Objectively analyzing the value of mill in high variance formats (draft/sealed)

[conboy31]

Recently I have been watching/participating in a lot of Innistrad drafts.  One aspect of this format that has caught my attention: the abilities of cards like Trepanation Blade, Deranged Assistant, Armored Skaab, Selhoff Occultist, Mindshrieker, among others.

The specific case that brought this to my attention was after round 2 when we saw the opponent had a Garruk, while our deck lacked burn and evasion except for a Mindshrieker.  I stated that we had a potential "out" with mindshrieker.   He instantly cringed and told me "I'm better then that".  His counter, which is true, is that if he does not have Garruk in his hand, and we do not mill Garruk he is now (barring shuffle effects) always one card closer to drawing the planeswalker.  However, in addition to this, the opportunity cost of attempting to mill the Garruk is consistent with our game plan of winning the game.  It is a cheap activation for 2 colorless mana that pumps the evasive creature.  This is opposed to purposefully side boarding in a weak card like cellar door and trying to live the dream.

My friend who was piloting MODO was opposed to the general idea of trying to mill an opponents "bomb" in formats like draft and sealed, whereas I have become extremely interested in the math and theory behind the strategy.  I believe the strategy behind it is usually wrong and/or weak, however Innistrad has so many mill/flashback cards and abilities (for you and the opponent) that the issue is worth examining.  Relevant information to take into account appears to be the strength of their deck, cards in hand, relevant flashback cards, cards in library, opportunity cost of drafting/playing/activating such cards along with all the knowledge and information about your own game state, deck, and answers.

However, I realized the intricacies of this phenomenon during the same round.   Each player had around 5 or 6 lands in play with close to a stalemate board.  He had the option to play armored skaab to get an addition blocker out and a creature to help maneuver around our equipment.  The skaab sat in his hand for two turns.  After I pressed him on the issue we evaluated the situation.  We did have some flashback cards to randomly get value, such as a think twice, and a grasp of phantoms.  However, he was not willing to risk the chance of losing Liliana, Curse of Death Hold, etc.  
I found it delightfully interesting that he was not interested in slightly advancing the game state, combined with the prospect of getting a flashback card in our graveyard, versus milling one of the few ways we had to win the game (curse would be game).

I guess this post has not actually advanced anything "objective", nor have I retained the math skills to pursue this issue.  However, if during the course of an Innistrad draft game every card (in all zones) had a fluctuating value of strength/relevance given the game state, that statistical ebbs and flows would occur where it is wrong to play your own Armored Skaab (with no threat of decking yourself), and if for some reason you have a choice to attack with a 3/3 intimidate and a 1/1 flyer carrying a Trepanation Blade the correct answer would take into account the average and cards/lands left and the very small, but non zero relevance of answers and cards in their deck.  Part of the problem with this is that we do not have perfect information regarding an opponents deck list, and hand.  However, perfect information is available for our own deck.  Additional scenarios like the risk-reward of casting desperate ravings with 0 or 1 cards in hand have also come up.

If anyone can expand on the relevance of this in limited, or specifically its complexity within Innistrad, I would enjoy reading their perspective.

-Edited for spelling

[Commandant]

MTG Salvation --------------> Thataway...

[Smmenen]

Recently I have been watching/participating in a lot of Innistrad drafts.  One aspect of this format that has caught my attention: the abilities of cards like Trepanation Blade, Deranged Assistant, Armored Skaab, Selhoff Occultist, Mndshrieker, among others.

I don't know what any of those cards do, so it's impossible for me to know their abilities :p

I'm sure I reviewed them in my set review, but I probably haven't seen them since.   

[conboy31]

I chose TMD over mtgsalvation because this place's members are more talented in statistics and magic theory.

I will edit the cards to link to oracle text and pictures.

[conboy31]

LSV briefly touches on this issue@ http://www.channelfireball.com/articles/channel-lsv-3-inn-draft-2/ at around 6 minutes.  He no longer deranged assistant's, and passes on an armored skaab+3 lands during his forbidden alchemy in anticipation of drawing his laboratory maniac.

[Diakonov]

I draft a lot of Innistrad.  I'll give my two cents.

I don't believe that the "attempt to mill their bomb" strategy holds water.  If you mill them to death, then there are X cards they will get to draw during the game, distributed throughout the deck.  Since the Garruk is equally likely to be any one of those cards, it does not raise or lower their chances of drawing him.  So, the same goes for milling yourself.  Unless there is a chance that you will deck yourself completely, it's not worth worrying about milling your bomb.

Since self-mill can often be a good thing in this format, I try to avoid milling my opponent unless I really believe that it is a realistic path to victory.  Trepanation Blade can be a dangerous card because of this.  Unless I have a ton of evasion dudes or a dedicated mill-you strategy, I generally avoid running it.

[Diakonov]

LSV briefly touches on this issue@ http://www.channelfireball.com/articles/channel-lsv-3-inn-draft-2/ at around 6 minutes.  He no longer deranged assistant's, and passes on an armored skaab+3 lands during his forbidden alchemy in anticipation of drawing his laboratory maniac.

Can't watch the video while I'm at work, but it definitely changes if you're trying to use Lab Maniac.  Since it is actually required that he make it onto the table to win with complete self-mill, you do have to be careful if you don't have Memory's Journey or Unburial Rites.  If you know you have time, you don't want to limit the number of cards you can draw before you deck yourself.

[Elric]

The value of milling an opponent (or the harm of milling yourself) can be seen in the following hypothetical situation.

The board is at a stalemate.  Either player who attempts to break it will lose.  However, your opponent has a bomb that will win the game the turn she draws it.  You have more cards in your library; thus, you have an inevitable victory without needing to mill the opponent, were the bomb not present in her deck. 

If you successfully mill the bomb, you will win.  Otherwise, you will lose.  Flip this scenario and you can see when milling yourself could be harmful. 

That isn't to say this situation, or something resembling it, comes up in actual Innistrad drafting.  But the strategy could hold water. 

[LotusHead]

The specific case that brought this to my attention was after round 2 when we saw the opponent had a Garruk, while our deck lacked burn and evasion except for a Mindshrieker.  I stated that we had a potential "out" with mindshrieker.   He instantly cringed and told me "I'm better then that".  His counter, which is true, is that if he does not have Garruk in his hand, and we do not mill Garruk he is now (barring shuffle effects) always one card closer to drawing the planeswalker.  However, in addition to this, the opportunity cost of attempting to mill the Garruk is consistent with our game plan of winning the game.  It is a cheap activation for 2 colorless mana that pumps the evasive creature.  This is opposed to purposefully side boarding in a weak card like cellar door and trying to live the dream.

If your limited deck has such an out, then I feel that is a valid plan of attack: Mill your opponent whenever you can, but not at the expense of other plays. You can't live in fear of helping your opponent find Garruk.

[Elric]

The value of milling an opponent (or the harm of milling yourself) can be seen in the following hypothetical situation.

The board is at a stalemate.  Either player who attempts to break it will lose.  However, your opponent has a bomb that will win the game the turn she draws it.  You have more cards in your library; thus, you have an inevitable victory without needing to mill the opponent, were the bomb not present in her deck. 

If you successfully mill the bomb, you will win.  Otherwise, you will lose.  Flip this scenario and you can see when milling yourself could be harmful. 

That isn't to say this situation, or something resembling it, comes up in actual Innistrad drafting.  But the strategy could hold water. 

I just stated some conditions where milling for bombs does matter.  Under what conditions does milling bombs not matter?  Assuming the opponent's deck has no tutors (which would increase the value of milling for bombs), if you can't mill enough cards over the course of the game that the opponent is at risk of running out of cards, milling won't have any value.  That is, if the game is certain to end before the opponent would run out of cards in library (I'm abstracting away from the fact that your opponent's strategy might change when you mill them), all the milling you do has no value. 

The reasoning: without loss of generality, milled cards in this example could come off the bottom of the deck (since each ordering is equally likely).  When the conditions in the previous paragraph are met, milling is just removing cards that would never be accessed anyway.

[Diakonov]

The specific case that brought this to my attention was after round 2 when we saw the opponent had a Garruk, while our deck lacked burn and evasion except for a Mindshrieker.  I stated that we had a potential "out" with mindshrieker.   He instantly cringed and told me "I'm better then that".  His counter, which is true, is that if he does not have Garruk in his hand, and we do not mill Garruk he is now (barring shuffle effects) always one card closer to drawing the planeswalker.  However, in addition to this, the opportunity cost of attempting to mill the Garruk is consistent with our game plan of winning the game.  It is a cheap activation for 2 colorless mana that pumps the evasive creature.  This is opposed to purposefully side boarding in a weak card like cellar door and trying to live the dream.

If your limited deck has such an out, then I feel that is a valid plan of attack: Mill your opponent whenever you can, but not at the expense of other plays. You can't live in fear of helping your opponent find Garruk.

Keep in mind that milling the opponent actually has no effect on how likely they are to draw Garruk.  The odds stay the same.  Also, in Innistrad, milling your opponent provides them with virtual card advantage.  There are countless effects that make use of  your grave, as well as flashback cards.  You have to be careful.

The value of milling an opponent (or the harm of milling yourself) can be seen in the following hypothetical situation.

The board is at a stalemate.  Either player who attempts to break it will lose.  However, your opponent has a bomb that will win the game the turn she draws it.  You have more cards in your library; thus, you have an inevitable victory without needing to mill the opponent, were the bomb not present in her deck.  

If you successfully mill the bomb, you will win.  Otherwise, you will lose.  Flip this scenario and you can see when milling yourself could be harmful.  

That isn't to say this situation, or something resembling it, comes up in actual Innistrad drafting.  But the strategy could hold water.

It's important to note that you aren't exactly "trying to mill their bomb," since mill can't affect the probably of them drawing it.  Really what you're trying to do is simply mill them to death so that they have fewer cards that they get to draw.  

Also, Elric's second post is right on.  Suppose you will only draw 10 cards after your opening hand in a game (plus no tutoring or other ways to get more cards).  There are exactly 23 cards that you will not get to draw that game.  So, if you mill yourself for 20, there are still exactly 23 cards that you will not get to draw that game.  It seems like it's risky to mill since you can actually watch Garruk go into the yard, but it's just an illusion.  Milling Garruk is equivalent to it being in the bottom of your library at the end of the game.

As for Innistrad strategy, there are a lot of weird scenarios that can happen.  I recently was in a game where my opponent had a Selhoff Occultist (mill target player for each creature that dies) and I had two Selhoff Occultists.  We had both been milling ourselves--since that's usually a good thing--but suddenly, something like 5 creatures died.  My opponent had 20 cards or so left in his library, and he paused.  He was the active player, so he smartly changed plans and chose me as his target, anticipating that I would also change plans and choose him.  He was right, but I ended up beating him with mill anyway.    

I love the mechanic.  It helps you more and more until suddenly, you lose.  There are a ton of interesting game states that can occur.

[Daenyth]

Actually, I think that on average, milling a deck will accelerate them towards a bomb.

Say that it's turn 4 and the player has 29 cards in their deck and you mill them for 5. The odds that garruk is in the bottom 24 is higher than the odds that it's in the top 5. If it is in the bottom, you've just accelerated them toward it by 5 draw steps.

That's not to mention the fact that you can also mill them into a flashback card.

Someone please correct me if my logic is faulty.

[vaughnbros]

Milling or not milling is completely independent from the odds of drawing a bomb unless of course you mill a skaab ruinator, think twice, desperate ravings, forbidden alchemy, or unburial rights, in which case you have obviously accelerated into the bomb, or you or they know what is on top of someones library in which case milling should have higher odds of hitting your opponents bomb and not hitting your own.   In innistrad limited from my experience milling yourself is almost always better than milling the opponent.

[Diakonov]

Actually, I think that on average, milling a deck will accelerate them towards a bomb.

Say that it's turn 4 and the player has 29 cards in their deck and you mill them for 5. The odds that garruk is in the bottom 24 is higher than the odds that it's in the top 5. If it is in the bottom, you've just accelerated them toward it by 5 draw steps.

That's not to mention the fact that you can also mill them into a flashback card.

Someone please correct me if my logic is faulty.

I think it is faulty, unfortunately.  The way I like to imagine it is that you have X cards in your library you will draw in that game.  If you draw the top 20 and then die, then you are equally likely to have drawn Garruk compared to milling a card after every draw and then dying.

Even if it's a one-time mill, consider this scenario: You have 30 cards left, and the game will definitely not last more than 20 more turns.  So, regardless of whether or not you mill your top 10 cards, there are 10 cards which you will never get to draw.  Either way it's a 2/3 chance of drawing Garruk that game.

EDIT: If you are only going to draw, say, 20 cards in a given game, then milling the top 5 in an attempt to get closer to your bomb is equivalent to simply taking the top 5 cards of your library and putting them on the bottom before the game starts.