I’m not much of a Vintage player, although if you have read Fun With Vintage, then you already knew that. However, I like to read all of the Vintage articles published by this fine site, because there’s something that (to me, at least) is strategically pure about a game of Vintage. There are few things as instructive as people trying to be the beatdown deck when their opponent is running Mana Drain Control, or the control deck against Dark Ritual Combo.

One thing that really fascinates me about Vintage deck design is the huge importance of every single deck slot. When the strongest cards from a dozen years’ worth of design are involved, changing even one card in your deck can radically alter the deck’s power level. For example, in Stephen Menendian’s first article about the revival of the Oath of Druids deck, he notes of the countermagic suite, “Mana Drain and Force of Will were automatic inclusions, but testing with the lone Misdirection proved so strong that we flirted with up to four.”

Think about that: running one copy of a card – in a deck with no Vampiric or Demonic Tutors – altered their deck’s testing performance so much that they wanted to change it to a four-of! Team Meandeck ended up running two copies of Mis-D in their list for Star City Power Nine II, where it placed four players into the Top 8.

So recently I began to wonder: is this purely a Vintage-related phenomenon, related to the absurd power level of the format? Does increasing a two-of to a three-of, or chopping it down to one copy, have an appreciable effect on a Standard or Block deck? To put it bluntly: just how important is one slot? I took some time exploring this question, and I thought I would share the results. But first…

Interlude: Now Opening for R. Kelly

… I have a weird story from U.S. Nationals that I wanted to fit it into the continuity of the article, but I couldn’t figure out how to do that, so before I get started, I’m gonna take a break to tell it now.

Since everyone I knew who had a car was either still playing, or had already left, I decided to take the train home from Baltimore on Saturday night of Nationals weekend. The Amtrak station was too far away to walk at night, so I took a taxicab. Here is a transcript of the conversation between the fifty-something driver and me:

[Five minutes of silence.]
Driver: Young man, can I ask you a question?
Me [There are cab drivers who ask before they give their opinions?]: Um,
sure.
Driver: Have you ever been to Europe?
Me [Huh?]: No, I haven’t.
Driver: See, because I heard that the women get married a lot younger over there, and I was wondering if you knew whether or not that’s true.
Me [Uh-oh]: I really don’t know.
Driver: Like, they get married at ages where it would be against the law over here…
Me [Wishing I hadn’t watched “Taxi Driver” last week]: Uh-huh.
Driver: …and, you know, once an American woman goes through puberty…
Me [Remembering Martin Scorsese’s appearance in “Taxi Driver”]: Yeah.
Driver: …you can’t hardly tell whether she’s of legal age or not!
Me [Checking to make sure seat cover isn’t made of women’s skin]: Uh-huh.
Driver: So I was just wondering if you knew anything about that.
Me [Not nearly as much as you do, I bet]: Sorry, I don’t know.
[Five minutes of silence.]

Back to Work

So, when considering a change of slots on a given card, the first thing I wanted to do was a little probability work. Grad school will have started up for me by the time you read this, so it seemed like good practice.

If you read Vintage articles, you’re probably familiar with the number 40%. This is the oft-quoted probability that you’ll draw at least one copy of a four-of card (Vintage writers are usually referring to Force of Will, of course) in a seven-card opening hand. I did some math on my own to confirm this probability, and I did in fact get an answer of 0.3995.*

Using this same method, I derived the probabilities that you’ll draw at least one copy of a card depending upon the other numbers of copies that you might be running:

Four-of: 0.3995
Three-of: 0.3154
Two-of: 0.2215
One-of: 0.1167

Also, we should consider how deeply people can dig into their decks on turn 1; with Sensei’s Divining Top, every deck that wants to has a chance to see its top ten cards. So the odds of seeing at least one copy of a card in the top ten are better in every case…

Four-of: 0.5277
Three-of: 0.4272
Two-of: 0.3079
One-of: 0.1667

…and the gap between each probability has widened even further than when we considered opening hands. So, if Team Meandeck had gone up to the full four copies of Misdirection in their Oath deck, they would have improved the probability of drawing at least one copy in the opening hand by more than 28%, and they would have improved the probability of having it in the top ten cards by more than 36%!

Of course this is some the most obvious analysis in the world. You mean to say that increasing the number of copies of a card increases the odds that I will draw it in the opening hand? Inconceivable! [I do not tink this word means what you tink it means. – Knut] Still, it’s nice to be able to take something that you already knew, and quantify it with a percentage. Anybody who makes money playing poker can tell you that it’s not enough to know that you are a favorite in a certain situation; it’s also important to know how much of a favorite you are, so that you can know how much to gamble on your edge.

So now the question becomes: how much can a card increase your edge? I conducted a little experiment to test this, but first…

Interlude: Isn’t “Rounders” Rated R?

…telling that earlier story has reminded me of a second, which is possibly more hilarious.

Since I couldn’t grind into U.S. Nats, I divided my time on Day 1 of that event between “playing side events” and “barning onto Teddy Cardgame.” Purely because Ted tolerated my presence, I was able to observe a four-man draft that pitted the team of Knutson and Flores versus the team of Buehler and David-Marshall. [For whatever reason, I actually like this Mark Young character. I’m going to see my therapist about this condition as soon as I get back from Mexico. – Knut]

During the draft, at a quiet moment when Ted and BDM were shuffling between games and Flores had gone deep into the tank to consider the wrong play against Buehler, a group of JSS kids walked by, chattering away. One of them loudly proclaimed his desire to play some rounds of “Hold ‘em – Texas style!” This was not one of those JSS kids who looks old enough to drink, either; listening to him proclaim his desire to take down some monster pots was like watching Dakota Fanning buy a rock of crack.

The entire draft stopped cold for about three seconds, long enough for the kids to get out of earshot. Before long, I was trying hard not to explode into laughter, and Flores immediately began throwing around various terms of poker slang in a giggly, high-pitched imitation, which drowned out the undoubtedly sarcastic responses of Ted and BDM.

I glanced up at Buehler, who is supposedly a quite strong poker player. Words cannot quite do justice to the look on his face at that moment. It appeared that hearing the language of Doyle Brunson and Amarillo Slim coming out of that pre-pubescent mouth had put arson into the man’s heart. I’m not sure if Randy wanted to set himself on fire, or incinerate the loudmouthed child, or perhaps set ablaze every casino and green felt table in the known universe; all I know is, you could have cooked raw meat under his stare.

As I struggled to keep my laughter under control, I said, “That was the funniest thing ever!”

Everyone ignored me.

Back to Work, Again

The thing about this whole experiment is that it’s pretty subjective. A card’s value changes not only dependent upon what deck it’s in, but also by what other cards are in the deck and the metagame.

For some cards, it’s clear that you want them as a four-of every time you run the deck. For example, running the so-called “Deck-X” with anything less than four copies of Isamaru just makes no sense to me; you want your odds of having a 2/2 legend on turn 1 to be maximized. A more standard White Weenie deck might only want three copies of the legendary hound, however, lest they find themselves unable to put the proper amount of pressure on the opponent because they drew two copies.

Even if a card would always be good every time you drew it, running more copies can actually lead to diminishing returns. Returning to the Oath case, running four copies of Misdirection might seem nice, especially since it maximizes your odds of your turning the opponent’s Ancestral Recalls against him. However, it also means that you’re running eight pitch counters, which can lead to a lot of card disadvantage against control decks. The situational nature of Mis-D is an additional disadvantage; against a lot of popular cards in Vintage, such as Gifts Ungiven, Standstill, or Mishra’s Workshop, having four copies of Mis-D doesn’t seem like such a great idea.

This article was inspired by some of my testing for the final Block Constructed PTQ in the DC area. I had tried Black Hand decks in a couple of earlier PTQs, and for a while I experimented with Hondens and Deck-X, but in the end I simply decided that none of these decks did a good enough job hating Gifts Ungiven Control out of the format, so I adopted Masashi Osio’s list from Grand Prix: Taipei and his first Star City article. There was just one problem: Oiso had three copies of Kagemaro in his maindeck, and at the time I thought I would have access to only two copies of Kagemaro for the PTQ.

(Rick Rust eventually loaned me a Kagemaro and some other rares to flesh out the deck for the PTQ. Thanks, Rick.)

I decided to see what kind of a difference this would make on the deck. I figured its absence would hurt most in aggro matchups, so I replaced the Kagemaro with an Exile into Darkness and played some test games against my White Weenie deck:

4 Isamaru, Hound of Konda
4 Lantern Kami
4 Kami of Ancient Law
4 Samurai of the Pale Curtain
4 Hand of Honor
3 Celestial Kirin
4 Otherworldly Journey
4 Umezawa’s Jitte
3 Manriki-Gusari
3 Shining Shoal
1 Eiganjo Castle

22 Plains

I played ten test games, and made note of every case where it would have been more advantageous to have the Exile instead be another Kagemaro. I didn’t think it would be that relevant, since I can always Gifts for an inevitable Kagemaro – in fact, Mike McGee’s Gifts list from a recent Pennsylvania PTQ runs only one copy of Kagemaro and four copies of Goryo’s Vengeance for this very reason.

However, the results were quite relevant. The games were split down the middle 5-5, which is not really surprising since, even though most people put the matchup in favor of the control deck, it’s not really an overwhelming edge and this is a very small sample size.

The really interesting result is that of the five losses for the Gifts deck, three of them involved the Exile being drawn at a moment when it was bad as itself but would have been a blowout as Kagemaro. One of those games might have been saved if the Exile had been Hideous Laughter; the others were decided by a Hand of Honor, a sufficiently large Jitte, and enough backup men to sacrifice to Exile into Darkness.

On the flip side, two games were won by using Exile to lock down the White deck’s creatures. However, these wins were not exactly due to the presence of Exile in the deck; rather, they were due to the fact that I was first able to draw or Gifts for one of my mass-removal spells, and only then lock them down with Exile. You could argue that the Exile would have just as easily won these games if it was instead another copy of Kagemaro, or any of the other legends in the deck.

We can see from this that your one-ofs will be drawn. Not often enough to plan your deck strategy around it, the probabilities tell us that, but often enough to be a statistical factor in a matchup. So while some folks might have scoffed when Mike Flores called his PTQ-winning deck "Critical Mass" despite running only one copy of Gnarled Mass maindeck (and later, Isao in that slot instead), this experiment has given me some newfound respect for that aspect of deck design.

Additionally, whether or not you have the right cards in each slot will be relevant, as in the Exile example. Or we can return to the Oath example: if instead of Mis-D, Team Meandeck decided for some reason to test one copy of an awful, awful counterspell – I dunno, Spelljack or something – their deck would not have tested as well. It might not have tested badly, just because you don’t draw your one-ofs with a high probability. It would have proved relevant to their deck’s results, though.

Obviously, if you are playing a control deck or some other design meant to stall out the game, drawing your one-ofs will happen all the more often. Again the test games were useful in demonstrating this; one game was lost despite a Hideous Laughter taking out the first wave of White dudes, because after some nice topdecking of creatures by the aggro deck, another Kagemaro or Laughter was needed to survive … and a Top activation revealed Exile instead.

Finally, to make up for those time-wasting stories, a decklist! I have been sketching out some Gifts lists for the new Standard, based upon some early Ravnica spoilers. Assuming that Moroii and Farseek are correct as I have seen them, I decided to build upon the McGee plan and create the following list:

4 Gifts Ungiven
4 Sensei’s Divining Top
4 Sakura-Tribe Elder
4 Farseek
4 Sickening Shoal
4 Goryo’s Vengeance
2 Hideous Laughter
1 Death Denied
1 Hana Kami
1 Ghost-Lit Stalker
1 Myojin of Night’s Reach
1 Meloku the Clouded Mirror
1 Kagemaro, First to Suffer
1 Ink-Eyes, Servant of Oni
2 Kokusho, the Evening Star
2 Moroii

6 Forest
6 Swamp
1 Island
3 G/B dual from Ravnica
1 U/B dual from Ravnica
1 Shizo, Death’s Storehouse
4 Tendo Ice Bridge
1 Miren, the Moaning Well

Moroii allows you to go beatdown much faster than in the Block Constructed version, and you can pitch him to Sickening Shoal also, as needs be. The sideboard would probably contain more Viridian Shamans to kill equipment and Pithing Needle, and Dimir Cutpurse for control matchups (again, asssuming that it has been spoiled correctly, as a 2/2 for 1UB which combines the abilities of Hypnotic Specter and Ophidian).

I prefer Farseek to Kodama’s Reach, because it makes turn 3 Gifts Ungiven happen more consistently. The spoiler has Farseek worded such that it can seek out the Ravnica dual lands, which is another big advantage over Kodama’s Reach (Reach searches out basic lands only, while the card type on the Ravnica duals is "Land – Swamp Forest," i.e., they’re not "basic" lands).

Until next time, here’s hoping you don’t lose to Enduring Ideal (as I did, knocking me out of the PTQ in Round 6. Stupid Rending Vines, having a drawback and stuff!).

This article written while listening to the Clash’s “London Calling.” Also, if you haven’t had a chance to read "Jonny Magic and the Card Shark Kids" – yes, it’s about that Jonny Magic – then you absolutely must do so, now. It’s amazing. [There will be a full book review of it on the site later this week. – Knut]

mmyoungster at aim dot com

mmyoungster on AIM

Later.

*This was calculated by first finding P, the probability that you won’t draw ANY copies of card X, and then taking 1-P. So, in the case of a four-of, I took (56/60)*(55/59)*(54/58)*…*(53/54) = 0.6005, and then 1 – 0.6005 = 0.3995. Now, this does include hands that would not quite be keepers, such as “card X and six lands” or “four copies of card X and no lands”, but eliminating hands such as those requires math beyond the time that I have available.