The Wescoe Connection – Counterfactual Reasoning in Magic

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Thursday, March 25th – In this excellent theory article, Craig Wescoe discusses the practice and application of Counterfactual Reasoning. Using a collection of in-game examples across a number of formats, Craig invites us into the minds of the highest level of spellslinger. Unmissable stuff!

An entire book could probably be written on how to employ counterfactual reasoning profitably to various aspects of Magic, but for the purpose of this article I would like to simply introduce some of its major applications: deducing the correct play, optimizing your play testing, and configuring card choices for your deck. There are many other applications that I will not go into due to the constraints of this article, but hopefully the examples and explanations offered will give you the tools to apply counterfactual reasoning to other aspects of the game.

Before we begin, let me first introduce for those unfamiliar with the term, what counterfactual reasoning entails and how it is employed by high level gamers. A counterfactual proposition is a conditional statement with a false antecedent but can nonetheless be evaluated as true or false based on whether the consequent would be true had the antecedent been true. For example, consider the following counterfactual: “If Sacred Foundry were currently in Standard, then Wild Nacatl would be the most played creature in the format.” It is clearly false that Sacred Foundry is currently in Standard, but what the counterfactual allows us to do is decide whether the consequent, namely “Wild Nacatl would be the most played creature in the format” would be true had the antecedent been true instead of false.

Counterfactual reasoning plays a central role in how high-level players of any competitive game approach their respective sport. World class chess players, poker players, as well as Magic players each employ counterfactual reasoning at a high level when considering in-game decisions and it is this kind of reasoning that is responsible for much of what separates them from lower level competitors. It is often said that a chess master is able to think many moves ahead of the chess novice and midway through the game be able to announce, “I have checkmate in seven moves, and you have no way to stop it.” Similarly an expert poker player will be able to narrow down the range of possible hands an intermediate poker player might have in a given situation, and an expert Magic player will know exactly what cards or series of cards an opponent can or might have that would potentially beat him and thus “take away his outs” by playing around such cards. All of this knowledge is gained through counterfactual reasoning. Allow me to explain.

The mindset of a chess master in a chess match is always, “What can or will likely happen if I make this move?” A chess master constantly re-evaluates the board state and is thinking many moves ahead. For instance, “If I move him into check with my Bishop, he has three options: he can move his King out of check, block the Bishop’s path to the King with his Bishop, or take my Bishop with his Rook. If he moves his King out of check, I can put him into checkmate with my Queen. If he blocks my Bishop with his Bishop, I can put him into check with my Queen, forcing him to block the Queen with his Pawn, and then I can take his Bishop without losing my Bishop or my Queen. If he takes my Bishop with his Rook then I can take his Rook with my Knight and gain value and board position. Therefore I will move him into check with my Bishop.” Intermediate chess players also use this kind of thought process but more frequently make mistakes in reasoning such as, “Oops, I didn’t realize trading my Bishop for his Rook would open me up to getting put into check and force me to lose my Queen to his Knight.”

In poker, the mindset is similar: “My opponent called my raise before the flop and now he checked to me after the flop. If I raise and he folds, I win the hand. If I raise and he calls, he is probably on a draw. If I raise and he re-raises, he is either trying to push me off the hand or he was trying to induce me to bet by checking with a made hand. So I’ll raise to find out where I’m at in the hand.” Then after the opponent calls, a third club hits on the turn, and the opponent bets. The reasoning continues: “Either he was on a flush draw and made his flush and is now betting with a made hand, or he is bluffing and wants me to think he made his hand. This guy has stayed in a lot of hands in the past and has been reluctant to bet unless he has a good hand, so I believe he is not bluffing and actually made his hand. I’ll fold and wait for a better opportunity to take his chips.” In each of these examples, a series of counterfactual scenarios are considered, and a decision was made based on the range of possible outcomes and the likelihood of each. Let’s now consider how counterfactual reasoning can be profitably applied to Magic.

Deducing the Correct Play

Probably the best way to demonstrate how to deduce the correct play in a game of Magic via counterfactual reasoning is to consider a few cases and to show how to employ such reasoning in each case. While based on actual situations, they have each been modified to better illustrate the points being made. It is arguable that some of the conclusions reached in these examples are not the optimal plays (though I am of the opinion that they are), but even still, the purpose of this exercise is to consider counterfactual reasoning as a method. So even if the examples are flawed, it should still be clear how to employ the method — and that is my goal.

Case A: I am playing an Extended Naya mirror match. I am at 1 life with a 3/3 Wild Nacatl, a 0/1 Noble Hierarch, and a 0/1 Steppe Lynx in play. The opponent is at 6 life with an untapped 4/5 Tarmogoyf. Both of us have plenty of lands (none of which are fetch lands) and no cards in hand. I untap and draw Umezawa’s Jitte. In order to deduce the correct play, it is best to employ counterfactual reasoning along the following lines:

“If I cast and equip the Jitte to Wild Nacatl and attack, Nacatl becomes a 4/4 from exalted, and if he blocks with Tarmogoyf I can remove a Jitte counter post-combat to kill the Tarmogoyf. But then if he draws Lightning Helix or Lightning Bolt I will only have 1 Jitte counter left and so I will still take lethal. If instead I attack with the Steppe Lynx, it will become a 1/2 creature and die to the Tarmogoyf, but I will get 2 Jitte counters and be able to survive a Lightning Helix or Lightning Bolt. Then I can re-equip the Jitte to the Wild Nacatl post-combat and if he attacks with the Tarmogoyf I can block with the Nacatl, gain 2 more Jitte counters, and be able to kill the Tarmogoyf after combat without losing to a burn spell. And if he does not attack with Tarmogoyf, the following turn I can attack with a 4/4 Wild Nacatl, forcing him to block with and lose his Tarmogoyf to a removed Jitte counter post-combat. This will leave me with a Jitte with three counters on it and a Noble Hierarch threatening lethal next turn, and I will still not be in burn range even if he draws two burn spells in a row. So the best play is to cast and equip Jitte to Steppe Lynx and attack into the Tarmogoyf this turn.”

In this example, the possible iterations of plays are relatively few, and it is the nature of Umezawa’s Jitte to take over the game if left unchecked. Hence a player should be able to figure out the play without taking too long. The next example requires more thought.

Case B: I am are playing a ZZZ (triple Zendikar) booster draft. I am Mono Black and the opponent is Mono Red. I am at 2 life with 5 Swamps in play and a Disfigure as the lone card in my hand. The opponent is at 11 life with 6 Mountains in play and 1 unknown card in hand. I untap and draw Crypt Ripper and employ counterfactual reasoning in the following way:

“I can’t beat a burn spell. If I play Crypt Ripper and attack for 2, he goes to 9 and I can Disfigure whatever he draws and next turn I can attack for 7, putting him to 2. This would give him two draw steps to draw burn. But if I pump the Crypt Ripper this turn, he goes to 8 instead of 9, and if I draw a Swamp next turn, I can attack for lethal and he never gets a second chance to draw a burn spell. But if I do pump the Crypt Ripper I die to a haste creature with power 2 or greater or a Hellfire Mongrel. If the creature is Tuktuk Grunts, Goblin Bushwhacker, Goblin Ruinblaster, Goblin Guide, or Hellfire Mongrel I could kill it with Disfigure, but I would be giving him an extra draw step to draw another haste creature or Punishing Fire, Burst Lightning, Unstable Footing, or Spire Barrage. Keeping Disfigure mana open will also keep Torch Slinger from killing Crypt Ripper. Had the unknown card in his hand been a haste creature or a burn spell, he would have cast it last turn to win the game, so I am convinced the card in his hand is not relevant unless it is Mark of Mutiny or Goblin War Paint. I could potentially play around Mark of Mutiny by casting Disfigure on my Crypt Ripper in response, or if he draws a creature with toughness two or less, I can cast Disfigure on it in response to the Goblin War Paint and survive. Nonetheless this would still give him another draw step to draw any of the cards mentioned. So all things considered, I have 13 Swamps remaining in my deck, which means approximately a 50% chance to draw a Swamp, which would give him just one chance to draw an out as opposed to two. So I decide to pump the Crypt Ripper and put him on a one turn clock if I draw a land.”

In DCI sanctioned Magic tournaments you must play at a pace where you will reasonably complete a three-game match in the allotted time limit (usually 50-60 minutes). So going through all these iterations of plays each turn is impractical given the time restraint. So what players tend to do is adopt shortcuts such as “burn spell” or “haste creature” to quickly determine approximately what the best play is. Save your time for the more complex board states by making the intuitive play when the board positions are simpler. However, as this next example illustrates, make sure you aren’t missing something crucial with your shortcuts.

Case C: I am playing the Mono White Standard deck that I used in Pro Tour: San Diego and my opponent is playing Mono Black Vampires. He is at 7 life, has a tapped Malakir Bloodwitch, six Swamps in play, and one card in hand. I am at two life with four Plains and a Steppe Lynx equipped with Trusty Machete in play, and I have one card in hand — a Plains. I consider during his end step what my outs are and how I will play if I draw any of them. If I draw Elspeth, Knight-Errant or Sigil of Distinction, I can attack for exactly lethal. If I draw Stoneforge Mystic or Basilisk Collar I can attack for 4 and gain 4 life to survive the following attack, and then I can attach Machete to the Mystic next turn or hope to draw a land to trigger the Steppe Lynx and be able to attack for the remaining three damage. Those seem to be my only outs, and if he has a removal spell in hand, I cannot win no matter how I play it. So I untap and draw Dread Statuary and employ the following thought process:

“If I play the Dread Statuary and attack for 4, he will surely attack with the Bloodwitch next turn since I will be threatening lethal with two separate creatures next turn and attacking is his only chance at victory — and it will get through. If I play the Plains and attack for 4, he might think I have some crazy life gain or damage prevention spell in hand so there is at least a possibility he will not attack with the Bloodwitch, since it can block the Steppe Lynx, and the Lynx is my only creature threatening lethal the following turn. This would give me an extra turn to draw… well, nothing really since Elspeth or an equipment spell gets trumped by the Protection from White ability of the Bloodwitch, and as soon as I play the Statuary he will know it’s time to attack with the Bloodwitch the following turn, and whenever he does I cannot stop it. So I have no outs, right?” I play the Dread Statuary, announce that Steppe Lynx gets +2/+2, making it a 4/4 with the Trusty Machete and landfall bonuses, tap 4 Plains to activate Dread Statuary, confirm that the opponent is at 7 life, and declare my combat step, asking him if the card in his hand is a removal spell. He says no and extends the hand in defeat.

In this example, if my opponent does not concede at that moment, the jig is up since Dread Statuary cannot legally be declared as an attacker once we move into the declare attackers step. My only chance is to somehow hope he forgets that the creature land has summoning sickness, which is not entirely unreasonable since no one ever activates a man land before combat unless their intention is to attack with it, and certainly there is no reason not to attack with it when I’m threatening lethal with no cards left in hand and a lethal Bloodwitch on the other side of the board. I’m basically relying on my opponent’s counterfactual reasoning to break down by neglecting to account for summoning sickness by suggesting via my mannerisms and question, “Do you have the removal spell?” that if he does not have it, he loses. Granted this play will rarely work, but the chances of it working do seem much higher than the chances of him not attacking me with Bloodwitch the turn after I play Dread Statuary. So it definitely seems like the optimal play in this scenario. This is certainly the proper time and place for a Jedi Mind Trick — when you essentially have no way to win without employing one; and carefully employing counterfactual reasoning will allow you to determine when you are in such a position.

Optimizing your Play Testing

In tournament matches, you want to be focusing on the things that are within your control and employing your reasoning faculties to decide what the optimal play is in each situation. In play testing, the objectives are a bit different. There is no time clock restraint, less pressure, and nothing riding on whether you win or lose the game. The goal is figuring out how best to play the matchup and what configuration of cards you should decide on for the tournament you are preparing for. I will talk about configuring card choices in the next section, but first let’s talk about how counterfactual reasoning can help you to figure out the best way to play in a particular matchup.

Let’s assume you are playing Standard RDW against Mythic Bant. The game begins by you casting Lightning Bolt on an opposing Noble Hierarch. Then later on you cast another Lightning Bolt on a Rafiq of the Many. Then the opponent lands a Baneslayer Angel and you have a Hell’s Thunder and Hellspark Elemental each in the graveyard but cannot get past the Angel and the opponent is at 2 life. He attacks with the Angel, gains 5 life, and plays another one. At this point the game is over. One of the nice things about play testing is that you can rewind the game and consider what would have changed had you played your cards differently. You should ask “What would have happened had I not killed the Noble Hierarch? Could I have lived without killing Rafiq? Was there an opportunity to Unearth the Hell’s Thunder or the Hellspark Elemental earlier before the Baneslayer Angel came down?”

By openly discussing these questions with your play test partner after the game, before the cards have been scooped up, you can basically ‘replay the game’ from the point of the questionable play, with hands revealed, and roughly determine what sorts of things would have happened had you played it differently. Even if you decide it was the correct play, it is a good exercise to start thinking in this way and to approach play testing with this attitude. Your games take a little bit longer, but you learn far more from fewer games. There is no sense playing 10 games poorly, making the same mistakes over and over when you can play 7-8 games, two or three of which are spent figuring out the right plays and five of which are played correctly. The key is to get in the mindset of thinking counterfactually: “Had X happened instead of Y, what would have changed?”

Configuring Card Choices for your Deck

If you approach play testing with the attitude described above, you will be in a better position to figure out how best to play each matchup. But if you simultaneously consider what would have been different had a particular card or cards been something else, you will really make headway in the matchup. For instance, drawing on the above example, you might ask, “Had this Hellspark Elemental been a Mark of Mutiny, would that have been enough to win the game?” You might conclude that Hellspark only dealt 3 damage and that Mark of Mutiny would have dealt 6 (by targeting the first Baneslayer Angel). The opponent would have been at 5 life instead of 2, but they would have taken lethal before being able to untap and attack with the Angel and cast the second one (or maybe he had Negate backup and it wouldn’t have made a difference). These are all good things to be aware of and will help you to determine what the important cards are in the matchups and how best to play them out. You and your play test partner will each benefit from learning in this way.

Also of relevance are sideboard considerations. By asking, “What difference would having the Deathmark for the first turn Steppe Lynx have made?” you aren’t necessary asking whether it is correct to play the Deathmark maindeck but rather how would such a sideboard strategy impact the matchup. Thinking about these things can be valuable when considering potential sideboard strategies. As a note of caution, be aware that the opposing deck will also look different after sideboard and so just because a particular sideboard card is great against an opposing maindeck does not necessarily guarantee that it will be great against the deck after sideboard. For example, you might think “Wow, Devout Lightcaster would be insane against all these Putrid Leeches and Sprouting Thrinaxes whereas Day of Judgment is garbage.” But then when your opponent sides out all their Black creatures and in all their Green creatures, suddenly the opposite is the case, “Wow, all these Lightcasters are garbage, but Day of Judgment would be insane against all these Masters of the Wild Hunt and Great Sable Stags!” Usually this is not an issue, but it is something to keep in mind, especially when the deck you are playing is well known and it is reasonable for an opponent to have a transformational sideboard strategy against you.

Concluding Remarks

All competitive Magic players employ counterfactual reasoning in various capacities and to varying degrees. Many are probably unaware of exactly what they are doing, and still others are aware but call it by a different name. All this is well and good since the goal is not to be able to articulate a strategy or employ fancy new lingo — it is to be able to utilize the strategy fruitfully and achieve success with it. Every one of the top Magic pros thinks counterfactually, and in large part it is their grasp of this method that sets them apart from the less successful competitors. As I said in the introduction, this article merely touches on some of the more salient applications of the method. Moreover the exercises herein are intended to demonstrate what it means to reason counterfactually and how doing so can be advantageous to you in your competitive Magic endeavors.

As always, I will do my best to address questions or comments in the forums.

Craig Wescoe