He lists a few exceptions (Lost in the Woods.dec, opponent is playing mill) as reasons to run more than 40, but as far as the mana ratio argument he ultimately concludes it's generally incorrect to run extra cards for that purpose based on an experiment he does. Interesting stuff. I have in constructed run 61 for the exact purpose of getting a specific mana ratio but after reading his article I feel inclined to agree with him. If I have even just 1 bomb then I want to be drawing it as much as possible and it's pretty rare when you have a deck where the 23rd card is as good as the 1st card meaning you don't want to reduce the chance of drawing that 1st card (however minor of a reduction it might be) by running more than 40 cards.
It's true if you have even 1 bomb, one legendary card that you can only run 2 copies of in good faith but want to see consistently, or one playset of cards that you wish wish wish the ruleset would let you run 5 of, then running more than the minimum number of cards becomes totally wrecked.
That's why Nassif's 61 card Cruel Control is the most compelling and convincing argument for a correct over-the-limit deck, because that deck actually managed to care very little about any particular playset it had. The deck runs little to no cards that can't be used in multiples and would be similar to the legendary bomb example, and its not clear that you would run a 5th card onto its playsets even if you were allowed to, especially when the large amounts of draw made them feel like 5-ofs to begin with. The closest any card comes would probably be Cryptic Command, but that's just one card, its roles are covered by other elements of the deck, and a fifth cryptic might actually be pretty taxing for the vivid charge counters.
In the article you linked, the simulation "disproving" Nassif's mana ratio argument is waaaay oversimplified. The decks aren't actually using a curve of any sort, all the decks he plugged into the simulator do absolutely nothing but cry if they mana flood. That drastically increases the "I draw a land, I thin my deck" significance he was talking about. If Nassif's deck draws a land, sure, it thins his deck less, but when he mana floods he just uses the extra land to spam more Divinations and it's much more of a wash than a "magic deck" full of 1 mana 2/2s (I'm starting to wonder why I feel the need to debunk the simulation the more I talk about it..) (Oh, wow, he goldfish killed with them, he didn't even bother to right a computer program that would handle the trivial attacking and blocking decisions of a format with nothing but 2/2s..).
The simulation probably at best indicates that my 41 card draft deck of a future block needs to have cards at different mana costs. That's not very hard. If, to my surprise, that simplification isn't that damaging, it might mean my draft deck of a future block needs Firebreathing or some other decent mana sinks to offset the significance of the drawing without replacement effect. It's again, not hard.
I don't know why it didn't occur to me before now, but I am starting to wonder whether its possible for a mana curve to want to be 41 cards on the play and 40 on the draw or vice versa. Limited is the only format that allows change in deck size, I think, so the concept would never have been toyed with in constructed right?
Good land ratio matters much more for *aggro* decks. The function of a good land ratio is to idealize the first few turns of the game. Every deck will eventually get its mana in the long game.
Much more here matters mulligen decisions, land ratio matters whole game - even if you don't like it(Yes, it affects mulligan decisions, but not as only factor - wrong colors, wrong curve,...).
Also control decks play card draw. Aggro decks generally do not, so they have to manipulate their draws in deckbuilding to a much greater extent.
Yes, control decks play card draw but it still sucks to lose when you draw 4 lands of Opportunity just because you play to much lands. Also every deck tries to play as much card advantage as possible but that usually doesn't mean it can play more lands then optimal.
I feel like you've already decided that 41 cards is okay and are trying to justify your position by making things up, rather than actually think about it.
Similarily, I feel you've already decided that 41 cards is always wrong and are trying to justify your possition, that there aren't possible other situations, by making things up, rather than try actually thinking about it.
I've been in arguments before where I was on the wrong side of a purely factual statement, and in trying to justify my position, I get around to right around the spot you're in now, where I'm pigeonholed into saying things that would do nothing but make people look at me cross-eyed. Usually at that point I just delete my post and give in.
I'm not prepared to take the argument far enough afield to try to convince you why everything here in your post is wrong, so if you want to continue to believe those things, I'm officially okay with it.
I remember reading that Karsten article and thinking, I don't think this actually proves the point you are trying to prove. It's a completely artificial construct and you are playing a goldfish. So, yes, I can see how, under those circumstances, having a minimum amount of land/cards is going to always be better. But how relevant is that in actual games where (1) you have more than one type of spell with (2) more than one type of cost and (3) your opponent is not a goldfish? It's an interesting thought experiment, but it doesn't "prove" that 40 is always correct.
The only argument I keep hearing is this idea of "it's all about getting to your 'best' cards, so anything that even slightly reduces your chance of drawing one of those cards is sub-optimal, Q.E.D." without really any more thought. I'm just not sure it's actually that simple, given, you know, that Magic is a complex game.
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Ambush Krotiq makes me laugh so much. I keep rereading the card and it keeps not having Flash. In what sense is this an ambush again? I just have visions of this huge Krotiq poorly concealed in some bushes, feeling slightly sad that his carefully planned ambushes never seem to work.
Frank's test was analyzing if improved mana ratios could conceivably make a difference if power levels between spells were completely flat. i.e. a situation in which it is *not* about getting your best cards. The reason he did the test this way is because if power levels between cards were *not* flat, it could only swing the pendulum in favor of minimizing the size of your deck. If his tests had shown that 41 cards was ever optimal with a perfectly flat power level, it still wouldn't overcome the consistency argument in a normal deck. The fact that it didn't show that, however, is further demonstration that there is no cause under any circumstances to think that 41 cards is ever a good idea.
He took the weakest set of constraints imaginable to allow 41 cards to be optimal, and it still wasn't. A more complex situation would only make it less so.
...Because making it more complicated makes it easier to refuse to understand?
Look, I teach math for a living. I see people all day every day who make things more complicated than they need to be. It's literally the defining problem with learning math (and most things). A concept like creating a lower bound to determine a simple threshold beyond which nothing needs to be considered is a hard one to grasp for people. I totally empathize.
This has officially morphed into the Defending Terrible Cards debate, where I scratch my head and wonder -- why do people so fiercely want to believe that there's a deck out there that would benefit from Feed the Clan and they refuse to admit that it's proper usage is 0% instead of 0.000001%?
Similarly, why do people want 41 cards to be OK? Like what benefit do you get from others acknowledging that 41 cards is an occasionally acceptable strategic decision? Are you just seeking validation? No one has hard evidence for debates like this so it's my theory vs. your theory. We're all free to follow our own theories so why do people feel that need to debate and get other people to agree with them (even after the opponent has clearly said he's not interested in embracing a new theory)?
It just boggles my mind. As several others have said, if you want to play 41 cards, or 47 cards, because you think it's correct, you are free to do so. But no amount of theorizing is going to convince many of us that it's a sound strategic play because we prescribe to a different theory. "You always play exactly 40 cards" has been a foundation of Limited theory for over a decade and there's no new evidence to challenge it.
From what I gather, almost everyone here - myself included - believes the 40-card deck is better than the 41-card deck in the majority of cases. Maybe even every case. What I'm not buying are the "proofs" presented so far to support this. Maybe it is not possible to prove it. Nevertheless, I think it's an interesting question.
What's not to buy? It's indisputable that 1st picks are better than 12th picks, and that drawing your 1st picks more often wins you more games than drawing your 12th picks more often. Given the choice, why would you choose to draw your twelfth picks more often?
Because it may not be that simple. Maybe the 41-card deck has better mana, maybe the 41-card deck has higher spell density (say 23/41 vs 22/40), and maybe these advantages trump the disadvantage of not drawing your 1st pick as often. I'm not saying they do, but I don't think they can be that easily dismissed.
I'm not saying they do, but I don't think they can be that easily dismissed.
I dunno, these arguments have been "dismissed" for like 15 years. I can just as easily argue that in the absence of new information or evidence, there's no reason to think the established theory is wrong. Like do you really think the Pros of the world have never entertained the idea of and experimented with ideas like mana consistency and spell density in Limited? The mistake here is assuming that in the absence of hard evidence, no one has actually tested these ideas and dismissed them.
If 41 cards was a valid thing, we'd see it more at the Pro Tour level. Maybe not often but 1 in 100 drafts by established Pros, and we're not seeing that.
I'm not saying they do, but I don't think they can be that easily dismissed.
I dunno, these arguments have been "dismissed" for like 15 years. I can just as easily argue that in the absence of new information or evidence, there's no reason to think the established theory is wrong. Like do you really think the Pros of the world have never entertained the idea of and experimented with ideas like mana consistency and spell density in Limited? The mistake here is assuming that in the absence of hard evidence, no one has actually tested these ideas and dismissed them.
If 41 cards was a valid thing, we'd see it more at the Pro Tour level. Maybe not often but 1 in 100 drafts by established Pros, and we're not seeing that.
"40-card decks are always superior because the pros play 40-card decks" is in no way proof of the superiority of the 40-card decks. However, in the absence of hard evidence, it is a good indication that 40-card decks are usually superior.
Because it may not be that simple. Maybe the 41-card deck has better mana, maybe the 41-card deck has higher spell density (say 23/41 vs 22/40), and maybe these advantages trump the disadvantage of not drawing your 1st pick as often. I'm not saying they do, but I don't think they can be that easily dismissed.
No, but see, those arguments are fairly simple statistical questions, which can, and have, been solved. It is absolutely true that 18/41 is a better mana ratio than 17/40 if the goal is to hit 4 lands by turn 4 as often as possible without flooding. It isn't in doubt that that's true, but the value of the effect is established to be several orders of magnitude smaller than the *already* small value of reducing your consistency. It isn't a question of maybes, where the two sides of the argument potentially have similar values and that therefore there's a judgment call involved. One side of the question is *much* smaller, to the point where no matter how you argue it, it isn't going to be close.
An ant can argue that it's bigger than a chihuahua all it wants. Maybe it's an unusually big ant. But when the dog accidentally steps on it without even noticing, the ant's unusual size isn't going to make much difference.
"40-card decks are always superior because the pros play 40-card decks" is in no way proof of the superiority of the 40-card decks. However, in the absence of hard evidence, it is a good indication that 40-card decks are usually superior.
I think at this point you're arguing with what you think I'm going to say, instead of what I'm actually saying. I didn't call it proof. But I do believe that if 41 cards was a legitimate strategic choice, some Pro would be touting it. Someone would be shouting from the rooftops that they've done the math, they've done the experiments, and the old way of thinking is incomplete.
That's the thing about Draft, people are practicing it all the time. People who are far more dedicated to the game than any of us, unless this board is shockingly populated with members of the top Pro testing teams. They're looking for any possible angle to get the tiniest edge of their opponents and none of them are bothering with 41 card decks, ever. No one's writing the article about how to deduce when you want the 18/41 ratio. (Plenty of articles about when to play 16/17/18 lands, in comparison.)
The proof cannot be obtained. We would need the Time Traveling Supercomputer that they joke about on LRCast -- the computer from the future where technology has advanced to the point that a complex system such as a Limited deck can be analyzed down to objective conclusions. In the absence of proof, I'm willing to follow the trail of evidence left by the people spending the most time experimenting vs. trusting my own intuition or my own homebrewed mathematical models. I can come up with my own theories, but I have no reason to think my personal conclusions are more valid than the conclusions reached by a group of players who are better than me, more experienced, spending more of their time on these questions, and pooling their results for greater sample size.
It's quite prideful to think you've cracked some secret of the game by yourself just by pondering it, simply because there's no "proof." Your argument does not have equal merit as the established theories simply because it can't be proven wrong.
what mu1000 might be reacting to is the people here who keep on saying that it is provably true that 40 cards are always superior. i still haven't seen anything in these boards that come close to a proof -- and as you say, there may be no proof to be had.
(the argument from the article about the computer program that tests all 1/1 or all 2/2 decks etc does not convince me at all as a lower bound, btw, for reasons others brought up).
what convinced me, though, was something very compelling to my intuition (the thought experiment posed to LSV, plus your commentary that your top four cards are THAT important). still, that argument wasn't anything close to a proof, or even with any partial data of hard evidence; it was still only appealing to my intuition.
one reason your argument was so compelling was because it specifically addressed my "but what about..?" objections (ie "but what about flexibility or other advantages as a better deal than consistency?"). maybe some people still arguing feel their own "but what about..?" objections aren't being addressed? it's one thing to say "look, the correct answer probably is 40 card decks and here are the reasons" but unless the objections are addressed, the natural response might be "yeah, you can be right, but i still can't help but wonder...".
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From what I gather, almost everyone here - myself included - believes the 40-card deck is better than the 41-card deck in the majority of cases. Maybe even every case. What I'm not buying are the "proofs" presented so far to support this. Maybe it is not possible to prove it. Nevertheless, I think it's an interesting question.
For me personally, the only reason to play a 41 card deck is when I want to have a 17.5 card land base (so 18 land in a 41 card deck).
Since I'm not nearly good enough at magic to know when I want to have precisely 17.5 cards, I mentally shortcut that to 'only play 40 cards'. Saves on time and mental energy.
To the people who basically don't want to be forced to decide between the 23rd and 24th card in their decklist, imagine that your game is going to take 8 turns on average, withou card drawing. That means you will draw exactly 15 cards from your deck. Let's assume that you have one bomb in your deck. By running a 41 card deck you are reducing your odds of drawing your bomb in any given game from 15/40 to 15/41. So in roughly 1% of your games you would have drawn your bomb, but you don't because of your suboptimal deckbuilding decision. In any given FNM you might play 9 games. So you'll never see that tiny mistake writ large in your life. But it is still the (wrong) decision to accept a worse result in your deck.
By refusing to choose between the worst cards in your deck you are giving yourself options on both of them, but those options come at the expense of all of the other (better) cards in your deck. The latter outweighs the former.
Haha, what? You say that "41 cards *is* unambiguously suboptimal" and that it is provable - so would You mind to give us such prove or at least some real argument?
Does the above make any sort of sense to you?
In addition, the larger the deck size is the greater the variance is. Imagine that you have a 40 card 16 land aggro deck. If you had the ability to copy each card 10 times (so you have 160 lands in a 400 card deck) that deck would be far worse because of the greater variance of the deck composition: You are more likely to run into a sequence of 7 straight lands in the 400 card deck than in the 40 card deck.
one reason your argument was so compelling was because it specifically addressed my "but what about..?" objections (ie "but what about flexibility or other advantages as a better deal than consistency?"). maybe some people still arguing feel their own "but what about..?" objections aren't being addressed? it's one thing to say "look, the correct answer probably is 40 card decks and here are the reasons" but unless the objections are addressed, the natural response might be "yeah, you can be right, but i still can't help but wonder...".
This is a fair point. I've been through enough of these arguments though to know that someone who is still arguing with a widely established established theory when the post count gets above 50 is not going to change their mind no matter how many of their intuitive objections are addressed. They are convinced of X, it is literally impossible to prove Y, therefore they will continue to believe X. By this point in the discussion they've likely already blown by several valid counterpoints and responded "Yea but that's still not proof" and the thing just goes in circles. I think we've already hit the key mile markers in this sort of debate:
"But a theory isn't proof!"
"Just because Pros do something doesn't make it right"
Convoluted nonsensical math
People exiting the conversation with a frustrated "Fine, I hope I play against you and your bad decisions"
I don't know why people come here to debate things when they have no interest in listening to the established wisdom or recognizing challenges to their beliefs that are anything less than "proof." It reminds me of another LSV saying...the only thing Magic players like more than winning is being right.
I guess I'll stop trying to share some of my wisdom collected over 20 years playing this game (cue the counterargument "Experience doesn't mean you're right!") because I don't have "proof." To anyone who refuses to embrace the argument that failing to draw your best cards outweighs the mana consistency, you are free to be willfully ignorant. The counterargument has been clearly laid out for you. We can't make you believe it.
Phyrre, i appreciated all the ideas in support of the forty card deck, because i appreciate ideas.
my read of what people are saying here (though i might be emphasizing only certain posts and forgetting the others) i that yes, it's probably correct to only play 40 cards unless MAYBE you have a super-flat power level and no bombs, but that we still don't have anything close to a proof.
and the "but it's not a proof" is a reaction to posts like Puddle Jumper's below:
The only thing I'm arguing here at this point is that 41 cards *is* unambiguously suboptimal. I'm not saying it's a big effect, or that there should be any value judgments about the people who choose to play that way. But there are people who still apparently believe that running 41 cards is helping their decks, and that is factually, provably false.
although i'm glad to have read Puddle's arguments, i still don't agree with their assertion that playing 41 cards is "unambiguously suboptimal", or that it is "factually, provably false". i've heard very good arguments, but nothing strong enough that i'd call it unambiguous or factual and provable.
magicmerl a few posts up gave a good summary of their understanding:
To the people who basically don't want to be forced to decide between the 23rd and 24th card in their decklist, imagine that your game is going to take 8 turns on average, withou card drawing. That means you will draw exactly 15 cards from your deck. Let's assume that you have one bomb in your deck. By running a 41 card deck you are reducing your odds of drawing your bomb in any given game from 15/40 to 15/41. So in roughly 1% of your games you would have drawn your bomb, but you don't because of your suboptimal deckbuilding decision. In any given FNM you might play 9 games. So you'll never see that tiny mistake writ large in your life. But it is still the (wrong) decision to accept a worse result in your deck.
By refusing to choose between the worst cards in your deck you are giving yourself options on both of them, but those options come at the expense of all of the other (better) cards in your deck. The latter outweighs the former.
but i still see this argument as appealing to intuition, much like your own argument that convinced me. merl says that "The latter outweighs the former", which is an assertion i agree with, but my understanding is that it still appeals to my intuition, not to anything close to being unambiguous or provable; intuition says that the benefits from keeping both worst cards are comparatively smaller than drawing yoru best card -- but this isn't proven. maybe intuition is incorrect here. (not that i believe this is likely the case, but it's not been proven).
to be clear, you /have/ convinced me, Phyrre. i /have/ changed my mind.
the only thing i'm "holding onto" and wanting to be shown wrong about, is the assertion that this (probably correct) conclusion is so "factually, provably correct". (and if it has been proved, i missed it, and any gentle redirection of my attention would be appreciated!)
How exactly do you want to be shown proof? I mean, using some very reasonable and even generous shortcuts I can lay out math right here in the thread which will demonstrate the point. I have done it. It's in my field, I know what I'm doing and what I'm talking about. But it won't make sense to you and therefore you won't be able to absolutely trust that I'm right, or that my shortcuts are valid, any more than you could Frank's article.
I guess what I'm saying is that lack of proof is not the problem here. Lack of understanding is the problem. I don't have the tools to express the facts in a way that both accurately expresses the facts and that you can understand. I can simplify the problem down to the obvious roots but then you won't believe it because it's "too simple". I can say things like "it's a proven fact" but you aren't believing me. I can cite Magic experts but you aren't believing them either. I'm not sure why. Science has had this same basic problem for centuries. Scientists make discoveries but can't "prove" them to people without educating them further than they want to be educated, so laymen don't believe it's really proof. And then scientists spend the next century developing the necessary tools to convince the masses, while they could be out doing useful things like not proving the earth isn't the center of the universe.
Frank's test was analyzing if improved mana ratios could conceivably make a difference if power levels between spells were completely flat. i.e. a situation in which it is *not* about getting your best cards. The reason he did the test this way is because if power levels between cards were *not* flat, it could only swing the pendulum in favor of minimizing the size of your deck. If his tests had shown that 41 cards was ever optimal with a perfectly flat power level, it still wouldn't overcome the consistency argument in a normal deck. The fact that it didn't show that, however, is further demonstration that there is no cause under any circumstances to think that 41 cards is ever a good idea.
He took the weakest set of constraints imaginable to allow 41 cards to be optimal, and it still wasn't. A more complex situation would only make it less so.
Exactly, this is why the experiment is a good example of why 41 cards is bad. In the very situation where you would expect 41 cards could possibly give you an advantage (where all the cards in your deck are of equal quality) it in fact does not give you an advantage but instead puts you at a disadvantage.
I mean, using some very reasonable and even generous shortcuts I can lay out math right here in the thread which will demonstrate the point. [....] But it won't make sense to you and therefore you won't be able to absolutely trust that I'm right, or that my shortcuts are valid, any more than you could Frank's article.
I don't have the tools to express the facts in a way that both accurately expresses the facts and that you can understand. I can simplify the problem down to the obvious roots but then you won't believe it because it's "too simple". I can say things like "it's a proven fact" but you aren't believing me. I can cite Magic experts but you aren't believing them either.
this part of what you wrote is standing out to me.
it is kind of like a summary of some of what's been happening.
i'm struggling to know what to say that could be constructive right now. i've thought to try to "argue" more about the topic at hand, but i know that i'm not very good at that, and besides i've always been wary of conflict and tension.
i think i feel a little guilty right now, because it's a thread that /i/ started that seems to have turned into conflict and tension. (i do like disagreement, and i do like discussion, but i get nervous when i feel that tension is high and that people are no longer able to "catch" what each other is saying).
about the topic at hand,
- i see that Phyrre and magicmerl's arguments have convinced me that it's probably always correct to play 40 card decks, unless your power level of every card is VERY flat. but i feel convinced still in ways i feel are "weak" or only intuition based.
- a "stronger" argument would be something like the computer analysis in Frank's article... except i feel like it's flawed becuase it is over-simplified! (am i correct in my feeling Frank's argument is flawed? is this something that is productive to try to discuss? i honestly am not sure).
so, if you're willing (or patient enough!), i would love a more rigorous, "stronger" demonstration of why 40 card decks are unequivocally better. i ask this not to "win" an argument with you, but out of curiousity. it might still be the case that i'm not convinced, but you make a good point that i might not ever be convinced because i cannot understand the higher math involved in the non-simplified proof.
in terms of my emotions,
- i don't want to concede that i'm convinced in "strong" ways, because i'm not!
- maybe what you're saying is true: that i don't have the mathematical capacity to understand the "strong" ways
- but i still love peering "under the hood" and seeing how things work. which is why i wish i could be as convinced that there is more "strong" proof, as you are convinced. maybe this is why i dont' want to let go: i am jealous that you are able to understand this "strong" proof and i am not, and it wish for it to be explained to me!
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about this thread,
- i feel it's gotten to a point where people (myself included) have trouble listening to what the other person is saying. it's easy to take a portion of what someone said that has to do with "your own agenda" and ignore the main thing that they were /trying/ to say.
- my last post, for example, my own agenda is "but nothing has been proven!". that's as much as i could cognitively keep in my attention. so, i quoted you in my response to Phyrre to make my-own-agenda point, but i still am unsure if i actually heard what you were trying to say.
- it's easy for me to see how mu1000's point got lost in posts #63 to #66, for example, (but only because mu1000 has the same agenda i have).
post #63: mu1000 says "40 card decks are probably correct. but i disagree that any proof has been given"
post #64: PuddleJumper says "you mean you don't agree that XYZ constitutes a proof?"
post #65: mu1000 says "no, i think XYZ might be oversimplified, missing the possibility that 41-card decks have advantages that haven't yet been proven to not matter. i don't think this is actually the case, but this hasn't yet been proven."
post #66: Phyrre says "but that possibility has been effectively dismissed by pros over the years"
and so mu1000's and my point has now been lost ("can we prove 41-card decks aren't correct?") because Phyrre needs to point out the fact that pros haven't used 41-card decks ("pros show that 41-card decks are likely not correct"). and Phyrre wanting to point this out isn't necessarily wrong, because it's still new information and an interesting idea.
my unease about the tension in this thread makes me suspect that
people aren't hearing what other people are trying to say. mu1000 and myself want it to be heard that we still don't see a proof. and my impression is that you (ie PuddleJumper) are convinced that it's certain that 40 card decks correct and are annoyed when people say it doesn't matter. and Phyrre is annoyed that we're still arguing about this because it's clear what the correct conclusion is. and throughout this all, i wonder if the tension makes us all feel that we have to "win" an argument against the other person, when in reality i felt inspired by Phyrre's ideas and i appreciate the way you very often give your ideas in my threads!
(be assured that when merl argues with you that XYZ doesn't constitute a proof (post #65) or when i keep pushing "no proof has been given!" to Phyrre, it's not to "win" against you two or to prove you two wrong or to dismiss you or to disagree for the sake of disagreeing. it's genuinely because i want to understand your stronger proof if one exists!)
forum discussion is hard to do constructively, it seems. i have seen threads devolve on mtgs before -- many times!
i don't even think anyone here is a jerk or is wrong. i suspect that it's just difficult to sort out the different points or agendas, and that crosstalk happens a lot.
Frank's test was analyzing if improved mana ratios could conceivably make a difference if power levels between spells were completely flat. i.e. a situation in which it is *not* about getting your best cards. The reason he did the test this way is because if power levels between cards were *not* flat, it could only swing the pendulum in favor of minimizing the size of your deck. If his tests had shown that 41 cards was ever optimal with a perfectly flat power level, it still wouldn't overcome the consistency argument in a normal deck. The fact that it didn't show that, however, is further demonstration that there is no cause under any circumstances to think that 41 cards is ever a good idea.
He took the weakest set of constraints imaginable to allow 41 cards to be optimal, and it still wasn't. A more complex situation would only make it less so.
Exactly, this is why the experiment is a good example of why 41 cards is bad. In the very situation where you would expect 41 cards could possibly give you an advantage (where all the cards in your deck are of equal quality) it in fact does not give you an advantage but instead puts you at a disadvantage.
i'll agree that the experiment shows that if all your cards are of equal value in terms of being vanilla creatures, 41 card decks don't offer an advantage.
but do you agree that the experiment doesn't prove that 41 card decks never gives you an advantage?
i still have the feeling that maybe:
- not cutting the 23rd and 24th card gives benefits (better curve, higher ratio of Humans for your Human-matters cards, anti-flier protection)
- that maybe outweigh drawing each of your best cards a turn later.
Phyrre's argument (your best four cards are THAT important that you want to draw them earlier) intuitively convinces me, but it doesn't strike me as a proof. (maybe not losing to fliers is SO important that it offsets not drawing your bombs. intuitively it doesn't sound correct but no proof has been given, and proofs are useful because they have the power to unequivocally show that strong intuition can be incorrect).
and it's this that i still feel Frank's experiment doesn't address. do you agree/disagree?
okay, so what i just wrote (now hidden by spoiler tags) doesn't make sense when i realize that i'm still talking about drawing your best cards, given that the experiment took that factor out the equation.
why do i still feel that the experiment is flawed?
it has something to do with "mana ratio is shown to not ever be better in a 41-card deck for a flat power level consisting only of vanilla creatures", but could the mana ratio be shown to be better for flat-ish power levels consisting of an actual curve of mana costs?
and, what about factors other than mana ratio, such as factors in my initial argument? ("not cutting the 23rd and 24th cards might give benefits such as a better curve, better synergy, or anti-flier protection"?)
why do i still feel that the experiment is flawed?
it has something to do with "mana ratio is shown to not ever be better in a 41-card deck for a flat power level consisting only of vanilla creatures", but could the mana ratio be shown to be better for flat-ish power levels consisting of an actual curve of mana costs?
and, what about factors other than mana ratio, such as factors in my initial argument? ("not cutting the 23rd and 24th cards might give benefits such as a better curve, better synergy, or anti-flier protection"?)
I wouldn't consider it flawed so much as just a singular example (but yet one that makes a compelling argument imo). What additional tests would need to be done to convince you? A deck that has X lands, Y 2/2s for 2 and Z 3/3s for 3 vs a deck that has X+1 lands for mana ratio reasons? Or more complex than that? I don't claim to be good at running statistical analyses but maybe someone else would be. If anyone actually has done more in-depth tests than Frank's I would be interested in seeing the results anyways but I feel they will only corroborate with Frank's simple example.
As far as the other factors you mention, I think they have been considered but overall the side effect of drawing your best cards less frequently outweighs any advantage of extra synergy or having more specific answers available in your deck. Also these additional synergies are hurt by having a larger deck now anyways as you are statistically less likely to draw the cards together than if you just cut a non-synergistic card for whatever 24th card you wanted for that purpose. There's certainly something of an argument to be made for sacrificing power for the sake of synergy, but sacrificing power and consistency for the sake of synergy is just not worth it to me.
Silph, I appreciate your sidebar about the nature of this debate and I'd like to share my motivations for even participating at this point. I appreciate this forum because this is where I learned how to draft, something that brings me much joy. If I never happened upon the MTGS Limited Forum and the wise teachers here, maybe I would have given up on the idea of getting better at drafting and missed out on a lot of fun.
I'm also the type of person who defends the truth, sometimes to a fault. I despise the spread of misinformation. It bothers me on a visceral level. For example, nothing will get me more worked up than the ongoing anti-vaccine debate. It's not even comparable to discussions we have here because in that debate, misinformation results in actual preventable deaths. But at the core it's a similar issue.
This forum is a place to teach and learn. But it's also a public forum meaning it's vulnerable to the spread of misinformation. It's never intentional, but misinformation is spread here constantly. We don't have any sort of system to sort out who's a good teacher, who typically has good advice vs. who just joined yesterday and has never even drafted but is presenting their opinions as facts because they *feel* that they must be right.
My goal is to join these discussions and make it clear what I believe while also pointing out the arguments I feel are unfounded and may lead a new player astray. That way when a novice is faced with the challenge of believing conflicting ideas X and Y, he's at least seen both sides of the argument from me.
While it is technically true in a semantic way that no one can prove 40 card decks are superior, I strongly believe it to be the underlying truth. All available evidence such-as-it-is also seems to support the idea. The only arguments against are pure theorycraft, in the same way that we have piles of clinical trial data showing that vaccines are safe and effective for the population but there's a small group that believes otherwise based entirely on theory. ("I don't trust this chemical"...even though it's been demonstrated to be safe.)
Intuition is a dangerous tool. Sometimes intuition helps us catch things that are disguised as truths. But unfortunately intuition is just looking for patterns and sometimes it finds a perfectly true axiom and tells your mind...ehh I'm not sure about this one, let's be real cautious. And the most annoying thing about intuition is that in an effort to protect us from being deceived by other people, it tells us...don't just be wary of this claim, also be wary of anyone supporting it because they might be trying to trick us. ("These vaccines are unsafe AND the doctors know it and it's all a conspiracy!")
It's why it took centuries for people to accept that the world is round -- there's nothing intuitive about it. Think about that for a moment. The world is and has been round for the history of humankind, and our sense of intuition can't remotely process that. It's a flawed tool. By working together we can try to parse out the true signals from the noise but someone who relies heavily on intuition is just going to gum up the process.
I think we can all admit that on an intuitive level, it really seems like 41 cards should be OK. It's such a small thing. It's a decision made with good intentions. But it might still be very wrong in the same sense that a person thinking the world is flat is very wrong regardless of their intentions. And generally it takes decades or centuries to make the transition from widely accepted theory to provable truth because we don't always have the technology to do so.
I know this is way off the rails but I think it's a good discussion because any difficult question about the game eventually wanders into this territory.
On the subject of a widely accepted theory, I was trying to come up with some kind of an example of a theory, which everyone just knew was true, everyone assumed was true, and it went unchallenged for however long it went unchallenged for - until someone actually demonstrated that it wasn't true, and the theory was actually incorrect, despite being accepted and unchallenged for however long it was.
I wanted to do that just to point out that because something is widely accepted does not automatically mean it is correct. And I believe the "play the minimum deck size" is a theory that has been accepted and assumed to be correct since the beginning of limited.
Please note I'm NOT saying that it ISN'T correct. Obviously many, if not most times something is widely accepted and assumed it does, in fact, turn out to be correct. Just not always. And, as I've said multiple times now, if the entirety of the argument comes down to "it means you draw your best cards more," then, that rationale seems ripe for finding exceptions - if anyone was inclined to go looking for them. Which no one really appears to be, since the default has been assumed correct, basically, forever.
That's all I'm saying. Well, that and it's not that big a deal in the overall scheme of things.
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Ambush Krotiq makes me laugh so much. I keep rereading the card and it keeps not having Flash. In what sense is this an ambush again? I just have visions of this huge Krotiq poorly concealed in some bushes, feeling slightly sad that his carefully planned ambushes never seem to work.
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It's true if you have even 1 bomb, one legendary card that you can only run 2 copies of in good faith but want to see consistently, or one playset of cards that you wish wish wish the ruleset would let you run 5 of, then running more than the minimum number of cards becomes totally wrecked.
That's why Nassif's 61 card Cruel Control is the most compelling and convincing argument for a correct over-the-limit deck, because that deck actually managed to care very little about any particular playset it had. The deck runs little to no cards that can't be used in multiples and would be similar to the legendary bomb example, and its not clear that you would run a 5th card onto its playsets even if you were allowed to, especially when the large amounts of draw made them feel like 5-ofs to begin with. The closest any card comes would probably be Cryptic Command, but that's just one card, its roles are covered by other elements of the deck, and a fifth cryptic might actually be pretty taxing for the vivid charge counters.
In the article you linked, the simulation "disproving" Nassif's mana ratio argument is waaaay oversimplified. The decks aren't actually using a curve of any sort, all the decks he plugged into the simulator do absolutely nothing but cry if they mana flood. That drastically increases the "I draw a land, I thin my deck" significance he was talking about. If Nassif's deck draws a land, sure, it thins his deck less, but when he mana floods he just uses the extra land to spam more Divinations and it's much more of a wash than a "magic deck" full of 1 mana 2/2s (I'm starting to wonder why I feel the need to debunk the simulation the more I talk about it..) (Oh, wow, he goldfish killed with them, he didn't even bother to right a computer program that would handle the trivial attacking and blocking decisions of a format with nothing but 2/2s..).
The simulation probably at best indicates that my 41 card draft deck of a future block needs to have cards at different mana costs. That's not very hard. If, to my surprise, that simplification isn't that damaging, it might mean my draft deck of a future block needs Firebreathing or some other decent mana sinks to offset the significance of the drawing without replacement effect. It's again, not hard.
I don't know why it didn't occur to me before now, but I am starting to wonder whether its possible for a mana curve to want to be 41 cards on the play and 40 on the draw or vice versa. Limited is the only format that allows change in deck size, I think, so the concept would never have been toyed with in constructed right?
I've been in arguments before where I was on the wrong side of a purely factual statement, and in trying to justify my position, I get around to right around the spot you're in now, where I'm pigeonholed into saying things that would do nothing but make people look at me cross-eyed. Usually at that point I just delete my post and give in.
I'm not prepared to take the argument far enough afield to try to convince you why everything here in your post is wrong, so if you want to continue to believe those things, I'm officially okay with it.
The only argument I keep hearing is this idea of "it's all about getting to your 'best' cards, so anything that even slightly reduces your chance of drawing one of those cards is sub-optimal, Q.E.D." without really any more thought. I'm just not sure it's actually that simple, given, you know, that Magic is a complex game.
He took the weakest set of constraints imaginable to allow 41 cards to be optimal, and it still wasn't. A more complex situation would only make it less so.
Look, I teach math for a living. I see people all day every day who make things more complicated than they need to be. It's literally the defining problem with learning math (and most things). A concept like creating a lower bound to determine a simple threshold beyond which nothing needs to be considered is a hard one to grasp for people. I totally empathize.
That doesn't make it wrong.
Similarly, why do people want 41 cards to be OK? Like what benefit do you get from others acknowledging that 41 cards is an occasionally acceptable strategic decision? Are you just seeking validation? No one has hard evidence for debates like this so it's my theory vs. your theory. We're all free to follow our own theories so why do people feel that need to debate and get other people to agree with them (even after the opponent has clearly said he's not interested in embracing a new theory)?
It just boggles my mind. As several others have said, if you want to play 41 cards, or 47 cards, because you think it's correct, you are free to do so. But no amount of theorizing is going to convince many of us that it's a sound strategic play because we prescribe to a different theory. "You always play exactly 40 cards" has been a foundation of Limited theory for over a decade and there's no new evidence to challenge it.
I dunno, these arguments have been "dismissed" for like 15 years. I can just as easily argue that in the absence of new information or evidence, there's no reason to think the established theory is wrong. Like do you really think the Pros of the world have never entertained the idea of and experimented with ideas like mana consistency and spell density in Limited? The mistake here is assuming that in the absence of hard evidence, no one has actually tested these ideas and dismissed them.
If 41 cards was a valid thing, we'd see it more at the Pro Tour level. Maybe not often but 1 in 100 drafts by established Pros, and we're not seeing that.
"40-card decks are always superior because the pros play 40-card decks" is in no way proof of the superiority of the 40-card decks. However, in the absence of hard evidence, it is a good indication that 40-card decks are usually superior.
No, but see, those arguments are fairly simple statistical questions, which can, and have, been solved. It is absolutely true that 18/41 is a better mana ratio than 17/40 if the goal is to hit 4 lands by turn 4 as often as possible without flooding. It isn't in doubt that that's true, but the value of the effect is established to be several orders of magnitude smaller than the *already* small value of reducing your consistency. It isn't a question of maybes, where the two sides of the argument potentially have similar values and that therefore there's a judgment call involved. One side of the question is *much* smaller, to the point where no matter how you argue it, it isn't going to be close.
An ant can argue that it's bigger than a chihuahua all it wants. Maybe it's an unusually big ant. But when the dog accidentally steps on it without even noticing, the ant's unusual size isn't going to make much difference.
I think at this point you're arguing with what you think I'm going to say, instead of what I'm actually saying. I didn't call it proof. But I do believe that if 41 cards was a legitimate strategic choice, some Pro would be touting it. Someone would be shouting from the rooftops that they've done the math, they've done the experiments, and the old way of thinking is incomplete.
That's the thing about Draft, people are practicing it all the time. People who are far more dedicated to the game than any of us, unless this board is shockingly populated with members of the top Pro testing teams. They're looking for any possible angle to get the tiniest edge of their opponents and none of them are bothering with 41 card decks, ever. No one's writing the article about how to deduce when you want the 18/41 ratio. (Plenty of articles about when to play 16/17/18 lands, in comparison.)
The proof cannot be obtained. We would need the Time Traveling Supercomputer that they joke about on LRCast -- the computer from the future where technology has advanced to the point that a complex system such as a Limited deck can be analyzed down to objective conclusions. In the absence of proof, I'm willing to follow the trail of evidence left by the people spending the most time experimenting vs. trusting my own intuition or my own homebrewed mathematical models. I can come up with my own theories, but I have no reason to think my personal conclusions are more valid than the conclusions reached by a group of players who are better than me, more experienced, spending more of their time on these questions, and pooling their results for greater sample size.
It's quite prideful to think you've cracked some secret of the game by yourself just by pondering it, simply because there's no "proof." Your argument does not have equal merit as the established theories simply because it can't be proven wrong.
what mu1000 might be reacting to is the people here who keep on saying that it is provably true that 40 cards are always superior. i still haven't seen anything in these boards that come close to a proof -- and as you say, there may be no proof to be had.
(the argument from the article about the computer program that tests all 1/1 or all 2/2 decks etc does not convince me at all as a lower bound, btw, for reasons others brought up).
what convinced me, though, was something very compelling to my intuition (the thought experiment posed to LSV, plus your commentary that your top four cards are THAT important). still, that argument wasn't anything close to a proof, or even with any partial data of hard evidence; it was still only appealing to my intuition.
one reason your argument was so compelling was because it specifically addressed my "but what about..?" objections (ie "but what about flexibility or other advantages as a better deal than consistency?"). maybe some people still arguing feel their own "but what about..?" objections aren't being addressed? it's one thing to say "look, the correct answer probably is 40 card decks and here are the reasons" but unless the objections are addressed, the natural response might be "yeah, you can be right, but i still can't help but wonder...".
Goblins have poor impulse control. Don't click this link!!
some of my favourite flavour text:
Wayward Soul
"no home no heart no hope"
—Stronghold graffito
Raging Goblin
He raged at the world, at his family, at his life. But mostly he just raged.
For me personally, the only reason to play a 41 card deck is when I want to have a 17.5 card land base (so 18 land in a 41 card deck).
Since I'm not nearly good enough at magic to know when I want to have precisely 17.5 cards, I mentally shortcut that to 'only play 40 cards'. Saves on time and mental energy.
To the people who basically don't want to be forced to decide between the 23rd and 24th card in their decklist, imagine that your game is going to take 8 turns on average, withou card drawing. That means you will draw exactly 15 cards from your deck. Let's assume that you have one bomb in your deck. By running a 41 card deck you are reducing your odds of drawing your bomb in any given game from 15/40 to 15/41. So in roughly 1% of your games you would have drawn your bomb, but you don't because of your suboptimal deckbuilding decision. In any given FNM you might play 9 games. So you'll never see that tiny mistake writ large in your life. But it is still the (wrong) decision to accept a worse result in your deck.
By refusing to choose between the worst cards in your deck you are giving yourself options on both of them, but those options come at the expense of all of the other (better) cards in your deck. The latter outweighs the former.
Does the above make any sort of sense to you?
In addition, the larger the deck size is the greater the variance is. Imagine that you have a 40 card 16 land aggro deck. If you had the ability to copy each card 10 times (so you have 160 lands in a 400 card deck) that deck would be far worse because of the greater variance of the deck composition: You are more likely to run into a sequence of 7 straight lands in the 400 card deck than in the 40 card deck.
This is a fair point. I've been through enough of these arguments though to know that someone who is still arguing with a widely established established theory when the post count gets above 50 is not going to change their mind no matter how many of their intuitive objections are addressed. They are convinced of X, it is literally impossible to prove Y, therefore they will continue to believe X. By this point in the discussion they've likely already blown by several valid counterpoints and responded "Yea but that's still not proof" and the thing just goes in circles. I think we've already hit the key mile markers in this sort of debate:
"But a theory isn't proof!"
"Just because Pros do something doesn't make it right"
Convoluted nonsensical math
People exiting the conversation with a frustrated "Fine, I hope I play against you and your bad decisions"
I don't know why people come here to debate things when they have no interest in listening to the established wisdom or recognizing challenges to their beliefs that are anything less than "proof." It reminds me of another LSV saying...the only thing Magic players like more than winning is being right.
I guess I'll stop trying to share some of my wisdom collected over 20 years playing this game (cue the counterargument "Experience doesn't mean you're right!") because I don't have "proof." To anyone who refuses to embrace the argument that failing to draw your best cards outweighs the mana consistency, you are free to be willfully ignorant. The counterargument has been clearly laid out for you. We can't make you believe it.
my read of what people are saying here (though i might be emphasizing only certain posts and forgetting the others) i that yes, it's probably correct to only play 40 cards unless MAYBE you have a super-flat power level and no bombs, but that we still don't have anything close to a proof.
and the "but it's not a proof" is a reaction to posts like Puddle Jumper's below:
although i'm glad to have read Puddle's arguments, i still don't agree with their assertion that playing 41 cards is "unambiguously suboptimal", or that it is "factually, provably false". i've heard very good arguments, but nothing strong enough that i'd call it unambiguous or factual and provable.
magicmerl a few posts up gave a good summary of their understanding:
but i still see this argument as appealing to intuition, much like your own argument that convinced me. merl says that "The latter outweighs the former", which is an assertion i agree with, but my understanding is that it still appeals to my intuition, not to anything close to being unambiguous or provable; intuition says that the benefits from keeping both worst cards are comparatively smaller than drawing yoru best card -- but this isn't proven. maybe intuition is incorrect here. (not that i believe this is likely the case, but it's not been proven).
to be clear, you /have/ convinced me, Phyrre. i /have/ changed my mind.
the only thing i'm "holding onto" and wanting to be shown wrong about, is the assertion that this (probably correct) conclusion is so "factually, provably correct". (and if it has been proved, i missed it, and any gentle redirection of my attention would be appreciated!)
Goblins have poor impulse control. Don't click this link!!
some of my favourite flavour text:
Wayward Soul
"no home no heart no hope"
—Stronghold graffito
Raging Goblin
He raged at the world, at his family, at his life. But mostly he just raged.
I guess what I'm saying is that lack of proof is not the problem here. Lack of understanding is the problem. I don't have the tools to express the facts in a way that both accurately expresses the facts and that you can understand. I can simplify the problem down to the obvious roots but then you won't believe it because it's "too simple". I can say things like "it's a proven fact" but you aren't believing me. I can cite Magic experts but you aren't believing them either. I'm not sure why. Science has had this same basic problem for centuries. Scientists make discoveries but can't "prove" them to people without educating them further than they want to be educated, so laymen don't believe it's really proof. And then scientists spend the next century developing the necessary tools to convince the masses, while they could be out doing useful things like not proving the earth isn't the center of the universe.
Exactly, this is why the experiment is a good example of why 41 cards is bad. In the very situation where you would expect 41 cards could possibly give you an advantage (where all the cards in your deck are of equal quality) it in fact does not give you an advantage but instead puts you at a disadvantage.
this part of what you wrote is standing out to me.
it is kind of like a summary of some of what's been happening.
i'm struggling to know what to say that could be constructive right now. i've thought to try to "argue" more about the topic at hand, but i know that i'm not very good at that, and besides i've always been wary of conflict and tension.
i think i feel a little guilty right now, because it's a thread that /i/ started that seems to have turned into conflict and tension. (i do like disagreement, and i do like discussion, but i get nervous when i feel that tension is high and that people are no longer able to "catch" what each other is saying).
about the topic at hand,
- i see that Phyrre and magicmerl's arguments have convinced me that it's probably always correct to play 40 card decks, unless your power level of every card is VERY flat. but i feel convinced still in ways i feel are "weak" or only intuition based.
- a "stronger" argument would be something like the computer analysis in Frank's article... except i feel like it's flawed becuase it is over-simplified! (am i correct in my feeling Frank's argument is flawed? is this something that is productive to try to discuss? i honestly am not sure).
so, if you're willing (or patient enough!), i would love a more rigorous, "stronger" demonstration of why 40 card decks are unequivocally better. i ask this not to "win" an argument with you, but out of curiousity. it might still be the case that i'm not convinced, but you make a good point that i might not ever be convinced because i cannot understand the higher math involved in the non-simplified proof.
in terms of my emotions,
- i don't want to concede that i'm convinced in "strong" ways, because i'm not!
- maybe what you're saying is true: that i don't have the mathematical capacity to understand the "strong" ways
- but i still love peering "under the hood" and seeing how things work. which is why i wish i could be as convinced that there is more "strong" proof, as you are convinced. maybe this is why i dont' want to let go: i am jealous that you are able to understand this "strong" proof and i am not, and it wish for it to be explained to me!
----------------------------------
about this thread,
- i feel it's gotten to a point where people (myself included) have trouble listening to what the other person is saying. it's easy to take a portion of what someone said that has to do with "your own agenda" and ignore the main thing that they were /trying/ to say.
- my last post, for example, my own agenda is "but nothing has been proven!". that's as much as i could cognitively keep in my attention. so, i quoted you in my response to Phyrre to make my-own-agenda point, but i still am unsure if i actually heard what you were trying to say.
- it's easy for me to see how mu1000's point got lost in posts #63 to #66, for example, (but only because mu1000 has the same agenda i have).
my unease about the tension in this thread makes me suspect that
people aren't hearing what other people are trying to say. mu1000 and myself want it to be heard that we still don't see a proof. and my impression is that you (ie PuddleJumper) are convinced that it's certain that 40 card decks correct and are annoyed when people say it doesn't matter. and Phyrre is annoyed that we're still arguing about this because it's clear what the correct conclusion is. and throughout this all, i wonder if the tension makes us all feel that we have to "win" an argument against the other person, when in reality i felt inspired by Phyrre's ideas and i appreciate the way you very often give your ideas in my threads!
(be assured that when merl argues with you that XYZ doesn't constitute a proof (post #65) or when i keep pushing "no proof has been given!" to Phyrre, it's not to "win" against you two or to prove you two wrong or to dismiss you or to disagree for the sake of disagreeing. it's genuinely because i want to understand your stronger proof if one exists!)
forum discussion is hard to do constructively, it seems. i have seen threads devolve on mtgs before -- many times!
i don't even think anyone here is a jerk or is wrong. i suspect that it's just difficult to sort out the different points or agendas, and that crosstalk happens a lot.
Goblins have poor impulse control. Don't click this link!!
some of my favourite flavour text:
Wayward Soul
"no home no heart no hope"
—Stronghold graffito
Raging Goblin
He raged at the world, at his family, at his life. But mostly he just raged.
i'll agree that the experiment shows that if all your cards are of equal value in terms of being vanilla creatures, 41 card decks don't offer an advantage.
but do you agree that the experiment doesn't prove that 41 card decks never gives you an advantage?
i still have the feeling that maybe:
- not cutting the 23rd and 24th card gives benefits (better curve, higher ratio of Humans for your Human-matters cards, anti-flier protection)
- that maybe outweigh drawing each of your best cards a turn later.
Phyrre's argument (your best four cards are THAT important that you want to draw them earlier) intuitively convinces me, but it doesn't strike me as a proof. (maybe not losing to fliers is SO important that it offsets not drawing your bombs. intuitively it doesn't sound correct but no proof has been given, and proofs are useful because they have the power to unequivocally show that strong intuition can be incorrect).
and it's this that i still feel Frank's experiment doesn't address. do you agree/disagree?
okay, so what i just wrote (now hidden by spoiler tags) doesn't make sense when i realize that i'm still talking about drawing your best cards, given that the experiment took that factor out the equation.
why do i still feel that the experiment is flawed?
it has something to do with "mana ratio is shown to not ever be better in a 41-card deck for a flat power level consisting only of vanilla creatures", but could the mana ratio be shown to be better for flat-ish power levels consisting of an actual curve of mana costs?
and, what about factors other than mana ratio, such as factors in my initial argument? ("not cutting the 23rd and 24th cards might give benefits such as a better curve, better synergy, or anti-flier protection"?)
Goblins have poor impulse control. Don't click this link!!
some of my favourite flavour text:
Wayward Soul
"no home no heart no hope"
—Stronghold graffito
Raging Goblin
He raged at the world, at his family, at his life. But mostly he just raged.
I wouldn't consider it flawed so much as just a singular example (but yet one that makes a compelling argument imo). What additional tests would need to be done to convince you? A deck that has X lands, Y 2/2s for 2 and Z 3/3s for 3 vs a deck that has X+1 lands for mana ratio reasons? Or more complex than that? I don't claim to be good at running statistical analyses but maybe someone else would be. If anyone actually has done more in-depth tests than Frank's I would be interested in seeing the results anyways but I feel they will only corroborate with Frank's simple example.
As far as the other factors you mention, I think they have been considered but overall the side effect of drawing your best cards less frequently outweighs any advantage of extra synergy or having more specific answers available in your deck. Also these additional synergies are hurt by having a larger deck now anyways as you are statistically less likely to draw the cards together than if you just cut a non-synergistic card for whatever 24th card you wanted for that purpose. There's certainly something of an argument to be made for sacrificing power for the sake of synergy, but sacrificing power and consistency for the sake of synergy is just not worth it to me.
I'm also the type of person who defends the truth, sometimes to a fault. I despise the spread of misinformation. It bothers me on a visceral level. For example, nothing will get me more worked up than the ongoing anti-vaccine debate. It's not even comparable to discussions we have here because in that debate, misinformation results in actual preventable deaths. But at the core it's a similar issue.
This forum is a place to teach and learn. But it's also a public forum meaning it's vulnerable to the spread of misinformation. It's never intentional, but misinformation is spread here constantly. We don't have any sort of system to sort out who's a good teacher, who typically has good advice vs. who just joined yesterday and has never even drafted but is presenting their opinions as facts because they *feel* that they must be right.
My goal is to join these discussions and make it clear what I believe while also pointing out the arguments I feel are unfounded and may lead a new player astray. That way when a novice is faced with the challenge of believing conflicting ideas X and Y, he's at least seen both sides of the argument from me.
While it is technically true in a semantic way that no one can prove 40 card decks are superior, I strongly believe it to be the underlying truth. All available evidence such-as-it-is also seems to support the idea. The only arguments against are pure theorycraft, in the same way that we have piles of clinical trial data showing that vaccines are safe and effective for the population but there's a small group that believes otherwise based entirely on theory. ("I don't trust this chemical"...even though it's been demonstrated to be safe.)
Intuition is a dangerous tool. Sometimes intuition helps us catch things that are disguised as truths. But unfortunately intuition is just looking for patterns and sometimes it finds a perfectly true axiom and tells your mind...ehh I'm not sure about this one, let's be real cautious. And the most annoying thing about intuition is that in an effort to protect us from being deceived by other people, it tells us...don't just be wary of this claim, also be wary of anyone supporting it because they might be trying to trick us. ("These vaccines are unsafe AND the doctors know it and it's all a conspiracy!")
It's why it took centuries for people to accept that the world is round -- there's nothing intuitive about it. Think about that for a moment. The world is and has been round for the history of humankind, and our sense of intuition can't remotely process that. It's a flawed tool. By working together we can try to parse out the true signals from the noise but someone who relies heavily on intuition is just going to gum up the process.
I think we can all admit that on an intuitive level, it really seems like 41 cards should be OK. It's such a small thing. It's a decision made with good intentions. But it might still be very wrong in the same sense that a person thinking the world is flat is very wrong regardless of their intentions. And generally it takes decades or centuries to make the transition from widely accepted theory to provable truth because we don't always have the technology to do so.
I know this is way off the rails but I think it's a good discussion because any difficult question about the game eventually wanders into this territory.
I wanted to do that just to point out that because something is widely accepted does not automatically mean it is correct. And I believe the "play the minimum deck size" is a theory that has been accepted and assumed to be correct since the beginning of limited.
Please note I'm NOT saying that it ISN'T correct. Obviously many, if not most times something is widely accepted and assumed it does, in fact, turn out to be correct. Just not always. And, as I've said multiple times now, if the entirety of the argument comes down to "it means you draw your best cards more," then, that rationale seems ripe for finding exceptions - if anyone was inclined to go looking for them. Which no one really appears to be, since the default has been assumed correct, basically, forever.
That's all I'm saying. Well, that and it's not that big a deal in the overall scheme of things.