Cardiology: Double Feature! Branching Fate/One Fate

Decision: Should You Play Branching Fate/One Fate?

TL;DR:

Do you stride far? Then you should probably be playing Branching Fate.  Other warbands with high dice counts should consider playing Branching as well.  If you can manage to regularly roll 3 magic dice on spell attacks, One Fate is quite good.  Otherwise, pass on it.

Prelude:Double Feature!

This week we're taking a look at two different cards for Cardiology; rest assured this departure from standard operating procedure is for good reason.  Namely, the math required to analyze One Fate is very similar to the math required to analyze Branching Fate.  We couldn't see a reason to stretch the same work into two articles, so this week you're getting a two-for-one special.

Factor: Warband

In order to score either of the Fate objectives, you've got to be rolling three or more dice on attack or defense.  Rolling three dice on attack is pretty common (defense - less so), but some warbands definitely come naturally better equipped to score these objectives than others.  The following chart summarizes the number of natural 3+ dice rolls available to each warband without adjuncts:

Warband	3+ attack	3+ defense
Garrek's Reavers	5	0
Steelheart's Champions	2	0
Sepulchral Guard	7	0
Ironskull's Boyz	2	0
Chosen Axes	4	0
Spiteclaw's Swarm	2	0
Farstriders	9	0
Magore's Fiends	4	0
Stormsire's Cursebreakers	3	0
Thorns of the Briar Queen	3	0
Eyes of the Nine	3	0
Zarbag's Gitz	6	1
Mollog's Mob	1	1
Godsworn Hunt	6	0
Ylthari's Guardians	1	0
Thundrik's Profiteers	3	0

Of course, not all attacks are equal.  Mollog's Mob only comes with a single 3+ die attack, but it targets multiple models.  Two of the three 3+ die attacks in Thorns come on the queen herself, and are likely to get a lot of use.  The orcs, on the other hand, come equipped with two 3+ die attacks, but those attacks are the worst of your options in general.  All around, Farstriders present the most options for 3+ die attacks, and - as a bonus - their attacks are actually likely to see quite a bit of use.

It's also worth noting a couple of anomalies.  One of the 3+ die attacks in the Godsworn Hunt can only be used once (the javelin), making it less useful than most.  Thundrik's Profiteers offers the only natural 4-die attack in the game at this time - which isn't good for scoring these particular objectives.

Finally, we should note that magic dice on spell attacks can be used to score either of these objectives.  We'll take a closer look at that in the next section, but for now, it's worth noting that no one starts with a natural 3+ die magic attack, so you'll need power cards to make either objective work off magic.

Factor: The Dice

Now we've come to the true crux of this question.  How likely are you to score either of these objectives, given that you are rolling a sufficient number of dice?

Let's start with Branching Fate.  When you roll 3 attack or defense dice, there are 216 possible outcomes of that roll.  Of those 216 outcomes, 96 (44.44%) will allow you to score Branching Fate.  If you were to use all 4 of your normal activations in a round making 3-die attacks (*cough*Farstriders*cough*), you'd score Branching Fate about 90% of the time in a single round.  Unlike most other dice-based objectives, the Fate objectives get harder to score the more dice you add to the roll, so it's worth looking at how that affects your chances.  A 4-die attack or defense roll has 1296 possible results, and only 216 (16.67%) allow you to score Branching Fate.  In this case, if you were to spend your whole round making 4-die attacks, you'll only score Branching 52% of the time. A 5-die attack scores Branching Fate even more rarely - only 3.08% of the time.  Any attempt to score Branching fate off an attack or defense roll that uses 6 or more dice will necessarily fail every time.

Branching Fate can also be scored off a spell attack that rolls 3 dice.  In that case, the probability of scoring Branching fate off a single 3-die attack roll is 16.67% - definitely a step down from a Farstrider boltgun.  Additionally, it's worth noting that any spell attack that rolls 4 or more dice can't score Branching Fate; there are only 3 available results on a magic die.

Now let's look at One Fate.  When you roll 3 attack or defense dice, you'll be able to score branching fate on 12 of the possible outcomes - a success rate of only 5.56%.  Rolling four 3-attack dice in a single round means that you'll be able to score One Fate about 20% of the time.  If you up the number of dice rolled to 4, you'll only succeed 1.54% of the time.  Finally, if you roll 5 dice, you'll only be able to score One Fate on 0.72% of those rolls.  Obviously, One Fate is quite a bit more difficult to score in these cases than Branching Fate.  However, it is worth noting a couple of things.  First, One Fate can be scored off any number of dice over 3; while the likelihood of a successful roll continues to decrease with additional dice, there is no "hard cap" for One Fate like there is for Branching.  Second, One Fate is worth two glory.  When comparing it directly to Branching Fate, we should essentially double the chance of success of One Fate, as when we do score it, we'll get the equivalent of scoring Branching Fate twice.

Finally, One Fate is quite a bit easier to score with magic dice than with attack or defense dice.  A 3-magic die roll has a 16.67% chance of qualifying to score One Fate.  With 4 magic dice, you'll still end up scoring One Fate 3.85% of the time.  The percentage of success continues to decrease as you add more dice, but once again it is worth noting that you can succeed with any number of dice. 

We should point out at this juncture that One Fate is simply equally likely or more likely to score in every case where magic dice are used - and it's worth double the glory of Branching Fate.  If you anticipate that all or most of your attacks will be spell attacks (and you can come up with a way to consistently roll 3+ dice on those attacks), One Fate is simply a better choice all around.

Factor: Adjuncts 

There are a few kinds of adjuncts that can make scoring the Fate objectives more reliable.  First, there are several upgrades that provide attacks that qualify to score Branching Fate or One Fate.  Upgrades like Swift Strike and Sword Breaker meet the basic requirements for scoring Fate Objectives.  The Nullstone Sword and Nullstone Darts also allow rerolling of dice in certain circumstances (we'll get into that more later), making them ideal for scoring Fate objectives.  Finally, cards like Dark Darts and Shadeglass Darts provide you with the ability to score Fate objectives from range, which should allow you to try more often than with melee attacks.  Overall, the ideal universal upgrade attack for scoring Fate objectives is probably Nullstone Darts, as it has a range of 3 and provides some rerolling.

You can also use power cards to upgrade the number of dice you are rolling.  If your warband is heavy on 2-die attacks, but you really want to use Fate objectives for some reason, you should probably invest in some of these attack-die boosters.  These kinds of boosts are more plentiful in temporary form from ploys and spells than they are from upgrades, so keep that in mind when you build your deck.  It's also important to remember that after you hit the 3-die threshold, adding more dice makes you less likely to successfully score the Fate objectives, so don't go overboard here.

Third, and perhaps most importantly, we come to power cards that let you reroll dice.  Cards like Awakened Weapon, Archer's Focus, and Trusted Defender all let you reroll a single die during an attack or defense roll.  This can mean a significant increase in your ability to score the Fate Objectives.  For example, in a 3-die attack roll there are 96 results where you won't need to reroll any dice to score Branching Fate.  There are also 12 results where rerolling a single die won't help you score Branching Fate.  However, rerolling a die on the remaining 108 results does increase your chances of being able to score Branching Fate significantly.  Overall, being able to reroll one die in a 3-die attack increases the success rate of Branching Fate from 44.44% to 72.22%!  Similarly, rerolling a single die on a 3-die attack increases the success rate of One Fate from 5.56% to 17.59%!  You'll see mathematically similar (but quantitatively different) increases in success rates if you apply a single reroll to a spell attack roll.  If you can manage to give K'Charik's Guided Greatblade an extra die (or play Fuelled by Fury on any 3-die attack), you'll be almost certain to score Branching Fate, and have a good chance to score One Fate.

Finally, we should look at cards that allow you to "change" a die result or cards in which certain results "count as" other results - cards like Arcane Familiar and Unparalleled Strike.  There's certainly room to debate whether or not using these cards will allow you to score the Fate objectives (similarly, it's unclear whether or not you could use Power Surge on your opponent's casting roll to ruin their chance to score Branching Fate).   If they do, they help you to do so a lot.  If they don't, then obviously, they aren't useful adjuncts for this scenario.  Until there's a clear ruling on the situation, we recommend that you don't count on them for scoring these objectives, just to be safe.

Alternate Path: What Armour?

What Armour has become a staple in pretty much any deck that can regularly conjure up Cleave attacks (and even some decks in which the definition of "regularly" seems quite stretched).  It provides a good point of comparison for the Fate objectives; they all score off a single attack, score immediately, and depend entirely on the die results of that single attack.  As we've explained in prior articles, one way to look at the success rate of a given attack is to compare it to a "random average" defense - an imaginary aggregate defense based on the general distribution of all available defense scores currently in the game.  When we do that for several common Cleave attacks, we get success rates that look like this:

Cleave Attack	RA Succes
1 sword	24.51%
2 sword	43.10%
3 sword	56.79%
4 sword	67.46%
1 hammer	35.71%
2 hammer	58.08%
3 hammer	72.07%

If we compare these numbers to those that we have for Branching Fate, we can see that there are certain situations in which Branching Fates is the better choice; any warband that regularly rolls 3 attack dice (or 3 defense dice) and doesn't have regular acess to a 3+sword or 2+hammer attack with Cleave should drop What Armour for Branching Fate.  If we compare One Fate to What Armour the comparison is initially significantly less rosy; there's no situation in which One Fate scores more often than What Armour.  However, we do need to account for the increased glory from One Fate!  With that factored in, there are some narrow cases where One Fate is a better choice than What Armor; any deck that is regularly rolling 3 magic dice for spell attacks and lacks regular access to 2+sword or 1+hammer Cleave attacks should swap out What Armour for One Fate.

In most cases, warbands with easy access to Cleave should stick to What Armour.  However, for warbands without good access to Cleave (Orcs, Skaven), warbands with good access to 3-die attacks or magic attacks (Cursebreakers, Sepulchral Guard), or warbands with both limited access to Cleave and lots of 3-die attacks (Farstriders!), putting in the appopriate Fate objective for your strengths should net you better results than What Armour in the long run.

Summary:

Decks that regularly roll exactly 3 dice on attack, defense, or spell attack rolls can probably benefit from the inclusion of one of the two Fate objectives.  Those that roll more attack and/or defense dice should choose Branching Fate; those that roll more magic dice should take One Fate.  Both Fate objectives can benefit significantly from the use of adjuncts, and if you're running a Fate objective, picking up a few specific power cards will help you achieve your goals.  Fortunately, most of the power cards that help you score Fate objectives are good anyway, so including them won't hurt your deck.