Introduction

I've dealt with some pretty heavy topics the last couple of weeks, so this week, I'm going to lighten it up a little bit. Before we get started, I'd like to share a thought I had while reading StarCityGames.com about an hour before sitting down to write this:

Some pictures are worth a thousand words; this one is mostly just those two.

In a related note, I was talking with my close personal friend Don last week, and we were discussing my mulligan strategy. Specifically, I was telling him about playing Game 1 against an opponent I know is piloting T.E.S. and keeping a hand with Swords to Plowshares, Moat, double Sensei's Divining Tops, Jace, the Mind Sculptor, and lands. I explained to him that while I knew this hand was essentially a mulligan to five, I couldn't bring myself to put it back since it had lands and a Top. I was probably going to find what I needed. Don had heard stories like this in the past, and at this point, before hearing the outcome of the match or even that game, he made a declaration in a bold voice:

"Of course you wouldn't mulligan, because you're Emperor Top-Deck."

I laughed and explained my reasoning behind keeping the hand a bit further. (It boils down to the fact that I know I'm really lucky, so it isn't helpful in any capacity, but you should see me play sometimes—I'm really that lucky.) I jokingly explained that if I mulliganed, my deck had more bad cards in it, so I had less of a chance of drawing exactly what I need.

Better Lucky than Good

Every time I think about the name "Emperor Top-Deck," it makes me think of what I've said to people for years when they remark about how lucky I am: "Better lucky than good." I've also said this about some of my losses, because there is an undeniable element of the game that is based on fortune. Skill and wisdom can leverage you out of many situations with a lot of hard work, but there are times when every conceivable factor clicks in your or your opponent's favor, and there are no right or wrong decisions. I feel that it's far more important to be lucky than it is to be good. Of course, you can't control when the cosmos is going to shine on you, so being good at the game isn't a bad fallback. Understanding that we can't control when we're going to be lucky is the first step, but we must also understand what role luck can play in the game.

In 2008, I was watching the coverage of Pro Tour: Hollywood with a friend of mine, and we were really rooting for a great friend of mine, Jan Ruess, the Merfolk player in the event (thinking of it now, it's ironic that Merfolk is now my biggest headache in Legacy). I believe it was in the quarterfinal match and it was looking like Jan was about to lose the match. He had a draw of what I believe was Cryptic Command into Lord of Atlantis. This draw allowed him to attack for the win. After a few moments of silence, one of the commentators said, "Well, I guess that's why you play cards like that in your deck, so you can draw them." And that's the lesson: You can only really expect to get lucky when you have great cards to draw into. When playing a lot of decks such as Green and Taxes or burn, you really don't have access to the lucky, unbeatable draws that a deck like ANT, T.E.S., or today's feature deck, Belcher.

Because I've been thinking about luck so much recently, today, I want to take an intimate look at Belcher. Belcher is an established deck that likely has the biggest luck factor of any deck in the format.

Belcher

"Belcher"

• Creatures (12)
• 4 Elvish Spirit Guide
• 4 Simian Spirit Guide
• 4 Tinder Wall

• Spells (47)
• 4 Desperate Ritual
• 4 Manamorphose
• 4 Pyretic Ritual
• 4 Seething Song
• 3 Empty the Warrens
• 4 Burning Wish
• 4 Land Grant
• 4 Rite of Flame
• 4 Chrome Mox
• 4 Goblin Charbelcher
• 4 Lion's Eye Diamond
• 4 Lotus Petal

• Lands (1)
• 1 Taiga

• Sideboard (15)
• 4 Xantid Swarm
• 4 Red Elemental Blast
• 1 Diminishing Returns
• 1 Empty the Warrens
• 1 Infernal Tutor
• 1 Pyroclasm
• 1 Reverent Silence
• 1 Shattering Spree
• 1 Tendrils of Agony

Buy This Deck

This is an old friend, Ben Perry's List of One-Land Belcher from SCG: L.A. I chose this list because it's one of the most recent to do well and it eschews Black to run just a single Taiga. I'm in favor of this because I literally always hit the Bayou when I activate Goblin Charbelcher. To avoid that bad streak, I think it's better just to omit that pesky card.

What It Does

Belcher is infamous for being the standby glass cannon of Legacy combo and the bane of non-Blue decks. Counting Empty the Warrens for ten-plus Goblin tokens, Belcher's turn-one win percentage is generally estimated to be somewhere around 50%. This is calculated by first determining the chances of drawing a win condition in the opening seven cards, and then factoring in the probability of being able to produce the amount of mana to generate the win.

Check this link for an explanation of the mathematics involved with discerning the probability of drawing a specific card.

The first step is relatively simple and can be done by calculating the hypergeometric distribution of the number of win conditions in the deck. Clearly, the deck has sixty cards in it, and there are eleven win conditions in the deck with limited deck manipulation. The link above deals with calculating the chances of not drawing a specific four-of in the initial seven cards. To determine the probability of drawing one of the cards we're looking for, we can either follow suit with calculating the odds of drawing one of these cards, or conversely determining the chance of not drawing one of these cards. We should generate the same result regardless of method.

Stat Trek has a hypergeometric calculator available on their site. If you'd like to run some of these numbers yourself for this deck or any others, I don't think they'll mind too much. Our data pool is going to look like this:

Population size = Deck size = 60

Sample size = Starting hand = 7 (but you can input smaller numbers to test on mulligans as well)

Successes in population = Win conditions = 11

The final variable is checking to see if you draw at least one or zero copies of a relevant card.

To check if you're going to draw no copies of these cards, Number of successes in sample = 0

To check if you're going to draw at least one copy of these cards, Number of successes in sample = 1

Regardless of which variable you tested for, the same numbers are going to come up: 0.7775 and 0.2224. These numbers represent the percentages of drawing a win condition in your opening hand (78%) or not (22%). This means that about one-fifth of your opening hands are going to be an automatic mulligan because they essentially don't do anything. When you're working with one fewer card due to a mulligan, you're looking at a 72% chance of starting with a business spell—and 65% when faced with the dreaded mulligan to five.

The math for looking to determine if you're able to produce the mana to cast your win condition is exponentially more difficult, so I won't be covering that here.

Essentially, all of the strength of the deck can be judged from looking at its opening hand, and part of that strength is the amount of mana in hand paired with but a single win condition. 81% of this deck is mana, which is higher than any deck in the format; the issue is that you need what I like to call "starter mana." Starter mana is the mana that lets you begin casting more spells: Chrome Mox, Lotus Petal, Land Grant, Taiga itself, Elvish Spirit Guide, or Simian Spirit Guide. In total, there are twenty-one pieces of starter mana in the deck.

Using the system above, we can learn that there is a 96% chance to get at least one form of mana to start with, but omitting Elvish Spirit Guide (as it can only cast Tinder Wall if it is your only mana source), that probability falls to 92% to have at least one. If you manage to draw a hand that can't produce any free mana, fret not; there is a 40% chance to top-deck it (Population 53, Sample 1, Success in population 21, Successes in sample 1; this is just an easy problem—relevant cards divided by cards in library). You're a gambler, anyway—that's why you're playing Belcher, right? 40% to win the game off a single draw isn't too bad.

A Place in the Sun

How well is Belcher positioned right now? Well, about as well as always; there are Blue decks, and that isn't amazing news, but it isn't the worst—we'll talk more about that in a bit. While I haven't written about the growth of Legacy, there has been a lot of discussion about it, and if Legacy keeps growing, the result is going to be non-Blue decks making up a larger portion of the metagame. This may already be visible in many metagames. Why is this? Well, Blue strategies are the most attractive; they have access to the best suite of cards that prevent you from losing the game. As has been discussed, the price of Legacy staples is increasing, and if new players want in, they're going to be faced with a barrier if they want to play some of the most expensive decks in the format. The result is that players are going to have to sleeve up decks that likely don't have the best Belcher matchups. With the growth we've seen in the format already, this trend should be apparent, and it's created a great place for Belcher in the metagame to pick on decks that are ill-equipped to fight it. This will likely get better as the format grows.

I don't want to spend too much time talking about this right now, but assuming that Mental Misstep sees play, Belcher is actually a deck that is fairly strong against it. In the main deck, there are eight targets for it (Rite of Flame and Tinder Wall), and considering that most of the time Belcher's card-filtering is simply to mulligan and the disruption is to kill the opponent, that means there aren't going to be a lot of opportunities for an opponent to catch you with Mental Misstep.

Other, non-Blue cards that really interact with Belcher have a pesky tendency of costing 2 mana, which incidentally is 1 mana too much to normally be played on the first turn, meaning that most disruption pieces that non-Blue decks use—Gaddock Teeg, Ethersworn Canonist, Hymn to Tourach, and so forth—are going to be weak choices. Even against Thoughtseize, you have a relatively good chance (about 20%) of top-decking a win condition at any point after the initial disruption spell.

But what about Force of Will!?

The amount that this deck loses to Force of Will is a bit exaggerated. First, your opponent has to have the Force of Will. Since we're playing with numbers, in an initial seven-card hand, that is about 40%, plus another Blue card drags the percentage down a little bit. For the most part, Daze is a nonissue; the deck has access to a lot of mana, and there is generally not a point when you are going to be vulnerable to Daze.

Let's take a look at some sample hands and see how they can potentially play out. All samples are provided with the top card available in case you're on the draw with the hand and additional cards if needed.

Sample 1:

Burning Wish, Chrome Mox, Rite of Flame, Empty the Warrens, Lion's Eye Diamond, Manamorphose, Elvish Spirit Guide

Keep

Chance to draw a mana source = 68%

Chance to draw a business spell = 32%

Eighth card – Elvish Spirit Guide

Ninth card – Goblin Charbelcher

That's two business spells, which gives the deck a rare opportunity to choose how it is going to attempt to go off.

Method 1. Burning Wish > Empty the Warrens

This is the play that is going to generate the most storm, and is solidly available from the initial seven cards that the deck opens with. I would play this hand close to this:

Storm / Action

1. Lion's Eye Diamond
2. Chrome Mox imprinting Empty the Warrens
3. Rite of Flame ()
4. Manamorphose for , drawing an Elvish Spirit Guide ()
5. Burning Wish, exiling both Spirit Guides and breaking LED ()
6. Empty the Warrens for twelve Goblins

This method will leave you cold to a Force of Will, and since this hand has the option to do some things differently, I suggest we explore it.

Method 2. Empty the Warrens

With this method, we're going to be a lot safer from Force of Will, especially considering that there aren't too many Rituals happening.

1. Chrome Mox imprinting Burning Wish
2. Rite of Flame ()
3. Manamorphose drawing Elvish Spirit Guide ()
4. Lion's Eye Diamond ()
5. Cast Empty the Warrens with the two Spirit Guides for ten Goblins

This plan is apparent if you're on the draw, or if you're counting on your Manamorphose to draw into another mana source (68% chance). If you're playing against a Blue deck, this is likely going to be the route you're going to want to take; even if you miss on the Manamorphose, the Empty the Warrens plan is so strong against most Blue decks that doing it a few turns later should turn out to be fine.

The reason I'm willing to cast LED later here is because an opponent is more likely to balk at that card than most others, so playing it later in the chain when the opponent is likely more tense should increase the chances of your being able to bait a Force of Will from them. It's the only spell we've played other than Rite of Flame that actually nets mana, so it should be rather attractive for some players.

Conversely, Lion's Eye Diamond is essential to the Burning Wish plan.

Sample 2:

Simian Spirit Guide, Manamorphose, Chrome Mox, Elvish Spirit Guide, Seething Song, Land Grant, Burning Wish

Keep

Chance of drawing a mana source = 74%

Chance of drawing a win condition = 19%

Chance of drawing a blank = 7%

Eighth card – Simian Spirit Guide

Ninth card – Tinder Wall

For this example, we can't count future copies of Land Grant or Taiga as mana sources, because this hand already features a Land Grant.

This hand leaves us with really only one course of play, and that is to Burning Wish for Empty the Warrens, so a-Storming we go. This is how I would play out this hand:

1. Chrome Mox imprinting Manamorphose
2. Exile both Spirit Guides to cast Seething Song ()
3. Burning Wish for Empty the Warrens ()
4. Land Grant for Taiga (); play it
5. Cast Empty the Warrens for ten Goblins

I've played this hand a lot differently than most people would have, because the knee-jerk reaction is to play Land Grant first. But when playing against Belcher, the big problem is that you have to guess how the opponent is going to go off. Generally, I'll wait for Seething Song or the first or second Pyretic Ritual/Desperate Ritual to come out, as those spells are the biggest investment that the Belcher player can make. Ideally, you'd wait as long as possible, but that plan can sometimes just kill you. However, if the opponent plays Land Grant, I then have all of the information that the opponent has; I can go through and do the math to see how the hand is going to play out. Is there an Empty the Warrens? If not, I'm going to be able to just counter a Belcher or Burning Wish, or perhaps find a place where my Spell Pierce is going to be most effective. By withholding that information for as long as possible, you increase the chance of your opponent countering an earlier spell. In this instance, that spell is Seething Song, the spell I said I will normally Force regardless, but at least then they haven't also taken your Burning Wish, and you are still able to use Land Grant for Storm on a later turn.

Sample 3:

Rite of Flame, Rite of Flame, Burning Wish, Burning Wish, Desperate Ritual, Simian Spirit Guide, Land Grant

Speaking of lucky, I haven't gotten a hand that is mandatory to mulligan yet. How lucky. Keep.

Once again, we have a hand with Land Grant, so that means that there are now four more cards in the library that are not actual mana sources.

Chance of drawing a mana source = 76%

Chance of drawing a win condition = 17%

Chance of drawing a blank = 7%

Eighth card – Lotus Petal

Burning Wish leaves us with but one line of play, which we've been presented with the last few times. Here is how I would go about it.

1. Cast Rite of Flame by exiling Simian Spirit Guide ()
2. Cast Desperate Ritual ()
3. Cast Burning Wish, getting Empty the Warrens ()
4. Cast Rite of Flame ()
5. Land Grant for Taiga and play it ()
6. Cast Empty the Warrens for twelve Goblins.

Once again, I think it's best to make a reasonable attempt to keep the opponent in the dark about what's happening. If the opponent has a Force of Will, he's most likely to use it at the Burning Wish, leaving us with several cards in hand and another Rite of Flame to get started with, drawing a Lotus Petal on the next turn and then another Desperate Ritual.

Sample 4:

Looking for a hand with Belcher, and boy, do I get it.

Goblin Charbelcher, Goblin Charbelcher, Empty the Warrens, Empty the Warrens, Chrome Mox, Rite of Flame, Lotus Petal

For this hand, drawing another Chrome Mox is essentially dead, except that it can add to Storm.

Chance of drawing a mana source = 82%

Chance of drawing a win condition = 13%

Chance of drawing a blank = 5%

Strangely, I don't think that this hand is an automulligan despite the fact that it has two dead Charbelchers in it. You can play a decent Empty the Warrens, presumably on the second turn.

Eighth card – Chrome Mox (well, how about on the third turn?)

Ninth card – Goblin Charbelcher

Okay, so perhaps this hand was best to mulligan anyway. I mean, it already is just a five-card hand. Assuming you did mulligan, the new hand could look like:

Taiga, Lotus Petal, Land Grant, Seething Song, Manamorphose, Burning Wish

Essentially another five-card hand; at least the Land Grant can be played to add a Storm. This hand isn't great, but let's take a look at the odds:

Chance of drawing a mana source = 76%

Chance of drawing a win condition = 18%

Chance of drawing a blank = 6%

I actually like hands with Taiga, because when you're in a Game 1, you get to pretend that you're Zoo or Aggro-Loam without an early play. Sadly, this hand pairs it with Land Grant. This hand can't do anything productive on turn one unless you gamble on your Manamorphose.

Seventh card – Empty the Warrens

Eighth card – Land Grant

Ninth card – Seething Song

This, as we now know, would be awful, so the hand is doomed to fail for at least five turns if you're on the play, which is going to be a killer. Despite the blessing of hindsight, I would be very likely to keep this hand, and even the initial seven on days I felt frisky. Despite even the lackluster pair of hands we got, there is still a good chance of killing the opponent before he is able to respond in the next game.

Closing

I presented the eighth card for these hands because I generally like to go on the draw for Game 1 if I suspect my opponent isn't playing with discard effects. While you can't always read people, and this choice opens yourself up to Daze and Thoughtseize, it even allows the opponent to play Brainstorm or Ponder to find action against you, the benefits of the eighth card for Belcher is huge. Generally, Daze shouldn't be an issue and is quite easy to play around when you're working with an extra mana, but one of the advantages of two-land Belcher is that it has access to Dark Ritual, which makes the taxing effects of cards like Spell Pierce and Daze much less of an issue.

Next week, I told myself I wasn't going to do it, but I'm going to throw my hat into the ring on the Mental Misstep matter. It's going to be a wild ride. Come back then and read all about it.

Oh, a good friend of mine runs a blog that I'd like to direct you to: The Rusty Machete is your source for both rust and machetes. They cover limited, Standard, and a bit more Legacy than the other two, so I think that some will like what's going on over there. Tell them what you think, as long as it's nice.

Until then, I'm going to see if I can get Emperor Top-Deck on Twitter.

In related news, if you have an idea how Twitter works, which I do not, you can find me @EmperorTopDeck

~ Christopher Walton

im00pi at gmail dot com

Master Shake on The Source

@EmperorTopDeck on Twitter