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Cardiology: Iara's Instant Shield

Decision: Should You Play Iara's Instant Shield?

TL;DR:

Cursebreakers should pick this one up, as should Wurmspat.  Spell-focused versions of Eyes of the Nine and Ylthari's should also probably play it, and anyone trying to build around The Scattered Tome should obviously include every Page they can.

Factor: Math

We're going to be straight with you right now, the math on rerolls is hard.  In the past we've used some shortcuts to approximate the math on these kinds of things, but for various reasons, those shortcuts aren't as useful here.  So let's take a look at the actual math on successfully defending with Iara's Instant Shield.  For this example, we're just going to be looking at a single attack roll: a 2-hammer vs. 2-shield attack - which you successfully defend against 61% of the time without modifications.   If we were to fully calculate out the odds on this attack, the possible results would look something like this:


0 Sh1 B2 B1 Cr1 Cr + 12 cr
0 Ha6.25%8.25%2.78%4.17%2.78%0.70%
1 Ha8.25%10.89%3.67%5.50%3.67%0.92%
2 Ha2.78%3.67%1.23%1.85%1.23%0.31%
1 Cr4.17%5.50%1.85%2.78%1.85%0.46%
1 Cr + 1 2.78%3.67%1.23%1.85%1.23%0.31%
2 Cr0.70%0.92%0.31%0.46%0.31%0.08%
Given these possibilities, you've got a bunch of situations where you don't need to reroll at all to succeed at defense (green), a few where you reroll 1 die and hope for a better result (yellow), and a few where you reroll both dice (pink).  We've also got a few numbers bolded up there; these are results where, as the defender, you might consider rerolling both dice, or keeping a single success and rerolling one.  After running the numbers on those, you're better off keeping your successful die and rerolling the other one.

Now, to fully see how effective something like Iara's would be in this situation, we have to refigure the results for each of the pink and yellow possibilities, and see how much rerolling improves the chance of your guy not getting murdered.  Even after we factor in results that don't need to be calculated individually (ones where the initial roll doesn't matter), you're still doing 7 distinct calculations for a single attack roll.  


(It's entirely possible there's an easier way to do this, but I don't know what it is.)  

If we take all of those new calculations for rerolls and integrate them into the overall success chance for defending this attack, we get the an increase from 61% to 75%. Except, that doesn't account for the spellcasting roll to successfully cast Instant shield (the actual result with spellcasting factored in is 68% for a 1 die caster or 71.5% for a 2 die caster).  So now we have to account for all the possible casting rolls, refactor our percentages for each one, and manually recalculate every possible attack and defense combination.  

Yeah, we're not going to do that.  If only we had some way to effectively estimate the results... 

Factor: Math-ish

While not a perfect solution, we can get a decent idea of how effective Iara's Instant Shield is by simply pretending that it only lets you reroll all of the dice or none of them.  For example, in our 2-hammer vs. 2-shield/2-die caster scenario above, the full calculation nets us an overall defense chance of 71.5% - using our shortcut gets us 72%.  Not too bad.

In general, this method will underestimate the results on 2-die calculations by 0-3%, and slightly more on 3-die defenses.  On the upside, it works perfectly on 1-die defense calcuations!  

So with that sorted, here's some tables that show the increase in chance for a successful defense when you attempt to cast Iara's Instant Shield, with spell failure chances factored in:

Level 1 Caster1D2D3D1B2B
1H12%10%8%11%8%
2H12%12%12%12%12%
3H10%12%12%11%12%
1S9%8%6%9%7%
2S12%11%10%12%11%
3S12%12%12%12%12%
4S11%12%13%11%12%

Level 2 Caster1D2D3D1B2B
1H0.170.140.120.160.12
2H0.180.190.170.190.18
3H0.140.180.190.160.19
1S0.140.120.100.130.10
2S0.180.170.150.180.16
3S0.180.190.180.190.18
4S0.160.180.190.170.19

Level 3 Caster1D2D3D1B2B
1H0.200.170.140.190.14
2H0.210.220.200.220.21
3H0.170.210.220.180.22
1S0.160.130.110.150.12
2S0.220.200.180.210.18
3S0.210.220.210.220.21
4S0.190.210.220.200.22
That's a lot to take in.  But there are a few things we can glean from the results.  First, Instant Shield is most useful in situations with high variance - attacks that are very likely to fail or succeed in the first place are still very likely to fail or succeed, respectively, after Instant Shield.  Second, we should also point out that the current favorite Instant Shield target (Stormdad) actually doesn't gain as much help from it as some other casters might.  Fortunately for Thunder-Grandpa, he's good enough on his own that it's worth dropping Instant Shield on him most of the time anyway.  Finally, it's worth noting that two- and three-die casters can hurt themselves with backlash when they try to cast Instant Shield.  For that reason, if the attack roll fails, or the attack would only do 1 damage, it may not be worth rolling for the spell reaction.  Unless...

Factor: Not Math

For many warbands, there may be non-mathematical rewards for using Instant Shield, even in situations where the chance of success may be outweighed by the chance of backlash.  In particular, Instant Shield is a non-activation, reusable spell action - and it's currently the only one available.  As such, it's invaluable for easily scoring objectives like Magical Storm and Master of Magic/Magical Supremacy/Rotbringers.  It's also currently one of the best (by which we mean, only) ways to score Sorcerous Retort.  Finally, it provides opportunities to score Overpower and Rising Power, cards that are likely to see increasing play in the future.


The Wurmspat have additional incentive to play Instant Shield, as it gives Fecula more chances to roll shields on defense and drop the damage taken.  In this case, you may want to reroll defense dice even if you can't possibly stop the attack, simply to have a better chance at mitigating oncoming damage.  

Finally, the release of the Wurmspat expansion came with a new twist on the Katophrane Relic/Katophrane Tome formula: The Scattered Tome, which rewards you for collecting lost pages on a single caster.  If you're playing Scattered Tome, you had better be playing Instant Shield. 

Summary:

Iara's Instant Shield offers a solid take on the defensive upgrade formula.  While not as reliable as Champion's Fortitude, it offers more reward for the risk.

Decks that go hard on spells and spell-based objectives should definitely take Instant Shield, as should any that are set on keeping a single powerful caster alive.  These two kinds of decks tend to overlap, so the choice should be easy most of the time.  Some decks that don't fit neatly into one of those categories might also benefit from Instant Shield, particularly out of Wurmspat.  Finally, anyone running Scattered Tome should obviously pick up Instant Shield.

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