Buddyfight Math - Choosing your Buddy and Counting Cards

What would Future Card Buddyfight! be without the ability to designate that one special card to be your one and only buddy?

As kiddy as this may sound, choosing your Buddy is actually quite a serious and important decision for your game. Not only does it mandate which card you must run at 4 copies, but it also dictates for both you and your opponent exactly what kind of grand strategy you are aiming to employ...usually. There's the idea of faking out your opponent with an awkward Buddy choice, which has its pros and cons.

This article will also be a good place to discuss just how often you should expect to draw into your Buddy and will cover some general basics about card counting that apparently nobody quite understands, so if you were thinking that a Buddy discussion was too simple for you then I'm throwing you a bone here. Fetch.

Buddy Call

Drum Nuigurumi

I swear, everybody gets the Buddy call wrong. For casual play, it's no real big deal, but if you ever feel like you want to step into the competitive scene then you better get this right before the judges start coming after you. Let's lay out the steps in a simple manner:

1. Reveal the Buddy card from your hand and declare a Buddy call.

2. Pay any of the call cost requirements. If you can't pay them, then don't freaking declare the call.

3. Call the card from your hand into the Buddy zone. Yes, the place right next to the flag.

4. Rest the card you just called into that zone.
* Your opponent gets to counter here *

5. Choose your Buddy monster from that zone and call it to the field.

6. If the call was completely successful, give yourself +1 life.

Cerberus Nuigurumi

At official events, please do not just rest your Buddy monster and call from hand to field. Even though it literally is the same thing, official judges want the above to be performed because, well, that's what the rules say. It's for this reason that you technically are NOT allowed to sleeve your Buddy with a different sleeve from your main deck. Keep this in mind, and don't say I didn't warn you.

Anyways, you've done this super-elaborate calling process, so what do you get out of it? Two things. The first is a free +0.5 in advantage. Don't underestimate this, every life point matters in a game of numbers. The second is the ability to proc a variety of effects of other cards, such as Ultimate Buddy and Buddy Charge. At the moment, most of these effects are pretty useless with the exception of Ultimate Buddy. We can talk about that in a bit.

Choosing a Buddy

The Original Buddy

Now that we've gone over the Buddy call, it's time to determine what exactly is the best choice for a Buddy. The answer is relatively simple: your Buddy should be the one card that you want to play as soon as you get it, whenever you get it. You want that extra life. You want to play this one totally awesome monster. Kill two birds with one stone by setting your Buddy to be that monster, thus increasing the likelihood of actually getting to Buddy Call.

Your Buddy should preferably cost very little, if not nothing at all. After all, who wants to be stuck on gauge when they draw their Buddy? As a standard, a Buddy that costs more than 2 gauge to play is probably a bad Buddy choice. In addition, it's very likely that your Buddy will be a Size 1 or 2 monster. Size 1 is probably the best, because you can call them basically at any given time and gain your free advantage. If you have a Size 2 on the field already and you draw into a Size 2 Buddy, then you're going to have to make a pretty hard decision.

Expelliarmus!

Of course, since Begone!! is in the format, you might want to consider using a Size 3 if you're really scared of your opponent nullifying a Buddy Call. If they nullify the call, you not only lose your Buddy but also your free life (the life is only applied when your Buddy monster enters the field safely). You can't Buddy Call after that, so if you're paranoid of that one card then choose a cheap Size 3 to be your Buddy.

Sometimes, your Buddy can be a dead giveaway. Like Jackknife Dragon. Nobody's going to have Jackknife as a Buddy and NOT run a totally Jackknife-centric deck, which then implies the 3 crit pressure columns that Jack and his evolutions create as well as the Aggressor Soulguard and the Thunder Storm field clear. Knowing that is literally half the battle, so why give yourself away? A Buddy Fake (I literally just coined that term) is a strategy where you choose a Buddy that has absolutely nothing to do with the overall strategy of your deck. In Jackknife decks, I would strongly recommend having Thousand Rapier Dragon as your Buddy. You're probably going to run 4 since he's so good, and he's SO vanilla. He fits in every single freaking Armordragon deck in the whole wide world. Nobody's ever going to see that French dragon by your flag and think "Wow, that's totally a Jackknife deck." You just scored yourself a huge psychological advantage over your opponent. Win for you.

The most obvious
give-away ever

Here are the list of the Buddies that I personally recommend for your respective decks if you want to hide your main gambit:

Armordragons: Thousand Rapier Dragon; Blade Wing Dragon; Tuck Sword Dragon; Blade Chakram Dragon
Dragon Knights: Dragon Knight, Maximilian; Dragon Knight, Red Baron
Armorknights: Armorknight Hellhound; Armorknight Eagle
Duel Dragons: Saberclaw Dragon, Valken; Clash Dragon, Gaelcorga
72 Pillars: Demon Lord, Asmodai
Wizards: Center of the World, Mary Sue
Ninjas: Nanomachine Ninja, Tsukikage; Accelerate Ninja, Hayate; Sky Ninja, Yamigarasu
Skull Warriors: Flash Strike, Yamaihebi; Blade Tiger, Gurenenbu; Tempest, Garo-oh
Dragon Lords: Flame Fairy Dragon, Tialvette
Wild Dragons: Ice Dragon, Knoke-isle
Adventurers: Dragonblade Wielding Sheila Vanna
Dungeon Enemies: Fate Skeleton; Mameshiba, Cobalt
Wydar Sarkal: King of Forest, Zlatorog
Heroes: King of Forest, Zlatorog
Asgard: King of Forest, Zlatorog, Valkyrie, Assault Cara
Black Dragon: Death Wizard Dragon; Death Dragon, Deathgaze Dragon
Death Ruler: Death Wizard Dragon; Death Ruler, Burial
- updated for BT04, CP01, EB01, TD06 -

Or you could just tout your Jackknife loud and clear, and lose a bunch of matches because your opponent totally read you like a book.

Note that the above list is mainly for decks that don't want to give away their primary strategy. For decks like Duel Sieger, when you're going to want to call Sieger out ASAP, you may want to have him as your Buddy (since you can't call Tialvette after you call Sieger). And for the even more specific builds like Thunder Knights and Shinsengumi, then you definitely want a Buddy that actually matches your deck.

Ultimate Buddy

Now it's time to talk about the only usable spell thus far created for Buddy cards: Ultimate Buddy.

SUPER SAIYAN

Ultimate Buddy is a GREAT card. I originally calculated this card to be -0.5 but forgot that power can be scaled by my advantage scale as well...which means that Ultimate Buddy is actually something like a +0.333 but I'll give the exact decimal value once I finish calculating (just consider it a +0.5). The ability to grant Soulguard to any monster in the entire world is something to be appreciated. I'll cover Soulguard and other abilities in a future article, but I'll briefly touch on it here. Soulguard is all about card quality: if the card with Soulguard is a quality card (Double Attack, Penetrate, 3 crit, good stats, etc), then Soulguard is more than worth it; otherwise, it's wasted. Ultimate Buddy is all about a good opportunity card to maximize potential.

It really doesn't matter if your Buddy already has Soulguard - as long as the card is a quality card, then the soul will be put to good use. Buddies that I would definitely try this card in tandem with are Jackknife Aggressor, Dragon Knight, Geronimo, and Evil in Heart, Yamigitsune, to name a few. Anything with Double Attack will probably earn a thumbs up in terms of quality.

Inferno Armor Dragon stands to be the only card in the game thus far that has an effect that puts cards into his soul, but doesn't have Soulguard. Well, with Ultimate Buddy, you can fix that! Thus Inferno Armor Dragon can function either as a field nuke by discarding the soul, or a huge tank with 3 soul and the added option of a possible field nuke. The +0.5 opportunity gain of Ultimate Buddy is suddenly transformed into a +2.5, making it one of the most efficient Ultimate Buddy transactions around.

Oh, I forgot to mention. Ultimate Buddy also gives a +5000 power to any and every card with the same name as your Buddy, as long as this card is in one of your Buddy's soul. Which means you could have some potentially high Size 1 beaters. Namely 3 of them. The +5000 power is really great already and is more than worth the 1 gauge cost. The +5000 power boost will likely last only a turn but it can help even the weakest Size 1 monster start hitting those magic numbers. Stacking Ultimate Buddy under a Penetrate monster like Dirge Drill Dragon can allow it to bust through any wall your opponent sets up and simultaneously deal damage...and if you just happened to have more than one on the field, then let's just say that no Soulguard is going to save your opponent now.

Of course, the only issue with Ultimate Buddy is that you have to hold onto it until you draw your Buddy which...shouldn't be too much of an issue, actually.

Drawing your Buddy

So since you have 4 copies of your Buddy in a 50 card deck, just how likely is it that you'll get to Buddy call in a game?

Let's first start with some basic ideas of statistics. Your deck is known as the sample space, which includes all possible outcomes of the probability. Here we'll be testing the probability of drawing a certain card, so it makes sense that the sample space would be the deck.

4 copies of a card in a 50 card deck will have 8% chance of being topdecked, generally speaking. Of course, the more you draw, the smaller your sample space becomes, but in calculations this factor can be discounted - as long as you approach it with the right statistical perspective and calculation.

However, I'm not operating a statistics class. I'm operating a Buddyfight blog. Thus I would like to expect you guys to learn the basics yourself. Go read up on statistics and probability, preferably hypergeometric calculations as well (as well as binomial probability, expected values, geometric distributions, and...). I'll continue with the point of my article.

Don't worry, it's actually not as difficult as you may think

Using a handy hypergeometric calculator, I can calculate the probability of drawing your Buddy in your opening draw of 6 cards (this is the sample size). It's 41.054%, which is reasonably close to 40%. Meaning that about every 2 out of 5 games you should end up with your Buddy in your opening hand (it's more like every 16 out of 39 games but w/e). If you can draw 20 cards after that, you can practically guarantee getting a Buddy (95%). Keep in mind that you draw 2 cards a turn, since you draw and then charge and draw. Turn 10, anybody?

Anyways, the point is that you will likely be able to Buddy call most games, and that the more you charge and draw, the more likely you will get your Buddy. Which is great because charge and draw converts your +1 every turn into a +1.5 so there's almost no reason NOT to charge and draw.

By the way, this applies to every and any card that you run 4 of in your deck.

But let's say you decided to go against my suggestions and run Jackknife as your Buddy. Well, the good thing is that you can actually use Jackknife Braveheart to search him out for the call, almost guaranteeing a Buddy Call once per game. It gets even crazier with Katana World and Skull Warriors. You can use Art of Explosive Hades Fall to grab a Size 1 Skull Warrior, screw your opponent over with it, use Return to the Underworld the following turn and Buddy Call it onto the field. Since tutoring isn't a really huge part of Buddyfight yet, overextending this much for a simple +0.5 isn't really worth it. As tutoring becomes more readily available in Buddyfight, this could change, but until then we'll have to wait and see.

For your information, running Jackknife Braveheart in tandem with Jackknife Dragon as your Buddy (both at 4 copies) will increase the chance of starting with a copy/pseudocopy of your Buddy in your opening hand to 66.998%. Hitting the magical 95% guarantee only takes 5 turns. The Skull Warrior combination is a bit more complicated, as we now have an AND function to deal with. We need to calculate the chance that we draw the Buddy OR the chance we draw both Art of Explosive Hades Fall AND Return to the Underworld. You actually want to run both spells at 4 copies, so we'll assume they are. Probability starts going crazy, but the idea is something along the lines of .41054 + .41054 * .41054 or 57.908% for your opening hand. You have to pull this x + x² calculation for every single draw AND charge-and-draw, which means that 95% hits at T3. It's faster because the cumulative probability of finding your combo increases exponentially.

Stats Debunking

I'm going to spend the last portion of this article outlining one of the basic errors and misconceptions people get about counting cards.

I have to address the 2 gauge in the beginning. For some reason everybody wants to be able to calculate that and factor it into their probability equations. I have no idea why. Can you control what goes into your gauge at that point? Do you know what goes into your gauge at that point? If the answer is no, then you don't need to factor that into statistics.

Unless you're this girl, you can't do anything about that 2 gauge

I see you still don't believe me; alright, I'll show you. I take out a deck of cards from my pocket. 52 cards, no jokers. I tap the top card of the deck and ask you what the probability of drawing the Ace of Spades will be.

Of course you should say 1/52, if you're not completely stupid. I then take the top 51 cards from the deck and hide them behind my back, leaving one card left on my palm. Now, what's the probability that the remaining card is the Ace of Spades?

Why, obviously 1/52, you answer.

So basically, if I gauge 51 cards, the probability won't change, right?

I place the cards back on top of the deck. I tap the top card again. What's the probability that this card is red?

1/2, you reply.

I slice the deck in half and hide the bottom 26 cards. What's the probability now?

Still 1/2, you reply.

50...50?

I hand you the cards. You flip them over to reveal 26 black cards. Before we began, I had already organized the cards and rigged the deck. However, even though I totally seeded the deck, the chance of drawing a red card is still 1/2. It's a chance.

Statistics is all about calculating a probability based on what you already know. Anything you don't know isn't factored in, because it doesn't really matter. Once you learn something new, then you need use that new information in the following calculations. Statistics has no room for assumptions. If you want to assume, just assume that those 2 gauged cards are at the bottom of your deck - it makes absolutely no difference.

Still don't believe me? Alright. I'll prove it to you.

Probability of drawing a Buddy on your Turn 1 draw is equal to the sum of twice the probability of drawing your Buddy multiplied by the probability of gauging your Buddy once, the probability of drawing your Buddy multiplied by the probability of gauging your Buddy twice, and the probability of drawing your Buddy multiplied by the probability of not gauging your Buddy, which should equal the probability of simply drawing your Buddy without factoring in the gauged cards.

P = 4/44 * 40/43 * 3/42 * 2 + 4/44 * 3/43 * 2/42 + 40/44 * 39/43 * 4/42 = 1/11

For all you students out there, try not to fall asleep in Statistics class.

All images were used obtained from the official Bushiroad website and used here solely for reference purposes. Future Card Buddyfight!, logos, and respective content belong to Bushiroad. Large images belong to the Buddyfight! Wikia.