3+ more than our opponent's fight value. 
  • RULE #6: The -1 duel roll penalty from two-handed weapons dramatically reduces our chances of winning the fight, regardless of our fight value. 
Let's start with shields.

(Bring on the maths…)


SHIELDS
Iron Shield Wall
Photo Credit: LordDainofIronHills

The rules for shields are found in the "Weapons and Wargear" chapter in the Rules Manual, on page 91. In addition to improving its bearer's defense characteristic by 1 (usually), a model with a shield doubles their attack value when making a duel roll (so one attack becomes two, two become four, four become eight, and so on--though that's usually it). There are a couple of caveats: you can't spear-support a shielding unit (so no uber-Spartan death formations), all models of the same side have to shield if any of them shield, and a shielding model can't make strikes if they win unless they have a special piece of wargear (like Thorin's Oakenshield). But you can shield while trapped or even prone, and if you win your opponents have to back away (and you get to stand up, if prone).

Let's return to our lowly Easterling who has been abandoned by his Black Dragon pike support and is now alone against an Osgiliath Veteran and Warrior of Minas Tirith with spear. His initial odds of wining aren't great... in fact, they're quite terrible:

x1 Osgiliath Veteran (FV4) + x1 WOMT (FV3, Spear)
vs.
x1 Easterling Warrior (FV3)

Duel Win %
Kill %
Death %
Good
74.54%
22.78%
4.24%
Evil
25.46%
4.24%
22.78%

If he opts to shield instead, his odds of winning the fight go up a fair bit (25.46% to 38.97%, or +13.51 percentage points:

x1 Osgiliath Veteran (FV4) + x1 WOMT (FV3, Spear)
vs.
x1 Easterling Warrior (FV3, Shielding) 

Duel Win %
Kill %
Death %
Good
61.03%
18.65%
0.00%
Evil
38.97%
0.00%
18.65%

He's still more likely to lose than to win, and surprisingly his odds of dying have dropped only slightly (from 22.78% to 18.65%). His chance of wounding the enemy goes all the way down to zero (you can't wound while shielding, that's the trade-off). Considering that he had only a 4.24% chance to wound anyway, this is probably worth it (unless you're trying to get yourself quartered or broken in Domination).

If instead our poor Easterling was killed in that 50/50 combat with the Osgiliath Vet and Warrior of Minas Tirith, leaving our pike-supporting Black Dragon to fend for himself, what happens if he shields? Both sides now have equal fight, and now have the same number of attacks. THe result is a 50/50 chance for each side to win the fight, only Gondor can make strikes while the Easterlings cannot:

x1 Osgiliath Veteran (FV4) + x1 WOMT (FV3, Spear)
vs.
x1 Black Dragon (FV4, Shielding)

Duel Win %
Kill %
Death %
Good
50.00%
15.28%
0.00%
Evil
50.00%
0.00%
15.28%

Again, this looks one-sided because Gondor has a 15% chance of killing the Black Dragon. But it is an improvement over what the Black Dragon would be doing if he only had one die to work with, albeit not a great one:

x1 Osgiliath Veteran (FV4) + x1 WOMT (FV3, Spear)
vs.
x1 Black Dragon (FV4, Pike)

Duel Win %
Kill %
Death %
Good
66.20%
20.23%
5.63%
Evil
33.80%
5.63%
20.23%

Conversely, if our Black Dragon were fighting two WOMTs with lower fight value, shielding makes quite a bit more sense:

x1 WOMT (FV3) + x1 WOMT (FV3, Spear)
vs.
x1 Black Dragon (FV4, Shielding)

Duel Win %
Kill %
Death %
Good
38.97%
11.91%
0.00%
Evil
61.03%
0.00%
11.91%

x1 WOMT (FV3) + x1 WOMT (FV3, Spear)
vs.
x1 Black Dragon (FV4, Pike)

Duel Win %
Kill %
Death %
Good
57.87%
17.68%
7.02%
Evil
42.13%
7.02%
17.68%

Having said that, shielding is an imperfect solution because it doesn't help us thin out the opposition (since we can't wound). It is best employed when we are temporarily outnumbered, and want to cut our losses before help arrives (which we are quite likely to do as long as we have a higher fight value than our opponents do). But as a long-term army-wide strategy, it's not a winning proposition. Hence:

RULE 7
Shield when we need to win selective, short-term duels if we match-or-exceed our opponent's dice count, and/or we match-or-exceed our opponent's fight value.

For prolonged contests and army-wide engagements, we're much better running with...

BANNERS
For Gondor #gondor #boromir #osciliath #arnor #numenor #faramir #soldiers #banner
Photo Credit: Kingdom of Tolkien

An underrated sub-plot in Tiberius' and Minutemankirk's discussion of Gandalf the White and Boromir (of) the White (Tower) dealt with the relative value of the 6" banner effect itself (in addition to its boost to fight value). The rules for Banners are found on page 89 of the Rulebook, and provide a single re-roll to friendly models who are involved in a Fight within 3" of the banner (although some banners, like Boromir's have extended range). The reroll can be made after your opponent has rolled their own dice to see who wins, but has to be made before anyone spends might (see step #5 in how to resolve a fight). You also need one of your models within range of the banner--if only your opponent is in banner range, you don't get the banner buff (even though technically the "fight" is in banner range).

The reroll from a banner essentially allows us to "add" an extra dice roll to the duel roll, just like shielding would, only we don't give up our chance to make strikes. If our re-roll from the banner is high enough to win the duel (or to force a roll-off, which we then win), we get to make strikes as normal. Which means our outnumbered, Shielding Black Dragon would go from having a 61% chance to win the fight and a 0% chance to wound, to having a 61% chance to win the fight and a 10% chance to wound, without incurring any additional risk of death (about 12% in either scenario). 


x1 WOMT (FV3) + x1 WOMT (FV3, Spear)
vs.
x1 Black Dragon (FV4, Pike) + Banner


Duel Win %
Kill %
Death %
Good
38.97%
11.91%
10.17%
Evil
61.03%
10.17%
11.91%

Yes, the Black Dragon is technically outnumbered, but he's just as likely to kill as to be killed... in which case, is he really outnumbered? Actually, yes, he really is. But he doesn't feel that way, because he suddenly has more staying power than his two opponents and he's as threatening to them as they are to him. That's the impact of banners.

But wait! There's more! Because you can both shield and get the benefit of a banner, if you really need to hold a spot. This makes our Black Dragon less threatening, but very difficult to remove:


x1 WOMT (FV3) + x1 WOMT (FV3, Spear)
vs.
x1 Black Dragon (FV4, Pike) Shielding + Banner


Duel Win %
Kill %
Death %
Good
28.07%
8.58%
0.00%
Evil
71.93%
0.00%
8.58%

Now it's still possible for the WOMTs to regain the odds of winning the fight, even with their lower fight value, but only if they stack a whopping eight models (yes, that's four shields supported by four spears) on our lowly single shielding Black Dragon. And then, only just:


x4 WOMT (FV3) + x4 WOMT (FV3, Spear)
vs.
x1 Black Dragon (FV4, Pike) Shielding + Banner


Duel Win %
Kill %
Death %
Good
50.60%
38.83%
0.00%
Evil
49.40%
0.00%
38.83%

Not bad for 25 points, right?

RULE 8:
Take banners. Take banners always. (No, duh.)


MOUNTS
drarves-battle-goats
Photo Credit: geekshizzle.com

If shields give us an extra attack at the cost of striking blows, and banners allow us the equivalent of an extra attack while still making blows, mounts not only give us a real extra attack, but can double our dice to strike blows. How's that for value?

There is a catch, of course: we have to be charging while mounted. Otherwise, there's no bonus. Given that "who goes first" hinges on both randomness (the Priority Roll) and finite resources (Might for Heroic Moves) that may devolve into more randomness (heroic roll-offs), it's far from a sure thing that taking a mount will improve our duel and wound odds. There are also maneuvering limitations: in addition to going first, we also have to charge into infantry to gain the attack bonus (without being counter-charged by cavalry models), and we only get the to-wound bonus if we win the fight against infantry models that are less than S6. So there are a lot of contingencies to worry about.

But when everything goes right--and it only has to go right once or twice a game to make the points back for mounts--it's a thing of beauty.

Let's say our lonely Dragon Knight, having survived a battle where he held up five WOMTs for the bulk of the game (thanks to shielding and banner rerolls) is a bit salty at his fellows for leaving him alone in the cold so long. Disillusioned by infantry life, he decides to pick up a horse, so he can lord it over them. He's still a Black Dragon (F4), but now he's a Black Dragon Kataphract (booyah!). In the next engagement, he recognizes a WOMT with whom he spent two hours in close proximity the previous battle. So he decides to charge him. His Fight value is the same, his strength is the same, and his defense is the same, but his attacks have increased (on the charge) from one to two. And if he wins the fight, he'll get to make not one strike against the model but two (because he has two attacks instead of one), and each strike uses two dice instead of one (because the WOMT will have been knocked to the ground). Suddenly, the stakes are a lot higher for the WOMT, especially if our Dragon Knight has a banner nearby:


x1 WOMT with Shield (FV3)
vs.
x1 Black Dragon Kataphract (FV4, Mounted)


Duel Win %
Kill %
Death %
Good
25.46%
4.24%
38.59%
Evil
74.54%
38.59%
4.24%

x1 WOMT with Shield (FV3)
vs.
x1 Black Dragon Kataphract (FV4, Mounted) + Banner


Duel Win %
Kill %
Death %
Good
17.36%
2.89%
42.79%
Evil
82.64%
42.79%
2.89%

Even though the Black Dragon needs 6s to wound the WOMT (S3 vs. D6), there's a pretty good chance of getting at least one six when you're rolling four dice to wound. Our WOMT can shield to try to up his duel odds... but it doesn't really reduce the risk all that much because four to-wound dice are still four to-wound dice:


x1 WOMT with Shield (FV3), Shielding
vs.
x1 Black Dragon Kataphract (FV4, Mounted) 

Good shields                                                   Good shields; Evil Banner


Duel Win %
Kill %
Death %

Duel Win %
Kill %
Death %
Good
38.97%
0.00%
31.60%
Good
28.07%
0.00%
37.24%
Evil
61.03%
31.60%
0.00%
Evil
71.93%
37.24%
0.00%

Let's say the WOMT hails a friend to bail him out. Now there's a spear-support backing him up, giving each side two dice. Life has become more dangerous for the Black Dragon, but he's still got a healthy lead, especially if he has a banner nearby:


x1 WOMT with Shield (FV3), x1 WOMT with Spear (FV3)
vs.
x1 Black Dragon Kataphract (FV4, Mounted)

No Banners                                                    Evil Banner

Duel Win %
Kill %
Death %

Duel Win %
Kill %
Death %
Good
47.16%
19.87%
27.36%
Good
35.23%
14.84%
33.53%
Evil
52.84%
27.36%
19.87%
Evil
64.77%
33.53%
14.84%
If there are no banners involved, three WOMTs can wrest control of the fight from the Black Dragon, but only if there are no banners; with a banner, the Kataphract retains a slight edge. To overcome the banner as well, Gondor needs five WOMTs holding up that single Kataphract… and even then, the Black Dragon has more than a 25% chance of wounding before any dice are rolled:


x2 WOMT with Shields (FV3), x1 WOMT with Spear (FV3)\
vs.
x1 Black Dragon Kataphract (FV4, Mounted) 

No Banners                                                    Evil Banner


Duel Win %
Kill %
Death %

Duel Win %
Kill %
Death %
Good
56.37%
33.72%
22.59%
Good
43.98%
26.30%
29.01%
Evil
43.63%
22.59%
33.72%
Evil
56.02%
29.01%
26.30%


x3 WOMT with Shields (FV3), x2 WOMT with Spear (FV3)
vs.
x1 Black Dragon Kataphract (FV4, Mounted) 
No Banners                                                    Evil Banner


Duel Win %
Kill %
Death %

Duel Win %
Kill %
Death %
Good
62.82%
48.21%
19.25%
Good
50.60%
38.83%
25.58%
Evil
37.18%
19.25%
48.21%
Evil
49.40%
25.58%
38.83%

Now less we overvalue this, and think we can charge cavalry pell-mell into infantry blocks, there's more to play here than just the inherent power of horses. Fight value plays a role in this, as does equipment. Our Black Dragon definitely benefits from being higher fight than all of the WOMTs he's facing. If the roles were reversed, and we had a F3 Knight of Minas Tirith riding down some F4 Black Dragons, just two Black Dragons (or a single Black Dragon with a banner reroll, not shielding) would have the edge in combat (although if the Knight were to manage the win, he'd be much more likely to wound in both cases):


x1 Knight of Minas Tirith (FV3, Mounted)
vs.
x1 Black Dragon (FV4, Pike)
Evil + Banner                                    Evil + 1 Black Dragon (FV4, Pike)

Duel Win %
Kill %
Death %

Duel Win %
Kill %
Death %
Good
38.97%
31.27%
10.17%
Good
38.97%
31.27%
18.65%
Evil
61.03%
10.17%
31.27%
Evil
61.03%
18.65%
31.27%
RULE 9:
Charging cavalry, with higher Fight, will win (and wound) a lot of fights.

Which brings us back to Heroic Strike. Now that we've looked at all the different factors that impact our dueling odds in isolation (fight value, attacks, wargear, and weapon/special strikes), we finally have the tools we need to assess when spending Might on Heroic Strike has value... and when it's just not good.


4 comments:

  1. A very interesting write-up - I will note that while a Black Dragon Kataphract in general has all the same stats as a Black Dragon on foot, fighting a column of these guys gets a bit trickier, since they have the equivalent of Shieldwall (making them D7). While this wouldn't have any impact on a Warrior of Minas Tirith/Osgiliath Veteran fighting them, it would help against (oh, say) Iron Hills Warriors and Uruk-Hai (to say nothing of S2 archery).

    I've also stayed away from banners in previous editions (mainly because it costs you 2-4 models to include one), but my armies are now moving towards having at least 1 banner in them - and often more than one, as you can't cover the entire field with only a single banner.

    ReplyDelete
    Replies
    1. I'm intrigued by Gleaming Horde on the Kataphrachts, although my experience with Shieldwall on Iron Hills Dwarves makes me skeptical. It should be incredibly useful for closing on ranged weapons. S2 bows and S4 crossbows get the defense bump for the rider (6/4 and 6s to wound, respectively). There's no benefit for the rider against S3 bows, but the mount goes up to D6, which means 6s to wound an armored horse, which is fantastic).

      I think it'll be a bear to keep up in combat, though. Shieldwall is hard enough to manage when you have infantry models with spears. The increased cav base size, plus the rule that cav can't spear support under any circumstances, basically means to keep it up you'll need to stack cavalry two deep like a shield wall formation, which is probably the last thing you want to do with expensive cav models with high mobility. They also probably want the F4 upgrade, which means they're very expensive for S3 cav with no lances.

      On banners, I am a card-carrying member of the Centaur/Green Dragon School of Banners, and try to have at least one banner or banner effect in an army. Yes, they cost 2-3 models per, but the odds of winning a fight go up significantly (especially in 1 v. 1 fights) that you probably prevent losing 2-3 models over the course of game by winning duels you were losing before. If you then go on to inflict 2-3 casualties on your opponent over the course of the game (which, over 4-6 rounds of combat, is a reasonable amount to expect, I think), I think it's a definite swing. And any banner reroll that allows a hero to win a duel without burning any of their precious might is probably worth a few standard infantry models.

      I like multiple banners in troop-dependent armies, too, as you can press your advantage in multiple places (while your opponent is almost always limited to contesting you in just one spot, if they have banners at all). A banner reroll coupled with higher fight and a shield is very difficult to overwhelm, so for something like elves or even dwarves they're a real force-multiplier.

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    2. Totally agree with the banner sentiment - part of the reason the King's Champion for Khazad-Dum/Moria is so good (comes with two banners automatically, basically an 80-pt hero model). I've been toying with banners for Mordor - since F4 is harder to come by from a $$$ perspective, getting that reroll is critical. It also helps heroes like Shagrat and the Witch-King from having to spend Might to win fights (as you note).

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  2. I've found that being able to Back Away into Shieldwall really helps the Gleaming Horde. You can leave 1 cavalry behind the lines about an inch every so often (so you only get about 2/3rds of your cavalry in on one charge), and then do your fights in order so that you Back Away into both the person you left behind /and/ someone who Backed Away from an earlier fight. Making Way with one model gives you some positioning flexibility as well, so you can Back into a shield wall.

    Leaving some cav behind sounds bad, but it's not really - in my experience, infantry walls don't often give you enough space to get EVERYONE in, so the kataphrakts who can't fit now have some way to contribute to the army.

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