A debate on the disruptive power of Mill
Standard forum
Posted on Jan. 21, 2014, 4:03 p.m. by SwampHippie
"It doesn't change the probability of drawing a particular card" is a line I've heard regurgitated all too often.
I've taken Stats and am well aware of the fact that I can't just will myself to mill good cards. But how can anybody with basic deck building skills suggest that repeatedly deleting random cards from their deck isn't going to cumulatively mess up their game plan.
Who hasn't sat there and pondered if that 25th mana was what won/lost them the game or if they had only a full playset rather than 3 of their powerhouse card they could have prevailed. Decks are often finicky and people keep hands partially based on what they SHOULD be drawing in the next few turns.
But that's all my personal opinion based on my experiences, perhaps I'm just abnormally lucky when it comes to mill but I doubt it. I'm very interested in hearing people's opinions on the matter so long as it doesn't devolve into "mill is booooring" and "I wreck in limited with mill" XD
thataddkid says... #3
It's relatively weak in standard, but if you can mill out combo pieces in eternal formats you might just be able to win from that.
January 21, 2014 4:11 p.m.
It's too slow in all formats. It CAN be done - but not often and not reliably.
January 21, 2014 4:12 p.m.
thataddkid says... #5
Well modern mill has some great tools with Glimpse the Unthinkable , Hedron Crab and fetches, and Surgical Extraction once they hit eldrazi. Legacy mill is a T3 combo win with Grindstone , Painter's Servant and then activating Grindstone . There is also Helm of Obedience with Leyline of the Void and buttloads of Dark Ritual effects, but those are less mill and more combo. Mill is generally a weak strategy but has very good matchups against combo.
January 21, 2014 4:16 p.m.
I love Mill as a win con, and I've always wanted to build a mill deck.
HOWEVER: As far as decks go, they either actively want cards in their graveyard or they couldn't care less what is or is not in their graveyard. Because it is all random, milling does not actively disrupt your opponent's game plan.
Now, that does not mean that milling does not have the potential to disrupt your opponent's game plan. All it means is that milling pales in comparison to the disruptive power of hand destruction like Thoughtseize or direct removal like Path to Exile .
January 21, 2014 4:25 p.m.
I played against mill in Standard... I won game one, just barely.
I sideboarded in 4-5 great cards to shut him down. (Witchbane Orb / Elixir of Immortality )
Game 2, he milled out the cards I side boarded in before I could draw one... I lost.
Game 3 he milled 15 or so cards, and landed me a Witchbane Orb for a draw, and I won.
- Interestingly, if he had not milled me I would have not seen the Witchbane Orb for 15 or so turns, and his alternate win-con ( AEtherling ) probably would have won it for him.
So, the idea that it's "disruptive", can also be used to say that it's "beneficial to be milled". - In truth, unless they are also able to look at the top of your library, there's no difference to your game state until after the mill occurs, thus there's no disruption... just random chance.
January 21, 2014 4:28 p.m.
SwampHippie says... #10
That's true... nobody knows whats about to be drawn that's the decks are face down.
My point is that the notion of mill being a completely neutral, since it is just as likely to help an opponent get to "the card they want" as it is to mill it (as if there are only a handful cards in a well built deck that somebody would want to draw), is half-baked. Because random deletion of cards will disrupt the intended flow of a carefully tuned deck that is built to have a specific propensity to draw certain cards as the game goes on.
Ex: say I took your Standard Constructed deck, shuffled it, then took the top ten off and handed it back to you. Would that not mess up the flow of you deck? Or to put it differently: would that be the 50 card deck you would have built? The odds of that are extremely low (but I'm fully aware of the fact that you could still draw a magnificent hand).
Now consider a much disregarded fact, Mill is nearly always Blue (U) and often Blue/Black (U/B). These are the colors of spot removal and counterspells. This means if mill does actually happen to dig them closer to a threat I can answer it, and if the mill does manage to hit the "card that they want" that's one less thing I have to counter/remove. The fewer critical cards there are in the Oppo's deck the more selective I can be with premium removal/counters.
This brings me to one last point, and that is how many decks will bank more on mid-late game draws against the U/B control shells usually supporting mill strategies. If your first couple heavy hitters were countered/removed then I am more likely to mill you next one than you are to draw it. Even 3+mill > 1draw when it comes to digging for good cards.
January 21, 2014 4:52 p.m.
lord_of_the_snakes says... #11
if you really wanted to, mill can be great in all formats, especially in standard, where it's been getting a ton of support, like phenax
here's my legacy mill attempt, the painter's grindstone
January 21, 2014 5:14 p.m.
SwampHippie says... #12
I actually like what EvenDryke said about mill paling in comparison to hand disruption, that is absolutely true and by no means did I intend to compare the two. I suppose that my (perhaps overly inflated) passion for mill came off too strong, as I do understand that it is a very subtle variation of disruption. I suppose what bothers me is people's reluctance to see how reliable mill really is with creating this minor disruption.
Rayenous did a good job of putting the counter argument in a nutshell but I still have to disagree. Random chance can be fairly well mitigated with proper strategy, mill played off the field frees up mana to hold back counterspells for situations like you described. If played correctly you should rarely mill yourself into a situation you can't handle.
Disclaimer: this was never a debate on whether or not Mill will dominate the format or even reliably top eight. Unless they start printing far more aggressive mill (and I mean $30 Chase-card aggressive) this wont happen. Too few people appreciate mill and thus it isn't financially feasible for WotC to market such a thing. So for now (and maybe forever) it remains a niche strategy that often straddles the line b/t casual and competitive.
January 21, 2014 5:17 p.m.
Arachnarchist says... #13
Consider the following two scenarios:
Scenario 1: You have 20 cards left in your library. Your opponent has an Invisible Stalker with Paranoid Delusions ciphered onto it. Say your opponent is at 3 life and you have a Lightning Strike in your deck which will kill your opponent should you draw it. In this scenario, out of the twenty cards in your library you will draw five, and if one of those 5 is Lightning Strike you win. The other 15 cards will be milled.
Scenario 2: You have 20 cards in your libary, one of which is again a Lightning Strike . Your opponent is at 3 life and you are at 5. And your opponent still has an invisible stalker this time without paranoid delusions. In this scenario you will still only draw 5 cards before you lose, and again if one of them is Lightning Strike you win, otherwise you lose.
Both scenarios play out similarly. You get the same number of draws before you lose. The only difference is what happens to the cards you don't draw. In Scenario 1, they're in your graveyard, in Scenario 2 they're still in your deck. My point is simply that Mill doesn't have any "disruptive power" in itself, and it doesn't do anything until you win by mill.
January 21, 2014 5:43 p.m.
@SwampHippie The problem with removing 10 cars off the top is this: is it equivalent to remove 10 cards off the bottom? Logically, that is also a 50 card deck that they may (or may not) have wanted, but I doubt almost any player (exceptions for singleton, tutor-heavy, or some really draw-heavy control) would care if you removed the bottom ten cards of their deck before a match. So, what is it about the top ten cards that is different than the bottom, other than location (or, why is location so important if there is no other difference)?
Arachnarchist puts perfectly the point why milling doesn't really change anything other than where the cards went. For most decks, milling is effectively just another life total, and barring a few (actually, quite a few) exceptions (scavenge, flashback, Consuming Aberration ), the only difference is amount and the relative power of cards to decrease it.
The issue with the argument that it gets rid of stuff to counter is that that is the wrong measure. I think the correct measure is the number of draws the opponent gets. If you average 2 damage a turn, the opponent gets 10 draws. If you average 5.3 cards milled a turn (don't forget the starting hand) the opponent also gets 10 draws (assuming no draw cards). Barring library manipulation, the two differences are where the cards end up (see above) and where in the deck you the cards were. Assuming that any card could be anywhere from sufficient shuffling, you have not really gotten rid of more threats, you have just changed which cards were drawn, without knowing if the new cards are better or worse than the other cards. You might have them hit the perfect cards. You might make them get mana-flooded or screwed. You can't know ahead of time which will happen. This is why milling isn't seen as disruption, because it is at best random disruption, no different in any key respect than the bad luck of a shuffle which brings all of your lands to the top.
January 21, 2014 6:22 p.m.
"It doesn't change the probability of drawing a particular card"
REALLY??! 
whoever believes THAT needs to learn some Math. I like what Rayenous said about mill allowing him to get his winning card. And SwampHippie hit it home: "say I took your Standard Constructed deck, shuffled it, then took the top ten off and handed it back to you. Would that not mess up the flow of you deck? Or to put it differently: would that be the 50 card deck you would have built?"
The Mill is a double-edged sword, but for those who play it, it's extremely fun.
January 21, 2014 6:28 p.m.
SwampHippie says... #16
All very true, and good scenario might I add. Lets also clarify (for the sake of controlling variables) that player controlling Invisible Stalker
has no counters in hand and that besides the single lightning strike neither player will draw any relevant cards for the rest of the game.
That being said, in Scenario 1 my opponent has the following chances of hitting Lightning Strike each turn provided it was neither drawn nor milled the previous turn: (1/20+1/19+1/18), (1/16+1/15+1/14), (1/12+1/11+1/10), (1/8+1/7+1/6), (1/4+1/3+1/2) or (1/19+1/18+1/17), (1/15+1/14+1/13), (1/11+1/10+1/9), (1/7+1/6+1/5), (1/3+1/2+1/1)
These are my chances of drawing Lightning Strike under the same circumstances:1/17, 1/13, 1/9, 1/5, 1/1 or 1/20, 1/16, 1/12, 1/8, 1/4
Now its been a while since I took Stats but it LOOKS to me as if my opponent has a greater chance of winning in Scenario 1 since he is more likely to hit the card i need than I am. To me that is "disruptive" but perhaps there is a better word for it.
January 21, 2014 6:38 p.m.
Schuesseled says... #17
It makes no difference what so ever if milling took from the top or the bottom. Except maybe physcologically. "I was never gonna draws those so it doesn't matter".
But it does uncertainty of what card you are drawing is most certainly a factor, knowing one of your needed cards has hit the graveyard and now their is less in the deck should have the same impact if it was from the bottom.
Milling can be a double edged sword for sure, every winning card hitting the bin is a huge blow to your likely hood of winning the match. Equally every time your milled and that 1 card that can save you remains in the deck, the more likely you are to survive.
January 21, 2014 6:46 p.m.
Schuesseled says... #18
There's no way to predict beforehand if milling someone will decrease or increase their chances of winning. But it certainly increases your chances.
January 21, 2014 6:50 p.m.
cr14mson - No, it doesn't change the probability of drawing a particular card when you carry out the milling action or cast the card. It only changes afterwards. Unless you can predict the future you do not know whether your actions are going to get them closer or further away from the card they want.
January 21, 2014 6:55 p.m.
Also - high level statistical probability theory says that actually reshuffling a deck changing decisions about where cards are is advantageous. High level maths would argue that being milled. makes you more likely to get what you need.
January 21, 2014 6:56 p.m.
SwampHippie says... #21
@ raithe000 The point here is whether or not you affect their probabilities of drawing certain cards. Removing from the bottom would be rather worthless since it would affect cards that few decks can touch as you yourself mentioned, the top on the other hand would directly affect their draw.
"This is why milling isn't seen as disruption, because it is at best random disruption, no different in any key respect than the bad luck of a shuffle which brings all of your lands to the top"
Perhaps this is where so many people get hung up... I KNOW its not Precise, Intentional disruption. But it is as you've said random disruption (although I find it to be more more Probable than Random), if played intelligently it should either have no effect or have a negative "disruptive effect" since you should usually be prepared for occasionally digging them into good cards.
@ cr14mson TY TY finally somebody who knows a lick of math rather than leaning on an elementary understanding of the word Random.
"The Mill is a double-edged sword, but for those who play it, it's extremely fun." Nailed it. If you're going to play mill anticipate it working in your opponents favor OCCASIONALLY. Just like you wouldn't likely build an aggro deck with 26 lands, you are likely going to build a better mill deck with a good handful of counterspells/removal included.
Thanks for all the great posts everybody, I really needed this to get the wheels turning again in preparation for school.
January 21, 2014 7:10 p.m.
SwampHippie says... #22
@ ChiefBell If that were true then why doesn't everybody mainboard Elixir of Immortality and selfmill?
January 21, 2014 7:15 p.m.
It's extremely theoretical mathematics. It's not actually something you want to do yourself but if someone is doing it for you then it's fine.
Mathematically milling does not hinder your opponent unless you have some way of pre emptively knowing what you're milling. Otherwise common sense dictates that it's a statistically neutral action. If you go by theoretical maths then it's actually advantageous for them.
January 21, 2014 7:22 p.m.
Arachnarchist says... #24
Your math is wrong. Since the game ends when Lightning Strike is revealed, either by mill or draw, iit's reasonable to assume that each successive card will be revealed if and only if Lightning Strike has been neither milled nor drawn.
So for the first card milled, the odds are 1/20. For the second card drawn the odds are 19/20 x 1/19, since at that point it's one of 19 cards in the library, but it only matters if it has yet to be drawn/milled. As you can see, the 19s will cancel leaving you with 1/20 once again. For the third card it's 19/20 x 18/19 x 1/18, which again reduces down to 1/20. Same for each successive card, So when you do the math and add it up, it comes down to a 15/20 (or 3/4) chance that the card was milled and a 5/20 (1/4) chance it was drawn.
January 21, 2014 8:13 p.m.
Each draw is a separate entity. Are you treating this as conditional probability when it's actually discrete?
January 21, 2014 8:28 p.m.
Arachnarchist says... #27
There is a 1/20 probability of it being the first card, and a 19/20 probabiltiy of it not being the first card. If it is the first card, you don't need to go any farther. But if it's not you need to account for that. Thus the probability of it being the second card is 19/20 (the odds that it wasn't the first card) times 1/19 (the odds of getting it now).
January 21, 2014 8:32 p.m.
No I think that's slightly wrong and an oversimplification. You're modelling this on Bayesian probability right? Shouldn't it follow a form somewhat along the lines of (I forget here): X power N + Y power M where X is your probability of success, N is the number of times you want it to happen, Y is the probability of failure, and M is the remainder of the trials?
Also higher level maths -
You have 20 cards in your deck and 1 Lightning Strike .
You can stay on 20 cards and the probability of the next card being Lightning Strike is 1/20.
Or you can be milled for an amount of cards (let's keep this to 1 for simplicity - but it can be extrapolated to X cards).
Here's what happens if you're milled:
The milled card is Lightning Strike and you lose - probability 1/20.
The milled card isn't Lightning Strike and you're now closer to getting it (next draw 1/19).
This is a bit like the Monty Hall problem which is a famous mathematical problem that a lot of people can't understand. Basically - here's how you explain it. It's extremely likely that the top card ISN'T what you want. The other player will then mill you. Because it's unlikely that top card is what you want they are therefore getting you one step closer to the card that you do want. If the initial probability is low then allowing 'another choice' of the top card is preferable.
This is a slight oversimplification but I think it elegantly gets across the fact that mill is helpful to the opponent if they're unlikely to draw what they want.
January 21, 2014 8:42 p.m.
Arachnarchist says... #29
As a question of probability, the probability all the individual possible scenarios must necessarily add up to 1, but if its as simple as 1/20, then 1/19, then 1/18, . . . (skip a few) . . . then 1/2, then 1/1, then it's quite clear that in this case the "probability" of it being one of those 20 cards is much greater than 1. I'm not %100 sure on my math, but this way definitely doesn't add up.
January 21, 2014 8:51 p.m.
If you're counting the likelihood in drawing the card each turn then it is a simple 1/20 or 1/19 or 1/18. The reason for this is that each separate event is discrete so you don't add them.
If you're modelling multiple draws in one turn then we have to look at binomial expansions or something and it's 2am in the UK and I only currently do medical statistics, not pure statistics so I can't be bothered to look at normal distribution curves right now.
I'm sorry :(
I'm pretty sure it has something to do with powers and factorials but I'm really tired and it's been 3 years since I've done this.
Just look at the Monty Hall problem and it becomes logically clear that getting opponents to mill you when your unlikely to draw what you need is advantageous.
January 21, 2014 9:01 p.m.
Arachnarchist is right, actually. No matter what, the chance of getting that one card is 1/20.
Let's say we're in the milling scenario. On the first draw, it's a 1/20 shot.
Assuming you don't draw it (a 19/20 chance), then the milling happens. There are essentially 19 choices: the Strike is the first card, the second card, and so on to the nineteenth (because apparently every other card is irrelevant, so order of the rest are equally irrelevant). Therefore, there's a 3/19 chance of it being milled (it's the first, second, or third card) in this instance, or a 16/19 chance it isn't.
Then we get to the second draw. There's a 1/16 chance that we draw the card. But, in order to get to this point, we need to be in the 19/20 possibilities that we didn't draw it first, and the 16/19 possibilities that it wasn't milled the first time around. So, there's a grand total of a (19/20)(16/19)(1/16)=1/20 chance, the same as drawing it the first time.
Once you get into multiple copies and getting AT LEAST one, then the math gets a bit more interesting (and too much for me to type). But in the meantime, if you only have one copy of the card you need in your deck, whether you're getting milled or not is entirely irrelevant to the chance you draw the card.
January 21, 2014 9:06 p.m.
And ChiefBell, the instances aren't discrete, because getting the top three cards milled off of your library are dependent on you not having drawn the card you needed beforehand.
January 21, 2014 9:08 p.m.
SwampHippie says... #33
lolol this is great, I'll be sure to read this all later. If either (or both) of yall prove my math wrong then I'll relish the enlightenment, its always great to participate in a debate more substantial than that of tits and sports.
Back to the books. Carry on.
January 21, 2014 9:11 p.m.
erabel - the instances are discrete if you look at drawing your 1 card per turn, but I completely agree that it's not discrete if you're being milled.
January 21, 2014 9:14 p.m.
Arachnarchist says... #35
ChiefBell: I am familiar with the Monty Hall problem. And I understand what your line of thinking but i don't think it applies.
Let's make this more similar to the Monty Hall problem. You only have three cards left in your library you choose 1 without looking at it. In order for the monty hall problem to be applicable, your opponent would have to mill one of the other two cards, and it would have to always be a non Lightning Strike one. And then you would have to have the option to switch cards.
So to recap, Monty Hall is not applicable (I think) because your opponent might very well mill your card (Monty never opened the correct door), and you don't really get a chance to switch.
January 21, 2014 9:15 p.m.
Arachnarchist says... #36
Also, I too am thoroughly enjoying this discussion of Mathematics and Statistics.
January 21, 2014 9:16 p.m.
But then if you examine the Monty Hall problem it's saying that it's more likely that the card you want isn't the top card and therefore in the majority of circumstances being milled is a good thing because it gives you additional 'chances' at getting the card you want.
Monty Hall problem on Wikipedia:
Contestants who switch have a 2/3 chance of winning the car, while contestants who stick have only a 1/3 chance. One way to see this is to notice that, 2/3 of the time, the initial choice of the player is a door hiding a goat. When that is the case, the host is forced to open the other goat door, and the remaining closed door hides the car. "Switching" only fails to give the car when the player picks the "right" door (the door hiding the car) to begin with. But, of course, that will only happen 1/3 of the time.
Monty Hall in Magic:
Players who get milled have a 2/3 chance of getting the Lightning Bolt , while players who don't have only a 1/3 chance. One way to see this is to notice that, 2/3 of the time, the initial choice of the player is the wrong card. When that is the case, the opponent is forced to mill the other cards, and the remaining cards hides the Lightning Bolt . Being milled only fails to give the Lightning Bolt when the player has the Lightning Bolt on the top of the deck to begin with. But, of course, that will only happen 1/3 of the time.
January 21, 2014 9:16 p.m.
Just saw the last comments, let me look at the maths.
January 21, 2014 9:17 p.m.
summons ChiefBell again
Even when drawing one card a turn, the chances aren't discrete. If there is only one card that can win you the game, then the probability that you draw it on the second turn is dependent on whether or not you draw it the first turn. If you do, it's a zero chance; there's no way you can draw the same card two turns in a row. If you don't, then you multiply the odds you DIDN'T draw it the first turn by the odds you DID the second turn. This is kind of the definition of non-discrete events.
January 21, 2014 9:18 p.m.
So then if this line of mathematics holds (given by erabel and Arachno-person then it's therefore concluded that milling neither helps nor hinders you in reaching the Lightning Bolt ?
January 21, 2014 9:18 p.m.
Assuming you've only got the one copy, and that it's the only thing that can win you the game, yes. If you've got multiples, then I think milling hurts your chances, but only slightly. I'd need to run the numbers again.
January 21, 2014 9:20 p.m.
I need to look at the numbers and check my probability tables. This isn't adding up for me. I'm certain there's something a bit deeper we can apply here.
January 21, 2014 9:22 p.m.
Also I understand what you're saying about the second draw being conditional on the first but in cases where the second draw hinges on the first not being something then I think you can assume that you don't have it. To put it basically - there is no T2 if you get the Lightning Bolt T1. Although your maths seems to be pretty solid. For example - the game wouldn't even continue if T1 isn't a Lightning Bolt therefore we can assume that no Lightning Bolt was drawn.
January 21, 2014 9:24 p.m.
The game continuing and changing is dependent on the card you need being drawn, ChiefBell. It either continues if it wasn't drawn or doesn't continue if it was drawn. In this case, the probability of you getting the card turn 2 needs to be multiplied by the odds you did not get it turn 1. It's how dependent events function.
Just as a quick question, what sort of stats/probability education didja have? Because you kind of don't understand the definition of independent and dependent events. Not trying to be rude, just trying to know where to start.
January 21, 2014 9:43 p.m.
I did a year of clinical statistics about two years ago. I know all of this stuff - it's just been such a long time since I did this and I'm being too stubborn to accept that your maths is flawless and mine was way off. In fact I should have realised when I started thinking about Bayesian probability models because the second half of the equation determines the likelihood of the 'target' event NOT happening. I was so close to not being a fool but it just didn't quite click.
I go to Oxford University, taking clinical Psychology, so in theory I'm exceptionally clever. In practice I'm exceptionally stupid. I think I'm just having one of those nights where I'm far too tired and I'm in far too much of an argumentative mood to accept that I'm wrong even if I quite clearly am.
Review of situations:
Maths carried out on 20 card decks, with 1 card that you wanted. 1 card being milled or drawn each time:
Situation 1 - 5% (draw what you need), 5.3% (don't get milled), 5.5% (draw what you need) = 15.8% chance to win
Situation 2 - 5% (draw what you need) 5.2% (draw what you need), 5.6% (don't get milled) = 15.8% chance to win.
Situation 3 - 5% (draw what you need) 5.26% (draw what you need), 5.55% (don't get milled) = 15.8% chance to win. (this one went to 3d.p and has rounding errors - basically it's the same).
Therefore overall: being milled has no overall effect on winning or losing.
If you know that the opponent is only going to choose to mill away cards you don't need then obviously letting them do it is fine (you can achieve this through scrying). This is the correct application of Monty Hall.
Therefore, as originally suggested milling makes no difference to your likelihood of winning or losing.
January 21, 2014 9:52 p.m.
As also suggested - I'm inept at maths (with an 's' in the UK :P)
January 21, 2014 9:53 p.m.
Going back, here's the Monty Hall problem from the movie '21'. But let's also not forget that of the 20, 40, or 60 cards in the deck, each one has a different effect EVERY game DEPENDING on the current board state. Won't matter if I mill 5 lands when you already have your land base setup. On the other hand, it also won't do much to me if I need a big creature instead of drawing the Lightning Strike
instead.
January 21, 2014 10:08 p.m.
SwampHippie says... #48
Ok I managed to read Post #14-20 on a break. My impression of the Monty Hall analogy is that Arachnarchist is quite right in saying that it isn't applicable since it doesn't take into account the possibility of Mill(Monty) actually hitting the "prize." So imo this debunks the argument that mill has a propensity to help the opponent based on the Monty Hall analogy.
That being said, I believe it was a novel analogy and we can still glean some information from it. ChiefBell I feel you're quite accurate in your reassessment of the reality of the 3-card single-Lightning Bolt situation suggesting that the mill is indeed neutral since depending on the turn order it has just as much chance of helping as it does hurting you.... YES I FINALLY AGREE :)
...and with that I believe we are all on the same page?
OK good, so now let me be so bold as to suggest that going back to the 20 card situation having a faster rate of mill (3) vs draw (1) per turn will tip the odds of hitting the oh so coveted Lightning Bolt
in Mr Mills favor. Perhaps I missed something along the way... OH FUCKIT now I'm way behind again... I'll hop back on tomorrow night hopefully.
Happy debating everyone.
January 22, 2014 1:08 a.m.
The maths gets very hard. I've started doing this on a hypergeometric calculator but when you start considering multiple cards that you could 'hit' and changing the ratio of mill to draw things get very strange.
Here's the model I ran - 53 card deck with 4 cards you want. Each mill is a sample of 5 cards, each draw is a sample of 1 card. Probabilities for mill were chance you don't lose any of the cards you want (out of the 4), probabilities for drawing were chance you obtain any of the cards you want (again, out of the 4). In order to obtain final probabilities I multiplied all the draw (success) and mill (don't fail) probabilities together because this is how conditional probability works.
Overall after running a few models we were looking at almost identical numbers in the 0.04% range for this particular model. The orders were
Situation 1. draw, draw, draw,
Situation 2. mill, draw, draw
Situation 3. draw, mill, draw,
Situation 4. draw, draw.
Situation (4) was the least likely, obviously because you're sampling fewer of the cards. This models 2 draw steps with no milling. Situations (1), (2) and (3) were extremely similar in probability - we're talking numbers like 0.004%, 0.0042, 0.0039% (can't remember exact figures but it was something like that). I'm not sure why I ran situation (1) because it's different from the rest because you have more draw steps. Interestingly, you were more likely to success in situation (2) than (3), where the milling took place when you had a greater number of cards in your deck. This seems to demonstrate the Monty Hall problem - given that the draw is unlikely to succeed, it is better to be milled and then draw because then you're slightly more likely to succeed overall. You know that with more cards in deck the mill is as likely to be unsuccessful as you are to be successful - so you allow it to mill away the cards tat are unlikely to yield the card you want. In (3) you're slightly less likely to succeed because you're drawing into a deck that's unlikely to yield what you want the first time around. This is because you initially draw before the milling takes place.
However the take home message is that you are far more likely to get what you want in situations (2) and (3) than you are in (4). It is more likely that milling won't hit what you need and that you will then draw into it than you will draw into it without being milled. I ran this on a probability calculator.
January 22, 2014 6:54 a.m.
SwampHippie says... #50
I understand now good sir, thank you so much. As stubborn and passionate as I can be about notions that make sense in my (sometimes contorted) sense of logic, I never refute solid arguments (esp. when backed up by some seemingly sound facts). ChiefBell, erabel, and Arachnarchist as much as I would have loved to participate more, yall have done a remarkable job of guiding this debate towards what I believe to be the final solution as presented by ChiefBell.
Now accepting that my previous understanding of mill and its potential for disruption was incorrect I intent to apply what I've learned to build a better deck or at the very least handle unique situations differently. This is what I've learned and intend to keep in mind if I want to maximize the POTENTIAL to disrupt opponents draws:
1) First of all this means early mill is LIKELY at best neutral and worst advantageous for the opponent. This in addition to the fact that expending resources early on mill rather than defense or removal was never a great idea in the first place makes it painfully clear this is something you should try to avoid.
2) Second if you are going to mill, mill big. Small mill has a low chance of hitting a good card AND if it doesn't, it INCREASES the chance the opponent hits a good card (so you're probably helping them), while more mill has a far greater chance of hitting a good card BUT if it doesn't, it significantly INCREASES the opponents chances. In other words if you're going to go for it, F#&$ing go for it man; things may backfire but that brings us to the last point.
3) Mill isn't disruption you can count on by any means. For most people this should stand as an extremely strong encouragement to load up on counters and removal. This serves a twofold purpose of helping you survive the early game (facilitating the strategy suggested in the first point) as well as serve as a safeguard against the potential for mill to improve the opponents draw.
...thank you Captain Obvious. Right, I know these are all fairly basic tenants of mill deck building but it is always good to review why fundamentals are... well, fundamental. In doing so we can reassess the foundation we are building upon, ensure it's sound, and feel confident in expanding upon it knowing what we should avoid.
ChiefBell says... #2
No one knows what they're about to draw. When you mill (ie - you making an opponent throw cards into the GY) you don't know which cards you're about to force the opponent to mill through. Therefore you don't know whether your getting the opponent closer or further away from the card they want.
AFTER you've milled you can see the effect that it's had (which cards have gone to the GY) but before you can't.
Also it effectively gives the opponent 60 life instead of 20 and generally encourages the use of inefficient creatures.
January 21, 2014 4:08 p.m.