We come
to it at last...
After a lengthy build-up breaking
down all the components of a successful duel role, we're finally read to talk
about Heroic Strike itself. When does it make sense? And when is it *gasp* a
waste?
There's actually a lot to unpack
here (far more than I thought there'd be when I originally started writing on
it). We'll start by looking at the overall mechanics of Heroic Strike, mostly
to understand exactly what benefits (and risks) it carries with it. It's that
balancing of benefit and risk that makes it game-winning or worthless (and a
lot in-between).
Because Blogger doesn't like long write-ups, this one is split into two parts. This section (part IV) goes over the three basic probability mechanics in Heroic Strike (the D6 roll to increase Fight Value, the "10" cap on Fight Value, and expected distributions of probable outcomes as dice scale upwards). Part V (which you can read here) applies those principles to a case study between two combatants (Faramir vs. Eomer), and also discusses an alternative use of Might ("boosting") and how that might--or might not--make Heroic Strike more attractive (sorry--those "might" puns were purely unintentional).
(Potential math overload ahead)
The Anatomy of Heroic Strike
Let’s start with a refresher on Heroic Strike (p. 72 of the
Rules Manual):
Heroic Strike (Fight Phase)
Outnumbered
and fighting for their life, it is times like these when a hero must dig down
deep in order to fight off their foes with all the skill they can muster.
A Hero model who declares they are using Heroic Strike adds D6 to
their Fight value for the duration of the Fight phase. This is rolled for at
the start of the model’s Duel roll and lasts until the end of the turn. This
cannot increase a Hero model’s Fight
value above 10. Note that this bonus is applied before other effects are taken
into account. Thus, a Hero who is
Engaged in a Fight with a Bat Swarm would add D6 to their Fight value (to a
maximum of 10) and then halve the total due to the Bat Swarm’s Blinding Swarm
special rule.
There’s an intuitive understanding that this is a powerful
ability. And it is. But it isn’t. It all depends on your point of view.
As we discussed when we began this series, a duel consists of eight components:
1.
Gather and designate dice;
2.
Declare special strikes or two-handed weapons;
3.
Roll all dice;
4.
Apply modifiers to dice as designated in #1 and #2;
5.
Apply rerolls;
6.
Apply Might to appropriate designated dice;
7.
Determine the winner of the duel (breaking drawn combats
by Fight Value or a roll-off); and
8.
The winner makes strikes (if the winner did not shield
or is otherwise prevented from striking).
Heroic Strike has no impact on most of this. It doesn’t
alter the number of dice we’re rolling. It doesn’t add any modifiers, positive
or negative. It doesn’t let us reroll any dice. If anything, it reduces our ability
to modify dice with Might (by depleting our Might store). Its clearest
application is only at step #7, because if we get the higher Fight Value via a
successful Strike, we’ll win a drawn combat outright. So we’ll start with that
interaction.
Note: It’s worth pointing out that while Strike only directly
impacts #7, it will indirectly impact #8 as well, because the higher our chance
of winning the combat, the higher our chance of wounding because our to-wound
chance if we lose a duel is always 0% (unless you’re Haldir). It may also
indirectly impact #6: theoretically, our opponent may not spend as much Might
if he knows we can match his spending and will win ties (which would be good for
us). Having said that, my (purely anecdotal and concededly limited) experience
is that most opponents will go ahead and spend the Might anyway, to prey upon
our inclination to throw even more of our hero’s valuable Might into winning
the combat … more on that in our "Strike in Miniature" discussion, here.
The Value of Contesting “Drawn
Combats”
Here’s the key observation: a successful Heroic Strike is going
to confer the same benefit as higher fight value confers generally: we win
drawn combats, when both our highest duel roll and our opponent’s highest duel
roll have the same value (see Rule #2: Having higher fight value (of any value) than our
opponent helps us win the fight, but only if we have a drawn combat).
Because each opponent in a duel uses only their highest duel roll, this always
comes down to pitting one six-sided die against another six-sided die, for a
total of thirty-six possible roll combinations, and three possible outcomes: “Win,”
“Lose,” or “Draw” (if both sides have the same fight value). Having the higher
fight value than our opponent (either natively or because of a successful Strike)
converts those six “draw” outcomes to “wins”:
Possible Duel Roll Outcomes
Challenger
has Same Fight Value (X)
|
Challenger
has Higher Fight Value (X+1)
|
|||||||||||||||
Target (FV: X) Duel Roll
|
Target (FV: X) Duel Roll
|
|||||||||||||||
"1"
|
"2"
|
"3"
|
"4"
|
"5"
|
"6"
|
"1"
|
"2"
|
"3"
|
"4"
|
"5"
|
"6"
|
|||||
Challenger (FV: X) Duel Roll
|
"1"
|
Draw
|
Loss
|
Loss
|
Loss
|
Loss
|
Loss
|
Challenger (FV: X + 1) Duel Roll
|
"1"
|
Win
|
Loss
|
Loss
|
Loss
|
Loss
|
Loss
|
|
"2"
|
Win
|
Draw
|
Loss
|
Loss
|
Loss
|
Loss
|
"2"
|
Win
|
Win
|
Loss
|
Loss
|
Loss
|
Loss
|
|||
"3"
|
Win
|
Win
|
Draw
|
Loss
|
Loss
|
Loss
|
"3"
|
Win
|
Win
|
Win
|
Loss
|
Loss
|
Loss
|
|||
"4"
|
Win
|
Win
|
Win
|
Draw
|
Loss
|
Loss
|
"4"
|
Win
|
Win
|
Win
|
Win
|
Loss
|
Loss
|
|||
"5"
|
Win
|
Win
|
Win
|
Win
|
Draw
|
Loss
|
"5"
|
Win
|
Win
|
Win
|
Win
|
Win
|
Loss
|
|||
"6"
|
Win
|
Win
|
Win
|
Win
|
Win
|
Draw
|
"6"
|
Win
|
Win
|
Win
|
Win
|
Win
|
Win
|
|||
With tied Fight Value, each side wins 15 of 36 scenarios (41.67%
of the time), and the remaining six scenarios (16.67%) are drawn combats which,
if neither side has an elven blade, they are likely to split 50/50 (meaning
each side is likely to win 18 of 36 combats, or 50%). The higher fight value
would give that player the six drawn combat scenarios, too, for total odds of
21/36 (58.33%) compared to his opponent’s 15/36 (41.67%). In other words,
Heroic Strike improves your odds by 8.33% (50% to 58.33%), and reduces your
opponent’s odds by 8.33% (50% to 41.67%), or from equal one-of-two odds to roughly
six-of-ten odds in your favor.
That 16-percentage point swing in our favor is what we’re
paying for (or gambling on) if we call a Heroic Strike, assuming that we start
the combat with the same fight value as our opponent. But if we start with a lower
fight value than our opponent, we’re already starting at that 60-40 disadvantage,
which means that while the number of scenarios in which we win doesn’t
change (we still top out at 21/36 scenarios, or 58.33%), we essentially flip
the chart on our opponent: instead of winning 15 scenarios outright and losing
21, we now win 21 scenarios and lose only 15. The magnitude of the swing in our
favor doubles (41.67% to 58.33%, or +16.66%), as does the negative swing for
our opponent (58.33% to 41.67%, or -16.66%):
Challenger
has Lower Fight Value (X-1)
|
Challenger
has Higher Fight Value (X+1)
|
|||||||||||||||
Target (FV: X) Duel Roll
|
Target (FV: X) Duel Roll
|
|||||||||||||||
"1"
|
"2"
|
"3"
|
"4"
|
"5"
|
"6"
|
"1"
|
"2"
|
"3"
|
"4"
|
"5"
|
"6"
|
|||||
Challenger (FV: X-1) Duel Roll
|
"1"
|
Loss
|
Loss
|
Loss
|
Loss
|
Loss
|
Loss
|
Challenger (FV: X+1) Duel Roll
|
"1"
|
Win
|
Loss
|
Loss
|
Loss
|
Loss
|
Loss
|
|
"2"
|
Win
|
Loss
|
Loss
|
Loss
|
Loss
|
Loss
|
"2"
|
Win
|
Win
|
Loss
|
Loss
|
Loss
|
Loss
|
|||
"3"
|
Win
|
Win
|
Loss
|
Loss
|
Loss
|
Loss
|
"3"
|
Win
|
Win
|
Win
|
Loss
|
Loss
|
Loss
|
|||
"4"
|
Win
|
Win
|
Win
|
Loss
|
Loss
|
Loss
|
"4"
|
Win
|
Win
|
Win
|
Win
|
Loss
|
Loss
|
|||
"5"
|
Win
|
Win
|
Win
|
Win
|
Loss
|
Loss
|
"5"
|
Win
|
Win
|
Win
|
Win
|
Win
|
Loss
|
|||
"6"
|
Win
|
Win
|
Win
|
Win
|
Win
|
Loss
|
"6"
|
Win
|
Win
|
Win
|
Win
|
Win
|
Win
|
|||
In both scenarios, the net result is the same: we win a
maximum of only six more scenarios (the ones where the highest duel roll for
both side ties), but psychologically, going from a “draw” to a “win” in those
six scenarios (or even better, from a “loss” to a “win”) can be enormous. As
anyone who’s played a high-fight army knows, rolling a “6” that stays a “6” and
wining the duel automatically is absolutely amazing. And as anyone who’s played
against a high-fight army also knows, losing those combats automatically can be
completely deflating.
Which brings us back to the central question: are either of
these swings worth a Might point? The second scenario (going from lower fight
to higher fight) is by far the easier sell: if we can not only improve our odds
of winning from four-in-ten to six-in-ten, that’s valuable right there; and to
be able to simultaneously flip our opponent’s odds of winning (from
six-in-ten to four-in-ten) is the icing on the cake. Going from a fifty-fifty
chance to win to a sixty-forty chance to win is still an improvement, but since
most heroes who can Strike can only call it 2-3 times a game (because they have
a limited Might store), I think it’s fair to ask if that added increase is worth
it. Against an enemy army leader with a single Fate point that you have trapped
against a wall? Very tempted. If you only have a single hero with two attacks
against a single troll? Maybe not… especially if your Hero has help coming next
turn, and has Heroic Defense in his arsenal.
Our troll scenario also raises another important factor in the
value of Heroic Strike. Getting higher fight than your opponent is great and
all, but how likely are we to actually get a higher fight value when we Strike?
And what happens if we tie or (heaven forbid) still end up with a lower fight
value than our opponent?
The curse of the D6: Variations
in Final Strike Values
Of all the probabilities that factor into Heroic Strike (and
there are a lot), this one—which is arguably the most important—is also the
most inflexible. At the start of the Fight Phase, any hero who wants to Strike
has to declare that they’re doing so (usually spending a point of Might then
and there, although sometimes none and sometimes two…). Then, when we get to
that hero’s combat, we roll a single D6 before any duel dice are rolled (more
on them shortly).
The importance of that single dice roll is pretty
self-explanatory: whatever result that single D6 produces is the amount our Hero’s fight value goes up. The
inflexibility is also pretty clear, if we stop and think about it. This die can’t
be modified. It can’t be rerolled. And we don’t get any second-chances (unless
we have multiple heroes who’ve called a Heroic Strike in the same fight… which
I’ve done exactly once, against Sauron, just to make sure).
The wonderful (or terrible) thing about a single D6 is that
we know exactly how probable each result is (assuming the die isn’t rigged, or cursed,
of course): we have a 16.67% chance of getting a “1,” a 16.67% chance of
getting a “6,” and a 16.67% chance of every other result between them. Yes, our
“average” roll is a 3.5. But all that means is that half the time our result
will be lower than that (1, 2, or 3) and half the time it will be higher (4, 5,
or 6). There’s a lot of difference between increasing your fight value by “1” and
by “6.”
Now there are some things that can reduce this variance. The
biggest is that a hero’s maximum fight value is always capped at “10,” which
means that heroes that start with higher fight values will have more “10”
results, making that single D6 less of a gamble:
Heroic Strike Results Based on Starting Fight Value
Starting Fight Value
|
|||||||
FV 4
|
FV 5
|
FV 6
|
FV 7
|
FV 8
|
FV 9
|
||
Heroic Strike Roll
|
"1"
|
5
|
6
|
7
|
8
|
9
|
10
|
"2"
|
6
|
7
|
8
|
9
|
10
|
10
|
|
"3"
|
7
|
8
|
9
|
10
|
10
|
10
|
|
"4"
|
8
|
9
|
10
|
10
|
10
|
10
|
|
"5"
|
9
|
10
|
10
|
10
|
10
|
10
|
|
"6"
|
10
|
10
|
10
|
10
|
10
|
10
|
|
Another way to look at the same information from a different
angle is through an “at least” chart. We discussed at least charts in ourseries on Heroic Strength,
so if you want to read more about what they do and how to create your own, you
can check out that series. This time, rather than an at least chart that shows
our odds of scoring wounds, we’ll look at our chance of scoring “at least Fight
Value X” when we call a Heroic Strike:
At Least Fight Value after Heroic Strike
Starting Fight Value
|
|||||||
FV 4
|
FV 5
|
FV 6
|
FV 7
|
FV 8
|
FV 9
|
||
At Least Fight Value from Heroic Strike
|
FV5+
|
100.00%
|
|||||
FV6+
|
83.33%
|
100.00%
|
|||||
FV7+
|
66.67%
|
83.33%
|
100.00%
|
||||
FV8+
|
50.00%
|
66.67%
|
83.33%
|
100.00%
|
|||
FV9+
|
33.33%
|
50.00%
|
66.67%
|
83.33%
|
100.00%
|
||
FV10
|
16.67%
|
33.33%
|
50.00%
|
66.67%
|
83.33%
|
100.00%
|
|
If our hero has a starting Fight Value of 4, they have only
a small chance of reaching Fight 10 (16.67%). It can and will happen, but is
probably not something we can (or should) count on. A much more realistic
expectation is for our hero to end up somewhere between Fight 6 (five-of-six
results on the Strike die) and Fight 8 (three-of-six results on the Strike
die). By contrast, a hero who starts with Fight 8 has a five-in-six chance of
reaching Fight 10—that’s what we call good odds.
The variance is also helped (usually) by the fact that we
have a target Fight Value we’re trying to reach. If we have a Fight 6 hero (like
Aragorn), and he’s confronted by a Fight 7 Mordor Troll, we know Aragorn needs
to at least get to Fight 7—which he will 100% of the time, if he Strikes.
Ideally, we’d like to get a higher Fight Value than 7, so that Aragorn will
also win ties. If he Strikes, he can do this pretty reliably as well—83.33% of
the time (i.e., as long as he doesn’t roll a “1” to Strike).
The problem is that this target isn’t always static. If our
Mordor Troll is instead a Mordor Troll Chieftain, that Chieftain can also call
a Heroic Strike—which means his Fight Value when all is said and done is going
to be at least 8, and could be as high as 1, just like Aragorn’s. It’s this interplay
of changing fight values where Heroic Strike tends to be the most important,
and also the most unpredictable.
Double the curses! (Heroic
Strike-Offs)
Now before we get into the mechanics of the Strike-Off, let’s
just reiterate what we’ve said before: winning (or losing) a Strike-Off does
not impact our odds of winning the fight as a whole. It impacts our odds of winning
the fight only in six specific scenarios, where both sides roll exactly the
same value on their highest duel roll—a “6” v. “6,” “5” v. “5,” and so on down
the line:
Target (FV: X) Duel Roll
|
|||||||
"1"
|
"2"
|
"3"
|
"4"
|
"5"
|
"6"
|
||
Challenger (FV: X) Duel Roll
|
"1"
|
Draw
|
Loss
|
Loss
|
Loss
|
Loss
|
Loss
|
"2"
|
Win
|
Draw
|
Loss
|
Loss
|
Loss
|
Loss
|
|
"3"
|
Win
|
Win
|
Draw
|
Loss
|
Loss
|
Loss
|
|
"4"
|
Win
|
Win
|
Win
|
Draw
|
Loss
|
Loss
|
|
"5"
|
Win
|
Win
|
Win
|
Win
|
Draw
|
Loss
|
|
"6"
|
Win
|
Win
|
Win
|
Win
|
Win
|
Draw
|
|
As with our one-sided Strike, the goal is still to try to
flip the chart. If our challenger wins the Strike-Off, he’ll end up with higher
fight, and thus convert all those “draws” (if he’s tied fight) or “losses” (if
he’s lower fight) to “wins.” If he loses the Strike-Off, the best-case scenario
is that nothing changes (“draws” remain “draws” or “losses” stay “losses”). The
worst-case scenario is that an opponent who was previously tied Fight now has
higher Fight, and those “draws” become “losses”—disaster!
Challenger
has Higher Fight Value (X+1)
|
Challenger
has Lower Fight Value (X-1)
|
|||||||||||||||
Target (FV: X) Duel Roll
|
Target (FV: X) Duel Roll
|
|||||||||||||||
"1"
|
"2"
|
"3"
|
"4"
|
"5"
|
"6"
|
"1"
|
"2"
|
"3"
|
"4"
|
"5"
|
"6"
|
|||||
Challenger (FV: X + 1) Duel Roll
|
"1"
|
Win
|
Loss
|
Loss
|
Loss
|
Loss
|
Loss
|
Challenger (FV: X-1) Duel Roll
|
"1"
|
Loss
|
Loss
|
Loss
|
Loss
|
Loss
|
Loss
|
|
"2"
|
Win
|
Win
|
Loss
|
Loss
|
Loss
|
Loss
|
"2"
|
Win
|
Loss
|
Loss
|
Loss
|
Loss
|
Loss
|
|||
"3"
|
Win
|
Win
|
Win
|
Loss
|
Loss
|
Loss
|
"3"
|
Win
|
Win
|
Loss
|
Loss
|
Loss
|
Loss
|
|||
"4"
|
Win
|
Win
|
Win
|
Win
|
Loss
|
Loss
|
"4"
|
Win
|
Win
|
Win
|
Loss
|
Loss
|
Loss
|
|||
"5"
|
Win
|
Win
|
Win
|
Win
|
Win
|
Loss
|
"5"
|
Win
|
Win
|
Win
|
Win
|
Loss
|
Loss
|
|||
"6"
|
Win
|
Win
|
Win
|
Win
|
Win
|
Win
|
"6"
|
Win
|
Win
|
Win
|
Win
|
Win
|
Loss
|
|||
The only difference between a one-sided Strike and a Strike-Off
is that both sides of the duel are trying to win control of those six drawn
duel rolls. They do this by each rolling a D6; those two D6 results are then added
to each side’s starting Fight Value, and then the final Fight Values are
compared to each other to determine who now has the highest Fight.
Because we’re comparing two D6s, we once again have
thirty-six possible roll combinations. Assuming that each side starts with the
same Fight Value, each of them will have exactly 15/36 outcomes in which they
will “Win” (end the Strike-Off with the higher Fight Value), and 15/36 outcomes
in which they “Lose” (end the Strike-Off with the lower Fight Value). This leaves
6/36 outcomes where both sides will “Draw” by rolling the same result on the
Strike-Off, leaving them with the same final Fight Value as their opponent:
Both
sides Start with Equal Fight Value (X)
|
|||||||
Target (FV: X) Duel Roll
|
|||||||
"1"
|
"2"
|
"3"
|
"4"
|
"5"
|
"6"
|
||
Challenger (FV: X) Duel Roll
|
"1"
|
Draw
|
Loss
|
Loss
|
Loss
|
Loss
|
Loss
|
"2"
|
Win
|
Draw
|
Loss
|
Loss
|
Loss
|
Loss
|
|
"3"
|
Win
|
Win
|
Draw
|
Loss
|
Loss
|
Loss
|
|
"4"
|
Win
|
Win
|
Win
|
Draw
|
Loss
|
Loss
|
|
"5"
|
Win
|
Win
|
Win
|
Win
|
Draw
|
Loss
|
|
"6"
|
Win
|
Win
|
Win
|
Win
|
Win
|
Draw
|
|
If one opponent starts with a higher Fight Value than their
opponent, the results become more compressed. The likelihood of “wins” goes up
for that player, and the number of draws steadily decreases. The higher that
opponent’s starting Fight Value, the more severe the disparity. A challenger
who starts one Fight behind his opponent is only likely to roll higher in a
Strike-Off in 10 of 36 scenarios (27.78%) and draw in only 5 of 36 (13.89%);
his opponent, who starts with higher fight, will end up with the higher score
in the remaining 21 scenarios (or 58.33% of the time). If the challenger starts
off trailing his opponent by four fight, his chance of outright overcoming his
opponent’s Strike score is just 1 in 36 (2.77%), and the chance of drawing is
just 2 in 36 (5.56%), compared with his opponent’s 33 in 36 odds of winning
outright (91.67%):
Challenger
starts with -1 Fight Value (X-1 vs. X)
|
Challenger
starts with -4 Fight Value (X-4 vs. X)
|
|||||||||||||||
Target (FV: X) Duel Roll
|
Target (FV: X) Duel Roll
|
|||||||||||||||
"1"
|
"2"
|
"3"
|
"4"
|
"5"
|
"6"
|
"1"
|
"2"
|
"3"
|
"4"
|
"5"
|
"6"
|
|||||
Challenger (FV: X-1) Duel Roll
|
"1"
|
Loss
|
Loss
|
Loss
|
Loss
|
Loss
|
Loss
|
Challenger (FV: X-1) Duel Roll
|
"1"
|
Loss
|
Loss
|
Loss
|
Loss
|
Loss
|
Loss
|
|
"2"
|
Draw
|
Loss
|
Loss
|
Loss
|
Loss
|
Loss
|
"2"
|
Loss
|
Loss
|
Loss
|
Loss
|
Loss
|
Loss
|
|||
"3"
|
Win
|
Draw
|
Loss
|
Loss
|
Loss
|
Loss
|
"3"
|
Loss
|
Loss
|
Loss
|
Loss
|
Loss
|
Loss
|
|||
"4"
|
Win
|
Win
|
Draw
|
Loss
|
Loss
|
Loss
|
"4"
|
Loss
|
Loss
|
Loss
|
Loss
|
Loss
|
Loss
|
|||
"5"
|
Win
|
Win
|
Win
|
Draw
|
Loss
|
Loss
|
"5"
|
Draw
|
Loss
|
Loss
|
Loss
|
Loss
|
Loss
|
|||
"6"
|
Win
|
Win
|
Win
|
Win
|
Draw
|
Loss
|
"6"
|
Win
|
Draw
|
Loss
|
Loss
|
Loss
|
Loss
|
|||
Fortunately for our challenger, there is a catch: because a
hero’s Fight Value is capped at a maximum of 10, it becomes much easier for a
challenger with lower fight value to catch and match the Strike roll of an opponent
that starts with higher Fight. If Faramir Strikes against Sauron and rolls a “5”
and adds that to his basic Fight of “5,” he goes to Fight “10.” If Sauron Strikes
(at Fight 9), he will automatically go to Fight “10” regardless of what he
rolls; which means if he also rolls a “5,” he ends up with exactly the same
Fight Value as Faramir, even though he rolled a Strike Score of “14” (9+5).
This artificial cap on fight value means that our final
charts (for Fight 5 and higher, at least) end up with far more draws than if we
were just looking at the Strike rolls themselves:
Challenger
starts with -1 Fight Value (X vs. X+1)
|
Challenger
starts with -1 Fight Value (F5 vs. F6)
|
|||||||||||||||
Target (FV: X+1) Strike Roll
|
Target (FV: 6) Strike Roll
|
|||||||||||||||
"1"
|
"2"
|
"3"
|
"4"
|
"5"
|
"6"
|
"1"
|
"2"
|
"3"
|
"4"
|
"5"
|
"6"
|
|||||
Challenger (FV: X) Strike Roll
|
"1"
|
Loss
|
Loss
|
Loss
|
Loss
|
Loss
|
Loss
|
Challenger (FV: 5)
Strike Roll
|
"1"
|
Loss
|
Loss
|
Loss
|
Loss
|
Loss
|
Loss
|
|
"2"
|
Draw
|
Loss
|
Loss
|
Loss
|
Loss
|
Loss
|
"2"
|
Draw
|
Loss
|
Loss
|
Loss
|
Loss
|
Loss
|
|||
"3"
|
Win
|
Draw
|
Loss
|
Loss
|
Loss
|
Loss
|
"3"
|
Win
|
Draw
|
Loss
|
Loss
|
Loss
|
Loss
|
|||
"4"
|
Win
|
Win
|
Draw
|
Loss
|
Loss
|
Loss
|
"4"
|
Win
|
Win
|
Draw
|
Loss
|
Loss
|
Loss
|
|||
"5"
|
Win
|
Win
|
Win
|
Draw
|
Loss
|
Loss
|
"5"
|
Win
|
Win
|
Win
|
Draw
|
Draw
|
Draw
|
|||
"6"
|
Win
|
Win
|
Win
|
Win
|
Draw
|
Loss
|
"6"
|
Win
|
Win
|
Win
|
Draw
|
Draw
|
Draw
|
|||
The charts on the left show what the results would be if
there were no max cap on Fight; the charts on the right show the same results, assuming
our challenger is Fight 5, the target starts at Fight 6, and there’s a maximum
Fight cap of 10. Our challenger goes from winning 10/36 (27.78%) to winning
9/36 (25%), losing 21/36 (58.33%) to losing 18/36 (50%), and drawing 5/36 (13.89%)
to drawing 9/36 (25%). In other words, our lower-fight hero has gone from not
winning any drawn combats to have a 50/50 chance of either winning those drawn
combats outright (25%) or forcing a roll-off (25%). Not bad.
Now unfortunately for our challenger, the greater the difference
between his starting Fight Value and his target’s starting Fight Value, the
less likely he is to notch outright “wins” (meaning he’ll end with the
undisputed highest Fight Value). This intuitively makes sense: the lower your
starting fight value is than your opponent’s, the higher you’ll have to roll (and
the lower he’ll have to roll) to beat him; conversely, the larger the lead your
opponent starts out with, the lower he’ll have to roll (and the higher you’ll
have to roll) to beat you. Fortunately, the cap at Fight 10 helps keep our
Fight 10 hero in the running, replacing what would be outright losses with
contested roll-offs for drawn combats:
Challenger
starts with -2 Fight Value (X vs. X+2)
|
Challenger
starts with -2 Fight Value (F5 vs. F7)
|
|||||||||||||||
Target (FV: X+2) Strike Roll
|
Target (FV: 7) Strike Roll
|
|||||||||||||||
"1"
|
"2"
|
"3"
|
"4"
|
"5"
|
"6"
|
"1"
|
"2"
|
"3"
|
"4"
|
"5"
|
"6"
|
|||||
Challenger (FV: X) Strike Roll
|
"1"
|
Loss
|
Loss
|
Loss
|
Loss
|
Loss
|
Loss
|
Challenger (FV: 5)
Strike Roll
|
"1"
|
Loss
|
Loss
|
Loss
|
Loss
|
Loss
|
Loss
|
|
"2"
|
Loss
|
Loss
|
Loss
|
Loss
|
Loss
|
Loss
|
"2"
|
Loss
|
Loss
|
Loss
|
Loss
|
Loss
|
Loss
|
|||
"3"
|
Draw
|
Loss
|
Loss
|
Loss
|
Loss
|
Loss
|
"3"
|
Draw
|
Loss
|
Loss
|
Loss
|
Loss
|
Loss
|
|||
"4"
|
Win
|
Draw
|
Loss
|
Loss
|
Loss
|
Loss
|
"4"
|
Win
|
Draw
|
Loss
|
Loss
|
Loss
|
Loss
|
|||
"5"
|
Win
|
Win
|
Draw
|
Loss
|
Loss
|
Loss
|
"5"
|
Win
|
Win
|
Draw
|
Draw
|
Draw
|
Draw
|
|||
"6"
|
Win
|
Win
|
Win
|
Draw
|
Loss
|
Loss
|
"6"
|
Win
|
Win
|
Draw
|
Draw
|
Draw
|
Draw
|
|||
Challenger
starts with -3 Fight Value (X-3 vs. X)
|
Challenger
starts with -3 Fight Value (F5 vs. F8)
|
|||||||||||||||
Target (FV: X+3) Strike Roll
|
Target (FV: 8) Strike Roll
|
|||||||||||||||
"1"
|
"2"
|
"3"
|
"4"
|
"5"
|
"6"
|
"1"
|
"2"
|
"3"
|
"4"
|
"5"
|
"6"
|
|||||
Challenger (FV: X) Strike Roll
|
"1"
|
Loss
|
Loss
|
Loss
|
Loss
|
Loss
|
Loss
|
Challenger (FV: 5)
Strike Roll
|
"1"
|
Loss
|
Loss
|
Loss
|
Loss
|
Loss
|
Loss
|
|
"2"
|
Loss
|
Loss
|
Loss
|
Loss
|
Loss
|
Loss
|
"2"
|
Loss
|
Loss
|
Loss
|
Loss
|
Loss
|
Loss
|
|||
"3"
|
Loss
|
Loss
|
Loss
|
Loss
|
Loss
|
Loss
|
"3"
|
Loss
|
Loss
|
Loss
|
Loss
|
Loss
|
Loss
|
|||
"4"
|
Draw
|
Loss
|
Loss
|
Loss
|
Loss
|
Loss
|
"4"
|
Draw
|
Loss
|
Loss
|
Loss
|
Loss
|
Loss
|
|||
"5"
|
Win
|
Draw
|
Loss
|
Loss
|
Loss
|
Loss
|
"5"
|
Win
|
Draw
|
Draw
|
Draw
|
Draw
|
Draw
|
|||
"6"
|
Win
|
Win
|
Draw
|
Loss
|
Loss
|
Loss
|
"6"
|
Win
|
Draw
|
Draw
|
Draw
|
Draw
|
Draw
|
|||
Challenger
starts with -4 Fight Value (X-4 vs. X)
|
Challenger
starts with -4 Fight Value (F5 vs. F9)
|
|||||||||||||||
Target (FV: X+4) Strike Roll
|
Target (FV: 9) Strike Roll
|
|||||||||||||||
"1"
|
"2"
|
"3"
|
"4"
|
"5"
|
"6"
|
"1"
|
"2"
|
"3"
|
"4"
|
"5"
|
"6"
|
|||||
Challenger (FV: X) Strike Roll
|
"1"
|
Loss
|
Loss
|
Loss
|
Loss
|
Loss
|
Loss
|
Challenger (FV: 5)
Strike Roll
|
"1"
|
Loss
|
Loss
|
Loss
|
Loss
|
Loss
|
Loss
|
|
"2"
|
Loss
|
Loss
|
Loss
|
Loss
|
Loss
|
Loss
|
"2"
|
Loss
|
Loss
|
Loss
|
Loss
|
Loss
|
Loss
|
|||
"3"
|
Loss
|
Loss
|
Loss
|
Loss
|
Loss
|
Loss
|
"3"
|
Loss
|
Loss
|
Loss
|
Loss
|
Loss
|
Loss
|
|||
"4"
|
Loss
|
Loss
|
Loss
|
Loss
|
Loss
|
Loss
|
"4"
|
Loss
|
Loss
|
Loss
|
Loss
|
Loss
|
Loss
|
|||
"5"
|
Draw
|
Loss
|
Loss
|
Loss
|
Loss
|
Loss
|
"5"
|
Draw
|
Draw
|
Draw
|
Draw
|
Draw
|
Draw
|
|||
"6"
|
Win
|
Draw
|
Loss
|
Loss
|
Loss
|
Loss
|
"6"
|
Draw
|
Draw
|
Draw
|
Draw
|
Draw
|
Draw
|
|||
It’s also worth noting that the Fight cap of 10 also alters
the results of Strike-Offs where the heroes have the same starting fight value.
Their odds of winning the Strike-Off doesn’t change (each fight has the same
chance as their opponent does to “win” and to “lose” the Strike-Off), but the number
of “draw” outcomes increases significantly the higher that starting Fight Value
is. A Strike-Off between two Fight 4 heroes (which would be rare, but can
happen) results in fifteen wins for each side, and six draws. That same
Strike-Off between two Fight 6 heroes (which happens a ton) results in only 12
outright wins for our challenger, 12 outright wins for the target, and 12 draws
(i.e., inconclusive results). And, of course, a Strike-Off between two Fight 9
combatants (Sauron vs. Gil-Galad) results in thirty-six inconclusive outcomes:
Both
sides Start with Equal Fight Value (F4 vs. F4)
|
Both
sides Start with Equal Fight Value (F5 vs. F5)
|
|||||||||||||||
Target (FV: 5) Duel Roll
|
Target (FV: 5) Duel Roll
|
|||||||||||||||
"1"
|
"2"
|
"3"
|
"4"
|
"5"
|
"6"
|
"1"
|
"2"
|
"3"
|
"4"
|
"5"
|
"6"
|
|||||
Challenger (FV: 5) Duel Roll
|
"1"
|
Draw
|
Loss
|
Loss
|
Loss
|
Loss
|
Loss
|
Challenger (FV: 5) Duel Roll
|
"1"
|
Draw
|
Loss
|
Loss
|
Loss
|
Loss
|
Loss
|
|
"2"
|
Win
|
Draw
|
Loss
|
Loss
|
Loss
|
Loss
|
"2"
|
Win
|
Draw
|
Loss
|
Loss
|
Loss
|
Loss
|
|||
"3"
|
Win
|
Win
|
Draw
|
Loss
|
Loss
|
Loss
|
"3"
|
Win
|
Win
|
Draw
|
Loss
|
Loss
|
Loss
|
|||
"4"
|
Win
|
Win
|
Win
|
Draw
|
Loss
|
Loss
|
"4"
|
Win
|
Win
|
Win
|
Draw
|
Loss
|
Loss
|
|||
"5"
|
Win
|
Win
|
Win
|
Win
|
Draw
|
Loss
|
"5"
|
Win
|
Win
|
Win
|
Win
|
Draw
|
Draw
|
|||
"6"
|
Win
|
Win
|
Win
|
Win
|
Win
|
Draw
|
"6"
|
Win
|
Win
|
Win
|
Win
|
Draw
|
Draw
|
|||
Both
sides Start with Equal Fight Value (F6 vs. F6)
|
Both
sides Start with Equal Fight Value (F7 vs. F7)
|
|||||||||||||||
Target (FV: 5) Duel Roll
|
Target (FV: 5) Duel Roll
|
|||||||||||||||
"1"
|
"2"
|
"3"
|
"4"
|
"5"
|
"6"
|
"1"
|
"2"
|
"3"
|
"4"
|
"5"
|
"6"
|
|||||
Challenger (FV: 5) Duel Roll
|
"1"
|
Draw
|
Loss
|
Loss
|
Loss
|
Loss
|
Loss
|
Challenger (FV: 5) Duel Roll
|
"1"
|
Draw
|
Loss
|
Loss
|
Loss
|
Loss
|
Loss
|
|
"2"
|
Win
|
Draw
|
Loss
|
Loss
|
Loss
|
Loss
|
"2"
|
Win
|
Draw
|
Loss
|
Loss
|
Loss
|
Loss
|
|||
"3"
|
Win
|
Win
|
Draw
|
Loss
|
Loss
|
Loss
|
"3"
|
Win
|
Win
|
Draw
|
Draw
|
Draw
|
Draw
|
|||
"4"
|
Win
|
Win
|
Win
|
Draw
|
Draw
|
Draw
|
"4"
|
Win
|
Win
|
Draw
|
Draw
|
Draw
|
Draw
|
|||
"5"
|
Win
|
Win
|
Win
|
Draw
|
Draw
|
Draw
|
"5"
|
Win
|
Win
|
Draw
|
Draw
|
Draw
|
Draw
|
|||
"6"
|
Win
|
Win
|
Win
|
Draw
|
Draw
|
Draw
|
"6"
|
Win
|
Win
|
Draw
|
Draw
|
Draw
|
Draw
|
|||
Both
sides Start with Equal Fight Value (F8 vs. F8)
|
Both
sides Start with Equal Fight Value (F9 vs. F9)
|
|||||||||||||||
Target (FV: 5) Duel Roll
|
Target (FV: 5) Duel Roll
|
|||||||||||||||
"1"
|
"2"
|
"3"
|
"4"
|
"5"
|
"6"
|
"1"
|
"2"
|
"3"
|
"4"
|
"5"
|
"6"
|
|||||
Challenger (FV: 5) Duel Roll
|
"1"
|
Draw
|
Loss
|
Loss
|
Loss
|
Loss
|
Loss
|
Challenger (FV: 5) Duel Roll
|
"1"
|
Draw
|
Draw
|
Draw
|
Draw
|
Draw
|
Draw
|
|
"2"
|
Win
|
Draw
|
Draw
|
Draw
|
Draw
|
Draw
|
"2"
|
Draw
|
Draw
|
Draw
|
Draw
|
Draw
|
Draw
|
|||
"3"
|
Win
|
Draw
|
Draw
|
Draw
|
Draw
|
Draw
|
"3"
|
Draw
|
Draw
|
Draw
|
Draw
|
Draw
|
Draw
|
|||
"4"
|
Win
|
Draw
|
Draw
|
Draw
|
Draw
|
Draw
|
"4"
|
Draw
|
Draw
|
Draw
|
Draw
|
Draw
|
Draw
|
|||
"5"
|
Win
|
Draw
|
Draw
|
Draw
|
Draw
|
Draw
|
"5"
|
Draw
|
Draw
|
Draw
|
Draw
|
Draw
|
Draw
|
|||
"6"
|
Win
|
Draw
|
Draw
|
Draw
|
Draw
|
Draw
|
"6"
|
Draw
|
Draw
|
Draw
|
Draw
|
Draw
|
Draw
|
|||
So here’s the basic pattern:
·
Strike-offs between heroes with low, tied
starting fight (F4 or F5) tend to be crap shoots. It is literally a random
roll-off, and the results are incredibly variable, but mostly decisive. With tied
F6 or F7 (most heroes in the game who can Strike), there’s still a lot of
variance, and the variance tends to result in more results that are indecisive
(i.e., both sides reach Fight 10, and the winner of the duel hinges on a random
roll-off). And at tied F8 or F9, a “Strike-Off” has very little variance that pretty
much guarantees (or does guarantee, if you’re F9) an indecisive result.
·
Strike-offs between low-fight (F4-5) and
mid-fight (F6-7) heroes are heavily swung in favor of the mid-fight heroes
(they will win or draw 2/3 of the time, or better). Forcing a Strike-Off
between a low-fight (F4-5) and high-fight (F8-9) hero is of much greater
benefit for the low-fight hero, who is unlikely to make their current situation
much worse, and a decent chance at forcing a draw; there’s a lot less to be
gained by the high-fight hero.
Still following this? Good. One last thing to talk about…
So after we have our final fight
values… what next?
We started off this discussion by emphasizing that all a Strike-Off
impacts is six of thirty-six possible results in a duel outcome: when our
highest duel roll ties our opponent’s highest duel roll. The goal is to turn
those six results into “wins” (or at least into “draws,” if we start the fight
behind our opponent in Fight Value). But even if we’re successful, we still
need to roll those duel dice, and we still need a highest duel roll that will
at least match (if not exceed) our opponent’s highest duel roll.
Now at some level, our overall results chart isn’t going to
change, because we always only ever compare two dice (our highest vs. our
opponent’s highest), and those dice can only ever produce a result that is a
whole number equal to or between “1” (no lower) and “6” (no higher). Which
means, at the end of the day, there are only thirty-six duel roll outcomes, no
matter how many dice we roll or how many modifiers we apply:
Target (FV: X) Duel Roll
|
|||||||
"1"
|
"2"
|
"3"
|
"4"
|
"5"
|
"6"
|
||
Challenger (FV: X) Duel Roll
|
"1"
|
Draw
|
Loss
|
Loss
|
Loss
|
Loss
|
Loss
|
"2"
|
Win
|
Draw
|
Loss
|
Loss
|
Loss
|
Loss
|
|
"3"
|
Win
|
Win
|
Draw
|
Loss
|
Loss
|
Loss
|
|
"4"
|
Win
|
Win
|
Win
|
Draw
|
Loss
|
Loss
|
|
"5"
|
Win
|
Win
|
Win
|
Win
|
Draw
|
Loss
|
|
"6"
|
Win
|
Win
|
Win
|
Win
|
Win
|
Draw
|
|
Unfortunately, this chart creates the impression that all of
these outcomes are equally viable. And if we were simply fighting a duel that
consists of one duel die on one duel die, they would be. But that only tends to
happen when one warrior is fighting another (and to be honest, even single
warrior-on-warrior combats are pretty rare, unless the battle lines have completely
broken down). And it almost never happens for heroes, and almost never never
when there’s a Strike-Off on the line because Heroic Strike heroes almost all
have two or more attacks (Gandalf the Grey Striking against a Witch-King
without the Crown of Morgul is perhaps the only scenario where you’d see that…
at which point, someone’s doing it wrong). Outside of those very rare corner-case
scenarios, we have at least two dice on each side, and more often three or four
if not more.
Here’s why this matters: Heroic Strike only changes the
outcome of six of the thirty-six possible scenarios. On its face that may sound
insignificant (only 1-in-6? Why bother?). It may also sound drastically
important (I can win a whole 16.67% more fights? Sign me up!). But unless each
side is only rolling one duel die (which, as we said, will almost never happen
in a Strike-Off), those 1-in-6 figures and 16.67% percentages aren’t actually
the odds for those scenarios. Why? Because the more dice you roll, the higher
your odds of rolling a high duel roll—and the less your odds of rolling a poor
one.
Let’s start with the simplest example: If each side rolls a
single d6 for its duel roll, and has no modifiers for that duel roll, each of
our six outcomes (“1” through “6”) is equally likely, for each side:
Player 1's Duel Pool
|
Player 2's Duel Pool
|
|||||
1d6
|
1d6
|
|||||
Highest Duel Die Result
|
1 High
|
16.67%
|
Highest Duel Die Result
|
1 High
|
16.67%
|
|
2 High
|
16.67%
|
2 High
|
16.67%
|
|||
3 High
|
16.67%
|
3 High
|
16.67%
|
|||
4 High
|
16.67%
|
4 High
|
16.67%
|
|||
5 High
|
16.67%
|
5 High
|
16.67%
|
|||
6 High
|
16.67%
|
6 High
|
16.67%
|
By the same token, because each participant’s duel outcomes
are all of equal probability, there’s an equal probability that each of the thirty-six
possible outcomes (1 v. 1, 2 v. 1, 2 v. 2, and so on) has an equal chance of
coming about: 1-in-36, or 2.78%:
Tied
Fight, each side rolls one (1) Duel Die
|
|||||||
Target (FV: X) Duel Roll (1d6)
|
|||||||
"1"
|
"2"
|
"3"
|
"4"
|
"5"
|
"6"
|
||
Challenger (FV: X) Duel Roll (1d6)
|
"1"
|
2.78%
|
2.78%
|
2.78%
|
2.78%
|
2.78%
|
2.78%
|
"2"
|
2.78%
|
2.78%
|
2.78%
|
2.78%
|
2.78%
|
2.78%
|
|
"3"
|
2.78%
|
2.78%
|
2.78%
|
2.78%
|
2.78%
|
2.78%
|
|
"4"
|
2.78%
|
2.78%
|
2.78%
|
2.78%
|
2.78%
|
2.78%
|
|
"5"
|
2.78%
|
2.78%
|
2.78%
|
2.78%
|
2.78%
|
2.78%
|
|
"6"
|
2.78%
|
2.78%
|
2.78%
|
2.78%
|
2.78%
|
2.78%
|
|
Coincidentally (or perhaps not so coincidentally), this
gives the Challenger a combined chance of 2.78% * 15 (41.7%) to win the fight, a
2.78% * 15 chance to lose the duel (41.7%), and a 2.78% * 6 chance (16.68%)
chance to draw the duel. Which happen to be numbers we’ve seen before… a lot.
Now watch what happens when we add a single die to each side
of the fight (two heroes with two attacks each). Because we’re now using only
the highest
result of those two dice, our odds of getting lower numbers change. Here’s each
side’s chance of rolling a “1” to “6” highest (calculated by our good friends
at anydice.com):
Duel Dice Pool
|
|||
1d6
|
2d6
|
||
Highest Duel
Die Result
|
1 High
|
16.67%
(1/6)
|
2.78%
(1/36)
|
2 High
|
16.67%
(1/6)
|
8.33%
(3/36)
|
|
3 High
|
16.67%
(1/6)
|
13.89%
(5/36)
|
|
4 High
|
16.67%
(1/6)
|
19.44%
(7/36)
|
|
5 High
|
16.67%
(1/6)
|
25.00%
(9/36)
|
|
6 High
|
16.67%
(1/6)
|
30.56%
(11/36)
|
|
Notice how our odds of rolling only a “1 High” has
plummeted, because now it only happens if we roll “double 1s” (which we have
only a 1-in-36 chance of doing). If we roll a “1” plus any other outcome, we
won’t roll a “1 High” (assuming no negative modifiers from banners, etc.). Our
odds of rolling a “2 High” and a “3 High” have also dropped, although by less,
and our odds of a “4 High,” “5 High,” and that all-important “6 High” have
risen—in the case of the “6 High,” significantly. This is because of our thirty-six
scenarios, eleven of them include at least one six, giving us a “6 high” (6:1,
6: 2, 6:3, 6:4, 6:5, 6:6, 5:6, 4:6, 3:6, 2:6, and 1:6). 11-of-36 translates
into (you guessed it) 30.56%.
How do these changing odds impact our win-lose-draw odds?
Like this:
Tied Fight,
each side rolls two (2) Duel Dice
|
|||||||
Target (FV: X) Duel Roll (2d6)
|
|||||||
"1"
|
"2"
|
"3"
|
"4"
|
"5"
|
"6"
|
||
Challenger (FV: X) Duel Roll (2d6)
|
"1"
|
0.08%
|
0.23%
|
0.39%
|
0.54%
|
0.69%
|
0.85%
|
"2"
|
0.23%
|
0.69%
|
1.16%
|
1.62%
|
2.08%
|
2.55%
|
|
"3"
|
0.39%
|
1.16%
|
1.93%
|
2.70%
|
3.47%
|
4.24%
|
|
"4"
|
0.54%
|
1.62%
|
2.70%
|
3.78%
|
4.86%
|
5.94%
|
|
"5"
|
0.69%
|
2.08%
|
3.47%
|
4.86%
|
6.25%
|
7.64%
|
|
"6"
|
0.85%
|
2.55%
|
4.24%
|
5.94%
|
7.64%
|
9.34%
|
|
Instead of an even distribution of likely outcomes, we now
have outcomes that are heavily skewed towards higher duel rolls. Just 6.25% of
our outcomes involve a “high” duel roll for both sides of three or less
(compared to 25% of our outcomes with just one die). By contrast, more than
half the likely outcomes involve both sides having a “high” of four
or more (56.25%), and almost one-third of the time, each side will have at
least a “5 High” on their duel roll (30.86%). Most importantly, those “drawn
combats” only accounted for 16.67% of all results when each side was rolling
just one die. But with each side rolling two? 22.07%, or almost one-in-four
combats, end in a “draw” where fight value—and Heroic Strike—could provide a
decisive edge. And of that percentage, nearly half (9.34%) arise when both
sides roll a 6 High, when only Fight Value (or a roll-off) will
determine the winner.
Those percentages only go up as we add more and more dice to
the pool, each of which pushes up our chance of that “6 High,” to the point when
not
rolling a six high becomes the exception instead of the expected outcome:
Duel Dice Pool
|
|||||||||
1d6
|
2d6
|
3d6
|
4d6
|
5d6
|
6d6
|
7d6
|
8d6
|
||
Highest Duel
Die Result
|
1 High
|
16.67%
|
2.78%
|
0.46%
|
0.08%
|
0.01%
|
<0.01%
|
<0.01%
|
<0.01%
|
2 High
|
16.67%
|
8.33%
|
3.24%
|
1.16%
|
0.40%
|
0.14%
|
0.05%
|
0.02%
|
|
3 High
|
16.67%
|
13.89%
|
8.80%
|
5.02%
|
2.71%
|
1.43%
|
0.74%
|
0.38%
|
|
4 High
|
16.67%
|
19.44%
|
17.13%
|
13.50%
|
10.04%
|
7.22%
|
5.07%
|
3.51%
|
|
5 High
|
16.67%
|
25.00%
|
28.24%
|
28.47%
|
27.02%
|
24.71%
|
22.06%
|
19.35%
|
|
6 High
|
16.67%
|
30.56%
|
42.13%
|
51.77%
|
59.81%
|
66.51%
|
72.09%
|
76.74%
|
|
Now I won’t do the full duel roll probability charts for all those outcomes (mostly because by the time we get even to four dice, we’re dealing with an absurdly large denominator of more than a million). Suffice it to say, once we start rolling three attack dice or more against three attack dice or more, the odds of both sides getting at least one “6” high are pretty good (about 20% and higher). As that percentage increases, so does the benefit of having the higher Fight Value (and thus, Heroic Strike… probably).
Due to an arbitrary Blogger cut-off, this is the abrubt end to this discussion. Click here for Part V (our Faramir vs. Eomer case study).
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