Introduction – Hello, and welcome to another edition of the Arcane Laboratory. On this month’s article, we are still talking about the infamous combo archetype. On the last article, we talked about how threatful this archetype can be on bigger tournaments, and how we should be prepared to it. As requested by the readers, this time we will talk through the combo player’s perspective.
It is no surprise that combo decks on the Legacy format are fast enough to win the game with no interaction. Decks like BR Reanimator, Storm, Belcher, OOPS ALL SPELLS, Spanish Inquisition and even Show and Tell are capable of going off on turn 1, ending the game – or causing unreparable damage, such as putting a Griselbrand into play. On the other hand, the format counts with some “meta police” cards, responsible to keep the combo decks at bay, granting response capabilities even on turn 0. We are talking about cards like Force of Will; Mindbreak Trap; Surgical Extraction; etc…, but most importantly the famous FOW, on pre-sideboard matches.
On more aggressive decks, a turn 1 combo may require loads of resources to be performed, being with card selection; setups; mana accelerators and, most obviously, with the combo pieces. In cases when the sequence of plays are interrupted, the combo player have his/her gameplan severely damaged by losing important pieces, which were traded for a very low price, which some times may cost the whole match. Concerned with this problem, a very frequent question from rookie combo players is: when to pull the trigger? This discussion reminded me one interview from the storm master (and creator of The Epic Storm – TES), Bryant Cook, for the channel Lefacy’s MTG Training Grounds, where he discusses this issue in depth. For those who never saw the video, it totally worth your time: http://theepicstorm.com/legacys-allure-ep-14-tes-gono-go-combo-bryant-cook/
During his interview, Cook comments that in cases when someone has a turn 1 kill in hand, he/she should go for it. The chances for an oponent to have one Force of Will in hand tostop the combo is about 40% (in case they play blue), and the scenario does not get better with the first land drop, when oponents gain access to cards like Daze, Flusterstorm, Spell Pierce and many other threats. Dispite its excelent insights, this video is a bit outdated and does not considers the position of combo decks on the current metagame. Other than that, Cook does not make a real risk analysis, but rather focuses on make his lines of thought clear to other players, when he faces this kind of situation. In the end, it is believed that one satystic analysis of the Legacy metagame may offer precise tools for decision-making aid during risk evaluation performed by combo players. This approach also can offer valuable information about pairings and how well people are prepared to deal with combo om their sideboard. Considering the factors cited above, this article focuses on answering the following questions:
- What is the chance to have my combo stopped on the first turn of the game, during a Legacy tournament with blind pairing, where the players are not aware of eachothers lists?
- What is the difference of risks to go off on the play or on the draw?
- What should we expect in terms of responses on post-sideboard games?
As this column talks about basically mathemathics and probability inside eternal formats, the objective of today’s article was to create one probabilystic model of the chances for us to have a turn 1 combo interrupted, being on the play or on the draw. After calculating the risks of comboing off on the blind, we are going to analyse how well the legacy metagame is prepared to interact with combo decks after sideboard. It is believed that those resuls will gibe us some thoughts about how we should behave on different scenarios. This article focuses more specifically on the first turn of the game aiming to reduce variance (have response or not), and also because from the seccond turn and beyond there are cards with permanent hate (such as Thalia, Guardian of Thraben; Gaddock Teeg and others), which are out of the scope of this study.
In order to acheive the purposed goal and answer the questions above, the following steps were performed: 1) one sample of the Legacy metagame was collected from the MTGGOLDFISH database, composed ofone weekwoth of lists that played on Legacy competitive leages on Magic Online. Afterwards,the pairing probabilities with each archetype were calculated; 2) based on the collected sample, most popular decklists were identifyed , and then was defined what are the most common cards for each deck, and in what quantity; 3) we looked on the lists how many cards are able to interact/answer turn 1 combos, being on the play or on the draw. The cards defined for this analysis can be seen on the table below; 4) based on the stablished lists and on the frequency of each card on then, the probability for someone to have an answer for a turn 1 combo on the initial hand was calculated on a hypergeometric distribution model – which models the probability of success of repeated random tests inside the same population. 5) With that in hand, allied with the pairing probabilities with each deck, we were able to cauculate the conditional chance of pairing with someone and he/she have a interaction card in their initial 7, having as a result the expected value to have the combo interrupted, without knowing what the oponent is playing. The expected value forumla can be seen below:
In case you are not familliar with expected value formulas, you can simply ignore this part and move on. On this formula, R represents the probability for someone to have an interaction card on their opening hand, playing with some specific deck (DI), and P is the probability of someone to pair with this deck. We used weighted averageas the extimator for the expected value due the fact this is a generic metric, applicable to deck bluilding. The individual chances of response with specific decks may vary, but,the weighted average presentsthe overall expectation of the the overall metagame, forus to have a rought notion about how we shouldbuild our decks.
List of cards selected as possible answer for turn 1 combos.
The conditional interaction cards are the ones that need some kind of mana ramp to be played on turn 1, such as Chrome Mox. The calculations presented below take into acount the chances todraw the pair (hate card+mana accelerator), and not the card alone.
The final sample was composed of a total (n) of 302 lists, and 42 different decks. It is just another indicative of how healthy the Legacy format is.
For those that are interested on cauculations and tables, see below the list of the raw data used for the analysis.
The results of the calculations shows one optimistic perspectives for all-in combo players. With the increase of the number of Grixis strategies, the natural response of the metagame was the appearance of more decks focused on board control, such as Death and Taxes, Elves, Lands and so on. Those decks more focused on board interaction generally do not run the blue collor, and consequently Force of Will, which is the mostcommon turn 0 interaction in the format. Analysing the listed decks carefully and their density inside the metagame, we can assume that only 51.66 of the decks run this powerfull counterspell (notallways the 4 copies). Thisresult, alied with the conditional probability of an oponent to have one copy in hand (plus blue card) leads us to one expected value of just 20.58% of chances for them tointeract on the first on the draw.
When we move to the draw, and the oponent have the oportunity to have at least one single land drop, the things change a whole lot. The access to cards such as Daze, Spell Pierce, Flusterstorm, Or even discard spells such as Thoughtseize increase the chances of answering the combo on the blind to 48.27%. Even so, despite the signigicant increase on the chances of survival of our oponents, the situation is very favorable for the combo player. A large amount of the decks will still have some hopeless openings against you, such as the famous: Plains+ Mother of Runes, the favorite meal of Belcher players. Decks like Death and Taxes, Maverick, Lands and simillar are simply not able to interact with a very fast combo. They depend of at least the seccond land drop to rely on cards like Thalia, Guardian of Thraben, ou Gaddock Teeg.
With this, we already answered two of our questions:In a big tournament, where players dont know what their are playing agains most of time, turn 1 combos on the play have huge chances fora free win. When we are on the draw, the cances change a little bit, but the major expectation is the absolute success. Considering the fact that we play first 50% of our matches, imagining that decks like BR reanimator or Belcher, the final expected value is that on 65.57% of the matches that we try to win on turn 1 we will succeed easely. This resultsjust show how the Legacy format is unpreparedfor degenerate decks,but we say the same thing during sideboarded matches?
First thing that I want to note is that most of the time after the game 1, we have clear notion of against what we are playing with. For this reason, the data presented on the folowing part is not related exactly about risks of going off in a general metagame, but rather how the probability is distributed along the sample. Different deckshave different density of answers, and a good playermust know how to adapt on each situation.
If before sideboard the answer was allways; GO FOR IT! Postboard matches present two different paths for a player to follow. As already shown on the table above, the probability of interaction on turn 0 on game 2 jumps to 48.27%,with the adition of tools tailored to deal with combo decks (such as Surgical Extraction, Leyline of Sanctity ou Mindbreak Trap). At least on the sideboard, the metagameis prepared for degenerated actions. Only 13.91% of the Legacy field have 0 copies of any of those cards.On the other hadnd, the density of them is low, and most of the cards have very specific answers that does not stop anycombo generically. For instance, Leyline of Sanctity does not impede a Griselbrand from hitting the battlefield, and one Surgical Extraction is generally unable to deal with Goblin Charbelcher. Considering the arguments presented above, I keep my opinion that luck smiles for the ones who combo in the first turn. Some deckssuch as ANT (Ad Nauseam Tendrills Storm) can even add more speed on their gameplan by adding Chrome Mox on the deck to avoid specific (but slow) hate. Even so, we must always watch out for oponents who mulligan agressivelly to find answers!
When we are on the draw, thigs get pretty grim. The probability for them to have answers on turn 1 goes up to scarry 76.14%. Iwould never risk a combo with no information about the oponent’s hand, fearing Flusterstorm, Coffin Purge or simillar. The answer for this puzzle is very simples: Timeto win the long and grindy game. In order to put more ways to interact against your combo, most of the “fair” decks opt to board out some of their threats, leaving a fertile ground for the ones aiming to play a longer game. The adition of cards like Defense Grid or Xantid Swarm afterboard allows the combo player to fight the hate in any stage of the game, regardless how much resource the oponent has.
This article aimed to analyse the riscs involved on turn 1 combos, considering pairing probabilities and different responses present on the Legacy format. In order to do so, the projection of 4 scenarios was made based on a hypergeometric model of probability, to malculate the expected balue for a unknown oponent to interrupt us during our combo, using only the 7 initial cards on their hands, on both pre and post sideboard, on the play and on the draw.
The results point out that the metagame is very favorable for combo players,specially the fasterones. There are many decks that simply do not have defenses against turn 1 kills on the mainboard. After sideboard, we could observe that the density of threats increases substantially, specially when we are on the draw. Considering this scenarios, combo players must be ready for both accellerate their decks post board on the play, or to grind the longer game and fight hate on the draw.
Answering once per all the questions on the introduction. On the play, without knowing the oponent, should we pull the trigger? Myopinion is simillar to Bryant Cook’s: YES! The chances of winning are very high, and as we saw, the perspective is not to get better as time progress. This articlemade clear that a single land drop increase the chances of failure in up to 30%, and things get even worse with the seccond land drop, where hatebears start to pop out. The only esception for this situation for my are in post board games, where the combo player can prepare the deck to fight against the hate, and win the grindy match.
As limitations, this article limits itself to talk about turn 1 combos/interactions, in order to reduce internal variance of lines of play on distinct decks. Another limiting part of the article is that it does not take into account the fact information about the opponent, as it is a qualitative measure and cannot be mathematically modelled. In the end, the techniques used on this study use as parameter for the analysis staple lists from online databases. Specific lists from different players might change the numbers and expected values for responses to the combos. Even so, the approach used on the study serves as a reliable indicator in terms of probability, taking into account internal variance and discrepancies that are present in every single prediction model.
I do not know about you guys, but I am sleeving up my Reanimator; TES and Belcher for the parallel tournaments of the GP São Paulo. See you there with your FOWs!