Heroic Strength: The Two Choices (Or, Why would I ever choose Heroic Strength over Heroic Defense?)

If you're just joining us, this is part 2 of a three-part homily on Heroic Strength. (No really, it's a proper homily, complete with alliterative points, inside references, and illustrations.) You can find part 1 here, which discussed the major defensive bonuses that we can give to heroes against cavalry and monster/monstrous mount units by calling Heroic Strength.

Of course, our prior discussion has begged the question: are these defensive benefits from Heroic Strength as good as what you’d get if Elendil spent that same Might point on Heroic Defense? The answer... in many cases... is “probably.”

(More maths incoming... and charts!)

Anatomy of Heroic Defense

Let's start by getting our bearings. The chief advantage of Heroic Defense (a new, special heroic action introduced in the MESBG core rulebook) is that the opponent has to roll natural 6s to wound your hero:

Heroic Defense (Fight Phase) [Rules p. 72]

When faced with insurmountable odds, a hero can ready themselves for the force of the blows coming their way, allowing them to lessen the impact and reduce the level of damage taken.

A Hero model that declares a Heroic Defense will only suffer a Wound on the roll of a natural 6 in the ensuing Fight phase, regardless of any modifiers or Brutal Power Attacks. If the Hero would usually have been wounded on a 6/4+, 6/5+, or 6/6, then they will only be wounded if both rolls are natural rolls. Note that a Hero model’s mount is not affected by Heroic Defense.

This is a very real advantage, as on average, only 1 of 6 dice an opponent rolls will be a natural 6. If an opponent would ordinarily wound you on a much lower number (like a 4 or a 3), or would usually get some sort of modifier on their wounding dice (like +1 from a 2H weapon), requiring natural 6s can dramatically reduce the number of wounds your opponent is likely to score. 

To take just one intentionally over-the-top example, here’s what happens to Aragorn and the pointy-sword-of-doom if his target pops Heroic Defense:

(Hey orcs, whatcha gonna do? Whacha gonna do when he comes for you?)

(Die probably... unless you pop Heroic Defense)

Odds of Aragorn dealing at least X wounds on Y dice

Wounds Dealt	3 Dice (4s/5s/6s)	3 Dice (H. Def.: 6s)
0+	100.00 %	100.00 %
1+	87.50 %	42.13 %
2+	50.00 %	7.41 %
3+	12.50 %	0.42 %
4+	0.00 %	0.00 %

Pretty scary, right? Unless he has to roll 6s.

But there are some catches to Heroic Defense. Four of them, to be precise.

First catch: “Note that a Hero model’s mount is not affected by Heroic Defense.”

We talked about mounts a lot in Part 1. They provide a lot of benefits to your hero (expanded threat range and more damage potential in the form of knock-down dice being the two most prominent), and you almost always are paying points for them, so avoiding the loss of a mount is always preferable if we can pull it off. Unlike Heroic Strength (which often provides some hidden benefits to mounted heroes), Heroic Defense does not. 

Given that most mounts are only D4 (and even the most armored mounts are only D6, outside of the Armored Fell Beast), their odds of surviving that attack? Considerably worse than your hero’s chance of being wounded on natural 6s. So if Elendil pops Heroic Defense, guess where at least one of the opponent’s attacks are going? That’s right: the mount (assuming the hero wasn’t automatically thrown by a charging Monstrous Cavalry model). Which means a risk of being prone, or Knocked Flying (with its cheeky S3 hit).

Second catch: while requiring natural 6s does reduce the odds that an opponent will wound you on average rolls, there’s no rule that says an opponent has to roll average. 

In our Aragorn example, Heroic Defense reduces his chance of dealing 3 wounds (which will kill most hero models, unless they have either 3 wounds or multiple Fate) from 12.5% to 0.42%. That’s a significant reduction, but it’s a reduction on a probability that was already low to begin with: 12.5%, or way less than 50% odds. Instead of being “lucky” to score 3 hits, Aragorn has to instead be “very, very lucky” to score 3 hits. Is Aragorn likely to be “very, very lucky” instead of just “lucky”? Probably not… except when he is.

What does this mean? There’s a limit to the risk that we can mitigate through Heroic Defense. We can make it harder for our opponent by making rolls natural 6s (particularly if our opponent has a substantial Might store remaining, or makes liberal use of a 2H weapon). But if our opponent gets “lucky,” even a Heroic Defense can leave our hero exposed. 

(By the way: Aragorn’s chance to deal 3 wounds under normal circumstances? A sneaky-good 12.5%, which doesn’t sound like much, until you realize (like I just did) that it equates to 1-in-8 attacks. A 1-in-8 chance to kill most heroes in a single go (unless they have and pass multiple fate rolls)? Pretty boss…) 

Third catch: Heroic Defense only provides a (significant) survivability boost if your opponent(s) can wound you on less than a “6.”

Anduril poses a special case for Heroic Defense. Understandably, the jump from a 4+ to natural 6s results in a huge reduction of damage. But this is actually a very rare phenomenon. Most heroes are S4. A S4 hero wounds a D5 or D6 hero (of which there are a fair number) on 5s. So unless we plan to run D4 heroes (which you can... but it's hard), Heroic Defense is actually going to be converting “5s” into “6s,” which is still something, but much less dramatic than what Heroic Defense does to Anduril. 

Then there's the fact that a S4 hero wounds a D7 or D8 hero (which includes most heroes who can pop Heroic Defense, including Elendil) on “6s” anyway. For heroes who are D7 or D8, up against S4 heroes (or S5 heroes, if our hero is D8), this means that the only tangible benefit Heroic Defense is conferring is that (1) our opponents can no longer spend Might to change “5s” (or “4s,” potentially) into “6s,” (2) our opponents can’t use other modifiers (like Hatred, 2H weapons, etc.) to convert their “5s” into “6s,” and (3) our opponents cannot abuse the combination of Might and modifiers to wound us on “4s” (or less). Yes, these are still advantages. Yes, they are also a lot more underwhelming than we probably expected.

The other major benefit (in theory) of Heroic Defense is that if an opponent needs to score some combination result to wound (6/4, 6/5, or 6/6), both rolls have to be natural. Theoretically, this benefit is best realized against an opponent who could spend Might, since usually spending a point of Might to change a modified roll improves both rolls by 1 (so a 6/4 becomes a 5/3, with both sides improved by +1 with Might). The problem is that heroes who can spend Might this way are almost always S4 or S5 (some exceptions apply, like Eowyn not charging), which means that unless our hero has D9 (Durin vs. S4) or D10 (Sauron vs. S5), we never get to the 6/4 threshold anyway.

To get that benefit at D8 (and we have to be D8 most of the time, unless we're fighting one of just a handful of S2 armies), our opponent can only be S3, which generally means troops, not heroes. There’s definitely a benefit to forcing swarms of regular troops to roll natural 6s followed by natural 4s… but then again, they are troops: which means they have no Might, and thus had to roll natural 6s by natural 4s anyway to wound us. And spending a Might point to force troops to do what they had to do anyway… is not exactly efficient.

One more…

Final catch: Remember those knock-downs?

Yeah… Heroic Defense doesn’t stop them.

Up in Catch 2, we mentioned that Heroic Defense is limited in the amount of risk it caps for us. Let's explore that a little more.

On the defensive, there are two ways to mitigate risk. Manipulating needed dice results is one, and one that Heroic Defense does very well (by forcing the opponent to roll natural 6s, and by locking the opponent out of modifying results with Might, 2H weapons, etc.). But there’s still an element of luck involved: Aragorn can still roll 3 natural sixes if he’s rolling three to-wound dice (even though he’s unlikely to do so). And if he does, Elendil could very well be dead.

The second way to manipulate risk is to limit the total number of wounds we can suffer (even if we’re unlucky) by reducing the number of dice our opponent rolls. Even if everything hits the fan, we know that our hero cannot suffer more than X wounds (where X is the number of dice he is rolling). In other words, we’ve reduced our risk by reducing the magnitude of our worst-case scenario.

We’ve already seen this in our discussion of cavalry models. A generic cavalry model has 2 dice on the charge, which means four dice to wound an infantry hero if they win the fight (because the hero is knocked prone at the conclusion of the duel, with all that entails). Halving the opponent’s dice pool (by depriving them of a knock-down) gives us an absolute chance of reducing their maximum number of potential wounds by half: instead of a greater than 0% chance of inflicting at least 3 or 4 wounds, they now have a 0% chance of inflicting at least 3 or 4 wounds. And by reducing the range of potential outcomes (0-4 potential wounds becomes 0-2 potential wounds) it also gives us a lower probability of suffering any wounds or multiple wounds:

Odds of rolling at least X 5s/6s or 6s on 4 dice

	5s/6s to Wound (KD: 4 dice)	5s/6s to Wound (No KD: 2 dice)	6s to Wound (KD: 4 dice)	6s to Wound (No KD: 2 dice)
0+	100.00 %	100.00 %	100.00 %	100.00 %
1+	80.25 %	55.56 %	51.77 %	30.56 %
2+	40.24 %	11.11 %	13.90 %	2.78 %
3+	11.10 %	0.00 %	1.62 %	0.00 %
4+	1.23 %	0.00 %	0.08 %	0.00 %

Ultimately, the debate between Heroic Defense and Heroic Strength—on the defensive side of the equation, at least—usually hinges in large part on which is more valuable to an opponent: getting double-dice from a knock-down that only wound on natural 6s, or getting half-dice (with no knock-down) that wound on less than natural 6s and/or can be modified by Might?

Before we try to answer that question by running the numbers, it’s worth noting that there are a lot of variables here. Obviously we don’t care about knock-down if we’ve been charged only by infantry models. And if we’ve been charged by a monster (or a monstrous mount), we may also have Rend or Hurl to consider (forcing a Monster to Rend on 6s is impossible for any monster who is S8 or higher, and that’s assuming we have a hero who could get up to S10... which, for reasons we'll explore next time... is highly unlikely, although not strictly impossible). In a write-up like this, we’ll have to generalize somewhat (because running each and every scenario isn’t practical). So to split the difference, we’ll generalize from a few different examples:

Example #1: 

Mounted Strider with Anduril (F6, S4, D6) charges dismounted Boromir, Captain of the White Tower, with Shield (F6, S4, D7)

We went with Aragorn since we’ve already opened the Pandora’s Box that is the pointy-sword-of-doom. Stat-wise, Boromir has a semi-decent chance of taking on Aragorn: he’s tied for Fight, has a huge Might store, and also has the “saving 3s” (3 wounds, 3 fate) that Aragorn does. On offense, Boromir is slightly behind, as he’ll need to roll 5s to wound Aragorn (S4 vs. D6). Normally Aragorn would need 6s to wound Boromir (S4 vs. D7), but pointy-sword-of-doom… 

Let’s say Aragorn (mounted) charges Boromir (not mounted) during the Move Phase. Here’s what we know at the start of the Fight Phase (when Boromir has to decide whether to call Heroic Defense, Heroic Strength, or any other heroic actions): Aragorn has three attacks base, plus one on the charge (for four dice to win the duel), to Boromir’s three attacks. If Aragorn wins, he’ll be rolling 8 dice to wound Boromir, needing a 4+ on each to wound. We’ll run the math on that in a minute… but just intuitively, we all know they’re not good odds for Boromir.

At this stage, Boromir has three options for purposes of our example (or four, depending on if you consider "calling nothing" an option... which it probably is...):

• Call nothing (saving his Might for, hopefully, winning the duel roll and then wounding Aragorn);
• Call Heroic Strike (so Boromir is able to win ties, and therefore, hopefully, win the duel and not have to worry about the pointy-sword-of-doom)
• Call Heroic Defense (forcing Aragorn to wound on natural 6s, instead of modifiable 4s, 5s, or 6s); or
• Call Heroic Strength (in the aim of increasing his Strength to at least 6, thereby reducing Aragorn’s wounding dice from 8 to 4, but still being wounded on 4s, 5s, and 6s).

Remembering that we have to choose before we know if Aragorn or Boromir is about to win the fight (because we have to declare Heroic Defense and Heroic Strength at the beginning of the Fight Phase), which do we choose? Well, let's run through some factors.

Who wins the fight?

Let’s start by figuring out the odds that Aragorn will win the Fight against Boromir. If Boromir is likely to win the fight, we might be more inclined to spend Might for an offensive heroic action (like Heroic Combat) or to save it to win the duel/wound Aragorn. But if he is unlikely to win the fight, Aragorn is dangerous enough that we’ll probably want to do something to keep Boromir upright.

If both models were on foot, they’d have an equal chance of winning the fight: 50-50 (well, almost) because they’re tied on Fight and Attack value. But because Aragorn is mounted, he has an extra attack to win the duel (4 dice to Boromir’s 3). This gives Aragorn a 51.77 % chance of rolling at least one “6” to Boromir’s 42.13 % chance of rolling at least one “6.” Advantage Aragorn (albeit slightly).

What if we account for the possibility that neither Aragorn nor Boromir roll a 6 (meaning they have the option to spend Might to improve their highest roll)? Once again, the odds (slightly) favor Aragorn, who has an 80.25% chance of rolling at least one “5” or “6” on four dice, compared to Boromir’s 70.37%.

Generally speaking, we’re talking about an even match here. If either of these heroes want to win the duel, they probably can… which means the odds are likely we’ll have a tie. That favors Aragorn, too: since Anduril is an elven-made weapon, he gets the benefit of winning the roll-off for drawn combats on a roll of 3+ (if he’s good; 1-4 if he’s “less good” than Boromir), or a 66.7% chance of winning ties.

Throw all this in a pot, and Jeremy Hunthor’s marvelous combat calculator gives Aragorn a very healthy 62% chance of winning the combat, compared to Boromir’s 38% (or roughly 2-to-1 in favor of Aragorn). Boromir can still prevail in the face of such odds, but the prudent money is on Boromir hedging his bets by calling some heroic action that will improve his surviviability.

What about Heroic Strike? Should Boromir consider doing that to improve his odds of winning the fight?

I’m hoping to delve into Heroic Strike later (there’s a lot to sort out), but the basic answer is “Yes, if…” Which seems kind of tentative...

The answer is a clear “Yes” if Aragorn either is out of Might (which is unlikely) or has already spent Might to call another heroic action during this Fight Phase, in which case he is locked out of calling a Heroic Strike (because a single hero can only call one heroic action per phase). If either is the case, then Boromir is guaranteed to have the higher fight value (because he will go up to at least F7, compared to Aragorn’s F6, no matter what he rolls). At F7+, Boromir has a 59.7% chance of winning the duel with his three attacks, compared to Aragorn’s 40.3% chance of winning with four attacks (and Aragorn’s elven-made weapon bonus has been effectively neutralized… as long as Boromir doesn’t feint. . . maybe. . . like I said, there’s a lot to sort out).

If Aragorn can match a Heroic Strike, however, the math gets a lot more dicey (sorry, inadvertent). Both Aragorn and Boromir are base F6, meaning that the winner is (literally) whoever rolls the highest result on a D6. Except … because your Fight Value on a Strike can never exceed F10, there’s also an inordinately high chance that Aragorn and Boromir will actually tie:

Outcomes for Boromir of a Contested Heroic Strike

	Aragorn “1”	Aragorn “2”	Aragorn “3”	Aragorn “4”	Aragorn “5”	Aragorn “6”
Boromir “1”	Tie	Loss	Loss	Loss	Loss	Loss
Boromir “2”	Win	Tie	Loss	Loss	Loss	Loss
Boromir “3”	Win	Win	Tie	Loss	Loss	Loss
Boromir “4”	Win	Win	Win	Tie	Tie	Tie
Boromir “5”	Win	Win	Win	Tie	Tie	Tie
Boromir “6”	Win	Win	Win	Tie	Tie	Tie

Aragorn wins: 12/36 roll-offs (33.3%)
Boromir wins: 12/36 roll-offs (33.3%)

Tie: 12/36 roll-offs (33.3%)

If Boromir wins the strike-off outright (which he has a 33% chance of doing), his odds of winning the fight improve from 38% to 60%. But the odds are that two-thirds of the time Aragorn will either tie him (giving Aragorn a 62% to 38% advantage, given his +1 die and elven-made weapon advantages) or exceed him in Fight Value (in which case Aragorn, who now has the above advantages plus higher fight value, sees his odds of winning the fight skyrocket to 73%). Which makes spending that Might point for Heroic Strike… less appealing.

How many wounds is Aragorn likely to inflict?

For this calculation, we’re looking for a benchmark: if Boromir loses the fight, and does nothing else, how much trouble is he in? Well…

Odds of Aragorn with Anduril rolling at least X wounds on Y dice

Wounds dealt	Double-Strikes (Anduril: 4+)
1+	99.61 %
2+	96.48 %
3+	85.55 %
4+	63.67 %
5+	36.33 %
6+	14.45 %
7+	3.52 %
8+	0.39 %

So the odds are pretty good (85% good) that if Aragorn charges Boromir with Anduril, and his mount knocks Boromir Prone, Boromir is suffering at least three wounds (which, if he fluffs his three fate rolls, will kill him). There’s about a 2-in-3 chance (63.67%) that Aragorn scores four or more wounds and a 1-in-3 chance (36.33%) that Aragorn will land five wounds. At the risk of stating the obvious, these are all bad-to-disastrous outcomes.

But wait… it gets worse. If Aragorn decides to two-hand with Anduril (because, you know, he has a free point of Might each turn to fix his duel roll):

Odds of Aragorn with Anduril (2H) rolling at least X wounds on Y dice

Wounds dealt	Double-Strikes (Anduril: 3+)
1+	99.98 %
2+	99.74 %
3+	98.03 %
4+	91.21 %
5+	74.14 %
6+	46.82 %
7+	19.51 %
8+	3.90 %

Yes, you read that right: that’s a 90% chance of rolling at least four 3s, 4s, 5s, or 6s on eight to-wound dice, and a nearly 50% chance (46.82%) of rolling six wounds on eight dice (which will kill Boromir no matter what he rolls on his Fate). Like I said before, Aragorn is boss.

Here’s what happens to each if Boromir pops Heroic Defense, meaning Aragorn now has to roll natural 6s to wound:

Odds of Aragorn with Anduril rolling at least X wounds on Y dice

Wounds dealt	Double-Strikes (Anduril: 3+)	Double-Strikes (Anduril: 4+)	Double-Strikes (H. Def.: “6s”)
1+	99.98 %	99.61 %	76.74 %
2+	99.74 %	96.48 %	39.53 %
3+	98.03 %	85.55 %	13.48 %
4+	91.21 %	63.67 %	3.07 %
5+	74.14 %	36.33 %	0.46 %
6+	46.82 %	14.45 %	0.04 %
7+	19.51 %	3.52 %	> 0.00 %
8+	3.90 %	0.39 %	> 0.00 %

Much better, right?

Unfortunately, Aragorn still has a 3-in-4 chance (76.74%) of rolling at least one natural 6, and a roughly 4-in-10 chance (39.53%) of rolling two or more natural 6s, so Boromir is certainly not invulnerable. But 40% is way better than 96-99%, and Aragorn’s realistic odds of wounding Boromir top out at 3 wounds (which, again, is still a pretty sneaky-good 13.48%, or a little shy of 1-in-7 odds), although if he gets lucky he can still score up to 8 wounds (theoretically… though the number is so small it didn’t have any numerical value on anydice).

Now, what happens if Boromir pops Heroic Strength instead? Aragorn is still wounding on 4+ (or 3+ if he’s two-handing), but as long as Boromir rolls a 3+ for Heroic Strength, he’ll deprive Aragorn of four knock-down dice. What are Aragorn’s odds of rolling wounds with just four dice, instead of eight? Well…

Odds of Aragorn with Anduril rolling at least X wounds on Y dice

Wounds dealt	Double-Strikes (Anduril: 3+)	Strikes (H. Str.: 3+)	Double-Strikes (Anduril: 4+)	Strikes (H. Str.: 4+)	Double-Strikes (H. Def.: “6s”)
1+	99.98 %	98.77 %	99.61 %	93.75 %	76.74 %
2+	99.74 %	88.89 %	96.48 %	68.75 %	39.53 %
3+	98.03 %	59.26 %	85.55 %	31.25 %	13.48 %
4+	91.21 %	19.75 %	63.67 %	6.25 %	3.07 %
5+	74.14 %	0.00 %	36.33 %	0.00 %	0.46 %
6+	46.82 %	0.00 %	14.45 %	0.00 %	0.04 %
7+	19.51 %	0.00 %	3.52 %	0.00 %	> 0.00 %
8+	3.90 %	0.00 %	0.39 %	0.00 %	> 0.00 %

If Aragorn is two-handing… there’s not a lot that can be done. The good news is that Boromir can’t suffer more than 4 wounds (because Aragorn is only rolling 4 dice), so Aragorn’s odds of scoring 5+ wounds drop from a whopping 3-in-4 (74.14%) to none-in-infinity (0.00%). His odds of suffering 3 and 4 wounds have also dropped by a fair bit, from 98% to 60%, and 91% to 20%, respectively. Again, these are definite improvements for Boromir.

The situation is even rosier if Aragorn needs a 4+ to wound: once again, his odds of scoring 5+ wounds have dropped from approximately 36% to 0%, and his odds of scoring 3 or 4 wounds have dropped from 86% to 31%, and 64% to 6%.

Having said that, none of these percentages are anywhere near as promising as the damage reductions we saw from Heroic Defense, which gives Aragorn just a 13% chance of scoring three or more hits (well below the 98% he’d otherwise have, if two-handing with Anduril). Against Aragorn, at least, manipulating the required roll on the to-wound dice results in greater protection than halving the pool of two-wound dice.

Example #2:

Mounted Boromir with the Banner of Minas Tirith (F7, S4, D7) charges dismounted Strider in heavy armor (F6, S4, D6)

So we’ve flipped the tables now. Boromir, with an extra attack on the charge (and a higher Fight Value than Aragorn), has a hefty 72.9% chance to win the fight, over Aragorn’s paltry 27.1%. It’s not quite Anduril-levels of damage, but assuming Boromir doesn’t flub and roll four 1s in the duel, his odds of wounding Aragorn (eight dice on 5s or 6s) are still pretty good:

Odds of Boromir rolling at least X wounds on Y dice

Wounds dealt	Double-Strikes (8 dice: 5s/6s)
1+	96.10 %
2+	80.49 %
3+	53.18 %
4+	25.86 %
5+	8.79 %
6+	1.97 %
7+	0.26 %
8+	0.02 %

Boromir still has a 1-in-2 chance (53.18%) of dealing three wounds to Aragorn, and a 1-in-4 chance (25.86%) of dealing four wounds. Don’t let Anduril’s outlandishly-high numbers spoil us: these are fantastic odds of dealing high-end damage to a hero model.

Like Boromir before him, Aragorn probably wants to do something to mitigate his risk. Let’s say he opts like Boromir did to pop Heroic Defense. How much harder is he to wound? It turns out, he’s exactly as hard to wound as Boromir was (because Boromir has to roll the same natural 6s using the same number of dice):

Odds of Boromir rolling at least X wounds on Y dice

Wounds dealt	Double-Strikes (8 Dice: 5s/6s)	Double-Strikes (H. Def.: “6s”)
1+	96.10 %	76.74 %
2+	80.49 %	39.53 %
3+	53.18 %	13.48 %
4+	25.86 %	3.07 %
5+	8.79 %	0.46 %
6+	1.97 %	0.04 %
7+	0.26 %	> 0.00 %
8+	0.02 %	> 0.00 %

We’re still seeing impressive reductions from Heroic Defense, although the difference is less marked. This makes sense, of course: Boromir has a harder time wounding than Aragorn did anyway, so it makes sense that forcing him to roll 6s instead of 5s would make less of a difference than forcing Aragorn to roll 6s instead of 4s (or 3s).

The question is: has this diminished return from Heroic Defense opened the door for Heroic Strength’s dice reduction to overtake it? As it turns out, yes:

Odds of Boromir rolling at least X wounds on Y dice

Wounds dealt	Double-Strikes (8 dice: 5s/6s)	Double-Strikes (H. Def.: “6s”)	Strikes (H. Str.: 5s/6s)
1+	96.10 %	76.74 %	80.25 %
2+	80.49 %	39.53 %	40.74 %
3+	53.18 %	13.48 %	11.11 %
4+	25.86 %	3.07 %	1.23 %
5+	8.79 %	0.46 %	0.00 %
6+	1.97 %	0.04 %	0.00 %
7+	0.26 %	> 0.00 %	0.00 %
8+	0.02 %	> 0.00 %	0.00 %

If your goal is to reduce Aragorn’s odds of suffering at least 1 wound, then Heroic Defense is a slightly better choice than Heroic Strength (76% to 80%), although neither is particularly “likely” to prevent Aragorn from suffering any wounds. Heroic Defense is also slightly ahead of Heroic Strength when it comes to the odds of 2 or more wounds (although at 39.53% vs. 40.74%, it does feel like we’re kind of splitting hairs here). But at 3 and 4 wounds, halving the number of to-wound dice (from 8 to 4) actually makes more of a difference than forcing those 8 dice to roll natural 6s. And, of course, while Heroic Defense still leaves open the possibility of suffering 5 or more strikes, Heroic Strength removes those outcomes from our risk assessment altogether.

So if your hero is facing a mounted opponent who will need 5s or 6s to wound you, both Heroic Defense and Heroic Strength (if you can get to S6 or above) offer about the same level of protection.

Last one…

Example #3: 

Mounted Boromir with the Banner of Minas Tirith (F7, S4, D7) charges dismounted Elessar in heavy armor (F6, S4, D7)

Boromir’s odds of winning the fight are the same as in Example 2 (72.9% to Aragorn’s 27.1%). What’s changed is the number Boromir has to roll to wound, which is now a 6 instead of a 5. In other words, we’ve hit that point we discussed in catch 3 to Heroic Defense, where that heroic action ceases to make the opponent’s to-wound dice any harder to roll, and is now just locking them out of using their might and other modifiers.

While Heroic Defense’s odds of wounding stay as constant as ever, its degree of effectiveness has essential disappeared altogether (because Boromir had to roll 6s to wound anyway). In the meantime, the dice reduction from Heroic Strength—now placed on an equal playing field where everyone needs 6s to wound—really shines:

Odds of Boromir rolling at least X wounds on Y dice

Wounds dealt	Double-Strikes (6s)	Double-Strikes (H. Def.: “6s”)	Strikes (H. Str.: 6s)
1+	76.74 %	76.74 %	51.77 %
2+	39.53 %	39.53 %	13.19 %
3+	13.48 %	13.48 %	1.62 %
4+	3.07 %	3.07 %	0.08 %
5+	0.46 %	0.46 %	0.00 %
6+	0.04 %	0.04 %	0.00 %
7+	> 0.00 %	> 0.00 %	0.00 %
8+	> 0.00 %	> 0.00 %	0.00 %

Now, to be fair, Heroic Defense is still contributing value: if Boromir wants to wound Aragorn in the double-strikes column, he can spend Might to turn his 5s into 6s (and we know from last time that he’ll have two or more 5s 80% of the time, so his odds of scoring 2+ wounds can be quite a bit higher than 40% if he wants it to be). But his odds of scoring two or more 5+ results on just four dice (the Heroic Strength pool) is just 40%, which means that even if Boromir pours the Might into wounding Aragorn with the Heroic Strength pool, he’s still looking at essentially the same odds of wounding Aragorn twice (40% vs. 39.53%) that he’d have against Heroic Defense… except he’s had to spend 2 more Might to do it. In this scenario, Heroic Strength is the clear choice over Heroic Defense, on added survivability alone.

Those three examples should be sufficient to show us the range of potential outcomes. But let’s do one more, just for old times sake . . .

Example 4: 

Witch-King on Fell Beast with Crown of Morgul charges Mounted Elendil with Narsil (2H)

We’ll assume the Witch-King has won the fight (which, as Tiberius is probably hollering at the screen right now, is far from a sure thing; but this is my example and we’re assuming the worst, so we’ll assume that Elendil has lost the duel). Here’s how things unfold depending on whether Elendil did nothing, popped Heroic Defense at the beginning of the Fight Phase, or popped Heroic Strength at the beginning of the Fight Phase.

Scenario 4.1: Elendil did nothing.
The Witch King knocks Elendil prone, meaning he loses his mount and suffers the Knocked Flying! Result and suffers a S3 hit. A D8 Elendil with a Shield probably suffers no wound (6s by 4s), but a D7 Elendil who forgot his shield has a 16.67% chance of taking a wound before the Witch King does anything (and maybe losing his fate).

The Fell Beast at S6 will wound a D7 or D8 Elendil on 5s if he strikes normally (using 8 dice); alternatively, he can rend a S5 Elendil on 4s, but only with 4 dice. Mathematically, he should probably go for the double-dice from strikes:

Odds of Witch-King on Fell Beast rolling at least X wounds on Y dice

Wounds dealt	Double-Strikes (8 dice: 5+)	Rend (S6 vs. S5) (4 dice: 4+)
1+	96.10 %	93.75 %
2+	80.49 %	68.75 %
3+	53.18 %	31.25 %
4+	25.86 %	6.25 %
5+	8.79 %	0.00 %
6+	1.97 %	0.00 %
7+	0.26 %	0.00 %
8+	0.02 %	0.00 %

Either way, Elendil is (surprisingly) probably still alive at the end, although the Witch-King does have a 1-in-4 chance of scoring 4 wounds, which would kill Elendil outright due to him having a single Fate point.

Scenario 4.2: Elendil popped Heroic Defense.
If Elendil pops Heroic Defense, the Witch-King opts to Strike normally instead of Rending, because that gives him 8 tries (dice) to roll natural 6s, instead of just 4. The resulting math looks very familiar (because we’ve done it before):

Odds of Witch-King on Fell Beast rolling at least X wounds on Y dice

Wounds dealt	Double-Strikes (8 dice: 5+)	Double-Strikes (H. Def.: “6s”)
1+	96.10 %	76.74 %
2+	80.49 %	39.53 %
3+	53.18 %	13.48 %
4+	25.86 %	3.07 %
5+	8.79 %	0.46 %
6+	1.97 %	0.04 %
7+	0.26 %	> 0.00 %
8+	0.02 %	> 0.00 %

We’ve successfully reduced the probability of 3 or 4 wounds from 26-53% to a much more acceptable-looking (though still sneaky-high) 3-13%. That’s something. But have we maximized Elendil’s survivability?

Scenario 4.3: Elendil popped Heroic Strength and rolls a 1-2 on the Strength check (33.3% chance, 2/6 rolls).
First off, even under this scenario, Elendil is going to match the Fell Beast’s S6, so we don’t have to worry about a knock-down. The question is whether the Witch-King strikes normally (needing 5s on 4 dice) or opts to Rend (which, in this scenario, he needs 4s on 4 dice). He probably opts to Rend.

Once again, we’ve already run these figures:

Odds of Witch-King on Fell Beast rolling at least X wounds on Y dice

Wounds dealt	Double-Strikes (8 dice: 5+)	Rend (S6/S6) (H. Str: 4 dice, 4+)	Double-Strikes (H. Def.: 8 dice, 6s)
1+	96.10 %	93.75 %	76.74 %
2+	80.49 %	68.75 %	39.53 %
3+	53.18 %	31.25 %	13.48 %
4+	25.86 %	6.25 %	3.07 %
5+	8.79 %	0.00 %	0.46 %
6+	1.97 %	0.00 %	0.04 %
7+	0.26 %	0.00 %	> 0.00 %
8+	0.02 %	0.00 %	> 0.00 %

If Elendil only manages the 1 or 2 on the Heroic Strength check, Heroic Defense ends up offering him greater protection. He’s still not all that likely to suffer the 4 wounds that would kill him outright (6.25%), but the three wounds and fluffed Fate roll is in play (31.25%).

But . . .

Scenario 4.4: Elendil popped Heroic Strength and rolls a 3-6 on the Strength check (66.7% chance, 4/6 rolls).

Now, Elendil is going to S7 or S8, which means that the Fell Beast now needs 5s to wound him whether he strikes or Rends, and has only 4 dice to do it. Our prior experiments with Boromir and Aragorn suggest that this is the point where Heroic Defense is likely to run out of steam (converting 5s to 6s), and it proves true yet again:

Odds of Witch-King on Fell Beast rolling at least X wounds on Y dice

Wounds dealt	Double-Strikes (8 dice: 5+)	Double-Strikes (H. Def.: 8 dice, 6s)	Rend (S6 vs. S7) (H. Str: 4 dice, 5+)
1+	96.10 %	76.74 %	80.25 %
2+	80.49 %	39.53 %	40.74 %
3+	53.18 %	13.48 %	11.11 %
4+	25.86 %	3.07 %	1.23 %
5+	8.79 %	0.46 %	0.00 %
6+	1.97 %	0.04 %	0.00 %
7+	0.26 %	> 0.00 %	0.00 %
8+	0.02 %	> 0.00 %	0.00 %

Wrap up… for now… 

All told, not bad for a single point of Might, right? Survivability for your hero. A protection on your investment in heroic mounts. Dice reduction for opponents. No stressing about whether your prone model is going to get to stand up. Cheeky debuffs for your opponent’s monsters. You could definitely do worse, especially against monsters and mounted opponents.

And again, all these benefits accrue if our hero loses the duel: we haven’t even talked about what happens if he wins.

(Next time…)