Welcome to the blog series here on Friend & Fow which deals with the complex decisions involved in the game and explores the probabilities, and statistics behind each topic. For this week we look at the Yamata Reanimator Combo.

The plan of the deck is to play some enablers resulting in Yamata-no-Orochi finding its way into the graveyard. This allows us to then cast a reanimation spell like Book of Eibon and start beating down the opponent with at least 1600 worth of ATK damage starting on turn 3. If we are able to pump Yamata’s base attack damage to at least 500, then that would result in a turn 3 combo kill.

**Yamata-no-Orochi – Necromancy of the Undead Lord – Book of Eibon**

Today’s discussion is going to revolve around how to maximize the probability of casting a Book of Eibon on turn 3, with at least one Yamata-no-Orochi in the graveyard, and at least +300 of no-mana-cost attack damage pumping.

These three cards are the meat of the combo and we’d want to play as many of them as legally possible to maximize statistics. The legal restriction prevents us from reaching more than 4 of each, but it would be an interesting puzzle trying to solve how much percentage points we could gain if allowed to increase the count.

## Reflect / Refrain

During the initial iteration of the combo, we had to rely on two instances of Necromancy of the Undead Lord from the graveyard. Fortunately for us the recently “fallen” Ruler serves as a much needed consistency to the combo kill. His draw-and-bottom ability allows us to look through 2 extra cards during the first two turns, helping us find the missing piece to the puzzle. And then on turn 3, he’s able to contribute one instance of the necessary no-mana-cost +200 attack damage pump. This decreases our requirement to needing at least one Yamata-no-Orochi and at least one Necromancy of the Undead Lord in the graveyard by turn 3.

Our resources and game plan are all set for Turn 3. Let’s now talk about what we can do using the 3 other mana we have available during Turns 1 and 2.

## 1-Cost

**Prowler of Niflheim**

Perhaps the most straight forward method of sending a Yamata-no-Orochi to the graveyard, this card allows us to mill (which means to put cards from the top of the deck directly to the graveyard/discard pile) the top 2 cards from our deck. Assuming that we are able to play 3 Prowler’s during the first 2 turns, we end up with 6 cards in the graveyard. If we have 6 cards in the graveyard, the probability of having at least 1 Yamata-no-Orochi and 1 Necromancy is **22.12%**.

* The 22.12% value was solved based on relevant combinations from the 6 cards and the Combination formula, denoted as “nCr”. The combination formula determines the number of possible combinations of r objects from a set of n objects. To get the probability of exactly 1 Yamata-no-Orochi and exactly 1 Necromancy, we can use 4C1 * 4C1 * 32C4 / 40C6. In english that translates to, (combinations of 1 Yamata out of the 4 in the deck) multiplied by (combinations of 1 Necromancy out of 4 in the deck) multiplied by (combinations of 4 of the other 32 irrelevant cards) divided by all possible 6 card combinations from a 40 card deck. Evaluated, the formula comes to about 15%, but that just shows the probability for “exactly” one of each. Since we don’t mind extra’s, we check for “at least” by adding up for 1 Yamata and 2 Necromancy, 1 Yamata and 3 Necromancy, 1 Yamata and 4 Necromancy, 2 Yamata and 1 Necromancy, and so on.

**Guinevere**

While Prowler is the best one cost creature at immediately placing a high quantity of cards in our graveyard, Guinevere allows us to select one of the cards in our hand and discard it into our graveyard while drawing two additional cards to help find those combo pieces to discard. In addition, we’re able to repeat the ability across multiple turns as long as we have other resonators to sacrifice.

Assuming that we are able to activate the queen twice, this results in 4 cards drawn and 2 cards discarded. This results in just 2 cards in the graveyard, but since we’re discarding them selectively from our hand instead of relying on the probabilities of our deck the computation is actually improved. We’re not solving for the probability of having the combo in just those 2 graveyard cards but from the 13 cards we’ve had pass our hand!

In addition to the 4 cards that we draw off the Guinevere’s activation, we also consider our starting hand of 5, the 2 draws we have (assuming we’re on the play), and the 2 extra draw-bottom effects we get because we’re using Reflect as our ruler. We already know that 2 cards are the Queen and another resonator, so we look for the combo pieces in the remaining 11 unknown cards.

From the unknown 11 cards, we need to have at least 1 Yamata and at least 1 Necromancy to discard and 1 Book of Eibon stay in our hand to play. Using the same mathematical approach as above, we end up with a **37.84% chance** of having the combo pieces in the graveyard and as an added bonus already have the Book in our hand. The 22.12% of the 3 prowlers does not even consider if we have the book in hand.

As we can see, discarding cards from hand is generally better than milling random cards from the library. However, the hand cards only need one discard outlet to become “live” pieces of the combo. Guinevere’s ability allows extra draws per activation, however it is limited by the number of resonators we are able to play. Only a single Guinevere would be able to activate twice (assuming one other resonator was played before turn 3), drawing 4 cards and discarding 2. Additional copies of Guinevere only provide one activation, as they would have to sacrifice themselves.

After the first Guinevere, it would be preferable to draw more Prowlers of Niflheim. Guinevere can use the prowler to activate her ability, while gaining the 2 additional cards milled into the graveyard. A good scenario is 1 Guinevere and 2 Prowler’s of Niflheim. This allows 4 cards milled directly to the graveyard, 4 extra draws and 2 cards discarded. This results in a potential of 14 unknown cards (4 + 4 + 9 from hand – 3 resonators) that can potentially fuel our combo. That’s a **58.85% chance** that we assemble the full combo by playing those three cards.

**Rukh Egg**

The unassuming Rukh Egg doesn’t enable cards to find their way into the graveyard, but it 100% guarantees that Yamata-no-Orochi finds its way into our hand. Rukh Egg is useless if we don’t have both a way to kill it, and an outlet to discard the searched Yamata-no-Orochi. Fortunately for us the Rukh Egg synergizes very well with Queen Guinevere. Note that the chasing of the effects requires us to resolve the searching from the egg before Guinevere’s draw 2 discard 1, which is basically the rules helping us play correctly.

Imagine having 1 Guinevere, 1 Prowler and 1 Rukh Egg. Instead of having 14 unknown cards to get one of each combo piece; we can have 1 guaranteed Yamata-no-Orochi in addition to 12 unknown cards (we replace the mill 2 effect of a Prowler, with the search effect of the Egg). 12 random cards have a **59.23% chance **of having at least one Necromancy and at least one Book, further increasing the success of our combo by about 1%.

## 2-Cost

**Forty Thieves**

While Forty Thieves can be considered as just a higher costed version of Guinevere, it provides much needed consistency in terms of additional effects to both draw and discard cards. The only key card in our combo that actually needs to be in our hand is the Book of Eibon. Since we’re reliant on this part of the combo, its important we dig heavily for the Book and prioritize playing effects that draw cards into our hand to find it. It’s a safe assumption to expect to play forty thieves whenever we don’t have the Book of Eibon in hand or we don’t already have a discard outlet on the table.

**Card Soldier Club + Niflheim**

With one Book of Eibon in hand, we can then shift our attention to the graveyard, and these two cards provide the highest mill-able card quantity at this cost. Take note that the most important number to maximize is not the amount of cards in the graveyard. Rather, we want to maximize the number of cards that have had the opportunity to enter the graveyard. We need at least one discard effect for the cards in our hand to contribute to our graveyard. After assuring that, the priority shifts to casting the card that allows us to “see” more cards.

For example, we have a turn 1 Guinevere, a book of Eibon ready in hand, and a choice between Card Soldier Club and Forty Thieves on turn 2. It would be correct to play the Card Soldier Club. This way, 4 random cards go into the graveyard, and then we have access to two Guinevere activations (sacrifice the Card Soldier and then herself) for 4 extra drawn cards and then discard 2.

This results in* 8 extra cards* *seen in addition to the 9 “hand” cards*.

If we were to pick the Forty Thieves the forty thieves activation plus 2 Guinevere activations result in just 6 extra cards seen.

On another scenario, we have a turn 1 Prowler of Nifleheim, book of Eibon still ready in hand, and a choice between Card Soldier Club and Forty Thieves. We now actually need to look into our hand and determine if we can discard the necessary combo pieces. If we have at least one Yamata or Necromancy in our hand and its missing from the Graveyard, Forty Thieves would be the better choice.

However, if our current hand can’t contribute any missing graveyard pieces, it would be better to play the Card Soldier Club, in the hopes of hitting the 2 combo pieces within the 4 milled from his activation (10.43%).

A quick note on Niflheim, if we have a turn 1 Guinevere then it is strictly worse than a Card Soldier Club. It isn’t a resonator, so it doesn’t provide sacrifice fodder for the Queen’s activation, resulting in 2 less seen cards and 1 less discard, negating the 1 extra milled card.

## Magic Stone Base

The single most important card to cast is Book of Eibon. There’s no point going through all the trouble of sending Yamata and Necromancy to the graveyard if we can’t cast Book of Eibon due to our stones. This means that we want 2 black sources by turn 3; we’ll need 9 magic stones that produce black to reach 100% certainty. We also want to maximize the amount of red sources that we have because of Queen Guinevere being the best turn 1 play for this deck. This leads us to the following mana base:

4 Magic Stone of Moon Shade

4 Magic Stone of Scorched Bales

1 Milest, the Ghostly Flame Stone

1 Little Red, The Pure Stone

Most of the time, we’ll state Fire as the attribute of choice for Little Red, but it can be called as a black source when needed. The Milest and Little Red add additional options to pump Yamata, but they can only be useful for activation on turn 4.

Cards 37-40

Unfortunately there currently aren’t any more cards in the Black and Red colors that help improve the probability of the turn 3 combo kill.

Knight of the New Moon would be a great resonator to add able to draw and discard up to 3 times, but it is a water resonator and the strain on the magic stone base actually decreases the likelihood of the combo. All other discard outlets don’t allow us to see more cards, so they don’t increase probabilities.

The remaining slots can be dedicated to shore up what happens if we don’t have the turn 3 combo kill. We can choose to increase the amount of reincarnation spells (Genesis Creation) or reincarnation targets (Susanowo, Arthur). We can also choose to add in some helpful interactive spells such as Soulhunt that benefit our plan.

I hope this was a fun and interesting look into the Yamata Reanimator combo. What topic should we analyze next week?

Card images are from the awesome http://db.fowtcg.us/ and the official FoW TCG website.