Thursday, September 19, 2013

Card Review:Pellinore's Problematic Probability

Okay, 1 last article before I finally get back onto the Request Box articles. Simply put, I wanna flesh out these Card Review articles just a little bit more, so I'm adding a section about Card Design.


A little fun fact about probability in card games? It never changes.

Okay that's a slightly inaccurate generalization, so let's do some actual math. Assuming your 49 card deck is properly shuffled and you run 4 Perfect Guards, what is the probability if you drew 1 card that it's a Perfect Guard? 4 Perfect Guards/49 cards, so 4/49. Now, what if you were to damage check a card first, then draw?

In this instance, there are now 2 different numbers to account for; if the damage check was a Perfect Guard, or if the damage check wasn't a Perfect Guard. The probability of damage checking a Perfect Guard is still 4/49, so the probability of drawing one afterwards will then be 3/48. On the other hand, the probability of not damage checking a Perfect Guard is 45/49, and the probability of drawing one immediately afterwards is now 4/48. So now if we multiplied the respective probabilities together and added them all up for the average, what do you think we'll get?


4/49. This means that after 1 random damage check, the overall probability of drawing a Perfect Guard is still 4/49.

The cool thing about this is that this is constant for however many random removals from the deck, not including removing 49 or more cards from the deck for somewhat obvious reasons. Remove 3 cards? 4/49. Remove 4 cards? 4/49. Remove 48 cards? 4/49. On average, probability involving something like your deck will remain constant if each and every removal is random. Interestingly, this same concept applies to drawing multiple cards in succession after the removal, essentially meaning things like the average probabilities involving Twin Drive will remain constant throughout the fight. This is actually the basis of why B.a.s.s. Values act the way they do, as their strength is, on average, constant. It is also why I base many of my probabilities off a full 49 card deck whenever the premise is broad enough, as it all essentially comes back to that.

Now with that somewhat large bit of trivia, onto the card review.

[AUTO](VC) Limit Break 4 (This ability is active if you have four or more damage):[Choose two of your «Gold Paladin» rear-guards, and put them on the bottom of your deck in any order] When this unit attacks, you may pay the cost. If you do, choose up to two of your «Gold Paladin», and those units get [Power]+5000 until end of turn.
[AUTO]:[Choose a «Gold Paladin» from your hand, and discard it] When this unit is placed on (RC) from your deck, if your opponent has a grade 2 or greater vanguard, you may pay the cost. If you do, put this unit on your (VC).

White Hare in the Moon's Shadow, Pellinore is the boss unit of GP's Bunny White Rabbit Corps. With the ability to distribute 2 stages upon anywhere on the field, and the possibility of a relatively cheap Superior Ride in the battle phase to enable yet another Vanguard attack, what does Pellinore have to offer?

Well, not much actually. I've already gone through the math with Pellinore's best buddies as far as Superior Calling him consistently without going overboard goes, and long story short, it's unimpressive. What should really be noted about Pellinore's Superior Ride capabilities is that it only barely offers much at all to the player. At only barely over a 1/4 probability to be Superior Called, the chances of actually being able to utilize Pellinore's Superior Ride in any single use is extremely slim. What's worst, is that at face value, the outcome of when its Superior Ride does exceed is...minimal.

To put this into perspective, let's assume you start with 4 cards in hand and a full field at the start of the Battle Phase, with Spring Breeze Messenger as the Vanguard booster. Not counting your Vanguard, you have 9 cards in total. If you attack with your Vanguard (and ignore any skills/draw triggers/etc.), you'll end the turn with 2 more cards in hand, 11 cards in total. On the other hand with Pellinore, you can attack with your Vanguard and end up at 6 cards in hand, and then activate Spring Breeze's skill. 5 cards in hand and 4 Rear-Guards, the next Twin Drive will immediately bring you back up to a grand total of...11 cards. From that fancy little jump from Spring Breeze Messenger to Pellinore to a standing Vanguard, you generate a net total of 0 cards. Of course, there is the fact that Pellinore is forcing cards out of the opponent's hand, right? Well, the problem is exactly how are you going to boost it?

Now, the established field is quite unfair for this point but, think about it for a moment.  Let's assume I only have 1 Spring Breeze to spare. If I were to place it behind the Vanguard Circle, I would be forced to boost it and move it away through its skill in order to actually get Pellinore out with it, so from there, there is no option for Pellinore to get power without resorting to skills. If I were to place it in a Rear-Guard column however, I could end up facing a severely underwhelming power line if I can't also supply a powerful beater, or if something happens to said beater. Along with this, the options for consistent and low costing beaters that exceed 15K are...rare. It's ha/rd to realistically expect that the column can truly generate real card advantage without the help of triggers, along with giving the opponent a really good opportunity to skirt damage anyway since at this point, the only way Pellinore will have a boost when it takes over the Vanguard circle is to attack unboosted the first time around. All in all, the options simply make it impossible or are far too prone to failure to really expect Pellinore to have a booster for the second Vanguard attack.

So with that, we are left with an unboosted 10K Vanguard attack. At its very best, it will force out another 10K shield out of a 10K or weaker Vanguard, or priority Rear-Guards while also supplying triggers that may or may not generate more forward advantage. At its worst, it will only be able to force out 1 stage of shielding at best, only 5K shield from the opponent and barely having much of an impact at all on the fight. Even if it's card advantage being generated, the only redeeming quality of this re-ride is either the added Triggers, which while useful in and of themselves aren't actually that influential on B.a.s.s. Values, oddly, or comboing off its Limit Break or utilizing the discard to clean up any poor quality card advantage hanging around. This of course assumes that your field was bad in the first place, and due to the nature of a bunny-centric GP deck, it was probably intentional as well. This is literally shooting yourself in the foot. Unless you had the early game justification for it and got the triggers to best complement the lackluster setup, this intentional sabotage of your field will only be a detriment to you in the long run, and is poor justification for Pellinore's ability to trade around card quality.

Okay, so its Superior Ride is...lackluster, to put it bluntly. On the otherhand, we still have its Limit Break. If we assume a R-V-R attack pattern with 16K columns all across against an 11K Vanguard, and use the first Rear-Guard column for Pellinore's Limit Break, we end up with these B.a.s.s. Values:

0 Perfect Guards:
+10K to Vanguard lane, +10K to Rear-Guard lane: 2365/49K, 272/49

+5K to Rear-Guard and Vanguard lane: 2365/49K, 250/49

1 Perfect Guard:
+10K to Vanguard lane: 1140/49K+PG, 223/49

+5K to Rear-Guard and Vanguard lane: 1385/49K+PG, 250/49

+10K to Rear-Guard lane: 25K+PG, 5

2 Perfect Guard:
+10K to Vanguard lane: 710/49K+76/49 PG, 223/49

+5K to Rear-Guard and Vanguard lane, +10K to Rear-Guard lane: 10K+2 PG, 5

Compared to the standard 1875/49K, 228/49, let's see how these compare.

With no Perfect Guards, pumping up the Rear-Guard lane is the same as pumping up the Vanguard lane, so let's just assume powering up the Rear-Guard lane. With that power up, Pellinore will force out 10K shield in the form of 44/49 more cards out of the opponent than normal, but at the same time, the cost to activate its skill leaves an overall -54/49 in card advantage, essentially only a little over a -1. This in mind, while it is great if the opponent is well within that danger zone, it would crash in effectiveness the more and more it is used. When 1 Perfect Guard is involved, the standard now falls to 1140/49K+1 PG, 228/49 cards. Once again, Pellinore sets up stronger danger zone, but this time isn't nearly as far ahead. This time only forcing out 5K shield more than normal in the form of 22/49 cards, virtually only a +1/2. After considering the costs, being forced down by a -1.5 cards in net card advantage means its performing even worst off. One can probably guess where this is leading to.

Overall, Pellinore just seems rather...lame. While in a vacuum, it is technically already balanced optimally, the support just does not exist to properly support Pellinore and may never will, since it is GP that we're dealing with. Trying too hard to be highly efficient in regards to its Superior Ride with a Limit Break to allow it to explode at a heavy cost, Pellinore's execution was just not properly supported by GP's Superior Call ability, making it extremely unlikely to ever utilize its Superior Ride or even come close to justifying its taxing Limit Break.

How to use this card

Pellinore is not a boss Vanguard. Or rather, if it was, it's way too lackluster to ever justify properly. Thanks to its Limit Break being an overall detriment to you, only being the least bit beneficial if your opponent is within the danger zone post skill and wasn't in the standard danger zone in the first place, you'll need another Vanguard to serve as the boss unit of the deck. While technically speaking, any boss unit that can use Spring Breeze Messenger can use Pellinore, here is a short list of optimal Vanguards:

a) Great Silver Wolf, Garmore: Easily the best unit to do the job, Garmore's ability to Superior Call a Grade 2 or lower unit of your choice on-ride only further complements the more quality based Superior Calls that the White Rabbit Corps. have access to. Being able to potentially swarm the field when used with Lop Ear Shooter, generate tons of Card Advantage through Dindraine, or simply do a good, all around job at optimizing your field, Garmore's strengths simply cannot be understated. The deck is also the most stable of any GP build. While its riding performance is standard, the amount of Superior Calls one can make all that they have some control over means that the viability of the field will always be top notch and quick to deploy upon the opponent. Very self supporting all on its own, the deck can only benefit from taking matters into its own hands, and allowing Pellinore to shine when the time comes.

b) Virtually any Liberator that requires Liberator CB: This is more of a response to those who are trying to justify this pairing. The problem with throwing Pellinore into a Liberator based deck is just how Liberator-centric the Liberators are. Most of the Grade 1s are almost all virtually negated without a Liberator Vanguard and you only have a limited pool of viable Grade 2s in the case that you are able to Superior Ride Pellinore. This constraint, on top of necessarily needing those units in the first place to more easily facilitate the main Vanguard's cost, simply is annoying to try to juggle around. That said, it is not impossible. Being able to still utilize Spring Breeze Messenger and Lop Ear for decent enough space, along with Josephus being a much more usable unit than Dindraine, and Barcgal Liberator also creating more opportunities. In fact, the Liberators serve as the closest thing to a viable deck for Pellinore's Superior Ride to really shine thanks to the opportunities that the Liberators' line up can create. However, if one really does want to go through with using Pellinore here, the deck's balance between Liberators and non-Liberators must be perfect in order to utilize either groups optimally.

That's...actually it. Spectral Duke Dragon with Rabbits is a fun casual build when everything goes right, but isn't exactly reliable in much any form. Along with this, Ezel+Pellinore Double Superior Ride is an interesting challenge for deckbuilders by giving you just enough consistency to be able to fight optimally, while also offering far more defensive value and field scalability, but considering the number of mathematicians who can actually figure that build out...

Alrighty, enough copping out. Eventually, whether your Superior Ride was successful or riding your main Vanguard wasn't, you'll need to use Pellinore's Limit Break in order to generate forward advantage. The 5 damage danger zones are all above in the main card review, but in short, if the opponent has 5 or less cards, gun it. From there, it will depend on how much shield the opponent has.

Unlike Raging Form Dragon which can regenerate almost all of the Card Advantage it loses through its cost, Pellinore is...Pellinore. The Pellinore player needs to be extremely proactive about their plays, dealing with triggers and weighing the risks to the rewards of pushing while the opponent can still take damage, so the idea of using B.a.s.s. Values to establish a 'danger zone' can only go so far. While advice can't be made with exactly how one executes Pellinore's skill, Pellinore still follows the same basic rules of any big finisher Vanguard. The most important priority is to outpace the opponent in some form, meaning that Early Guarding and Scaling the field right away is imperative to reaching victory.

How to Fight Against This Card

The only dangerous part about Pellinore is if it gets its Superior Ride while you can't defend it. The problem is that there's very little that you can actually do to influence its effect on the fight, and that's even if it matters in the first place.

For a start, falling prey to pressure is only shooting yourself in the foot. Remember, Pellinore at best is a +1 in raw card advantage with its Superior Ride. With one of the only (somewhat) viable ways of actually calling it being Spring Breeze Messenger, technically a pressure unit, this means that an attack will force you to have to decide between a -1 from Pellinore attacking, or a technical -1 from burning through your guard, if the opponent's Vanguard lane is powerful enough. The problem here is that guarding only works for the turn, so if you really want to keep Pellinore at bay, you'll be facing minuses every turn from there on out, forced to drop more and more guard and most likely jeopardizing the game by giving such an easy opportunity for the Pellinore player to set up into the late game. Essentially, the best out to this is to simply save your guard, and watch the opponent fail to Superior Call Pellinore over 70% of the time, and guard Pellinore if it does appear the last 30%.

Again, standard rules of a finisher Vanguard. What's really important as the defender is to somehow outpace the opponent and keep revealed as little of your hand as possible. Due to the nature of Rabbit Corps Gold Paladins, you may legitimately face problems with trying to keep up with how quickly your opponent's field is going to develop, ultimately meaning that emphasizing your deck's capabilities and maintaining as much control of the fight as possible with efficient guarding is going to be your main goal of dealing with the deck. What's really important in the fight is trying to put emphasis on how expensive Pellinore may be. For example, if your deck is capable of it, try over-telegraphing your late game potential to ward off the opponent from jeopardizing themselves through Pellinore's expensive Limit Break. While Pellinore does have the potential to be a threat to you when it's given the proper set up, dissuading the opponent and making them feel as though they're in no position to be able to properly use Pellinore's skill without major repercussions can be key to staying ahead in a fight.


Card Design

Alrighty, so let's put this into use.

The funny thing about Pellinore is that if somebody has an opinion of him, the opinion will be a stark black and white view about whether or not Pellinore is legitimately good or bad. On one hand we have the people who glorify Pellinore as their lord and savior, not especially caring how inconsistent he is or building false illusions that he actually is far more reliable than probability tells us. On the other hand, we have haters that absolutely cannot see Pellinore as good in any context. 'Sure, he may sound nice on paper once he actually goes off, but in reality he's just so incredibly lame and it's not like he's consistent enough to go off much anyway'. So, let's put this to rest.

Starting with his Superior Ride skill, the incredibly inconsistent +1 that requires another skill to Superior call it, it can essentially be chalked up to 1 Counter-Blast in total value. Next, his Limit Break skill to lose 2 units to power up 2 others, can be described as a high quality -1, so let's leave it as that, a skill worth only 0 Counter-Blasts. On top of this, we must remember that Pellinore is a 10K Vanguard, meaning that we should reduce a cost somewhere by 1 Soul. Furthermore, a Limit Break is added onto Pellinore's first skill, reducing the overall costs of Pellinore's skill by another Soul. Because Pellinore's Superior Ride is the conditional skill of the two, and potentially sets Pellinore up for its Limit Break, Rule 7 allows for the transfer of its cost to the Limit Break skill. So, with both the Limit Break and Pellinore's 10K status stacking up to a reduction of 1 Counter-Blast, the cost is completely mitigated.

For those who didn't understand all of that, this essentially means that in a vacuum, Pellinore is already completely balanced, at least by my interpretations using the Grading Scale. This essentially means that, in and of itself, Pellinore is simply a solid card. Neither intrinsically good, nor bad, it's simply sitting exactly where it should be on the power curve. So, why all the black and white views?

I guess what's really important is how inconsistent Pellinore is, but this isn't actually Pellinore's fault. Due to its placement in the Gold Paladin clan, the only access it has to Superior Calls are those that have extremely limited reach, and won't often give the player any particular unit they want anyway. With Pellinore's most consistent means of being Superior Called only having a 28.5% probability, the entire combo just can't be seemed viable and the end result, being able to Superior Call Pellinore, will too seam weak. It's this failure of viable ways existing to initiate this combo that really makes Pellinore so lackluster to many, even despite the fact that Pellinore in and of itself isn't actually terrible.

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