Sixty First Card Discussion

[onelovemachine]

Here's the link to the Vintage forums. 

http://www.themanadrain.com/forums/index.php?topic=23117.0

The first thing that needs to be noted about the odds of a sixty first card is this, if you want to draw that one-of in a sixty card deck, your odds of doing so are .01666....
in your 61 card deck it is .01639 so realistically we are talking about two thousandths of a difference in odds that are created by that additional card.  Now of course that difference will play a factor over a very long period of time, but over a tournament?  Maybe.  Maybe that will cause your opponent to rip recall off the top before you when your in topdeck mode in game three of the finals at Richmond this weekend, maybe it won't.  In fact, odds are it won't affect the game enough to make a difference either way.  With the vastly powerful draw engines at the disposal of the modern control decks, we don't really need to worry about not drawing into that one card. 

I am a long time supporter of playing 60 cards especially in combo where your options are more draw dependent since you plan on either winning or losing in the first few turns of the game.  I am dead sure storm based combo would be ridiculous if 40 cards were the lower limit.  But in control?  I am on the fence.  I friend of mine plays 61 cards in every deck he bulds.  Why?  I am not sure.  Supersticion really.  But when disecting his deck I am always amazed at the fact that he has so much in his build I could never fit into mine.  I constantly ask, "how did you fit this, what did you cut?"  Forgetting that he doesn't need to cut anything. 

The ability of gifts belcher, goth slaver, and even psychatog to draw cards is ridiculous.  Each has the ability to see at least half of the cards in deck throughout the course of a game.  So the question becomes:  I really want this one card so what of the creamy goodness in my deck can be cut?  The fourth brainstorm?  (I chuckle to myself, ahhh.... european decks.)  Cut a mana source?  A win condition maybe?  Why don't we assume that your deck is full of good cards and it has no room.  There isn't a single subpar card in there.  So now what?  Maybe that extra invisible slot should be filled.  At the end of the day, my decks still have sixty cards, but I won't bash anyone with one more. 

With sideboards, we have limited space to work with; therefore, that one card error in your build can absolutely kill you later on in a tournament.  With a maindeck there is some flexibility and as the numbers show, one extra card can't possibly kill you.  Vintage is all about the correct build and with that in mind, maybe those decks with 61 in them are really just blind to the fact that there are subpar cards in the build.  What are your thoughts?

Whining deleted. The exam is open to everyone, just post in the thread to get a copy.
-Jacob

[PacmanXSA]

Joshy: I'm glad your whining was deleted...  I'm continously sick of your bad attitude  :lol:

Anyways, on a more serious note, there really isn't any reason to run the 61st card.  Even if the percentages are low, they are still percentages against you drawing the bombs that your deck uses in order to win.  Plain and simple.  Proper deck building enlists all of the creators thoughts and abilities to eliminate, as best as possible,  any negative aspects of the deck in question; running that 61st card would be one of those negative aspects.

Pac

[jcb193]

I disagree on this issue.  To say that "tightening your deck" to 60 is a law, i think is misrepresenting deck construction.  Not every change in a deck is a substitutive change.

Example:

Removing a 4th shock from a straight burn deck to get down to 60 cards can sometimes make sense.

Removing a vampiric tutor to make way for a duress is not.  These are not subsitutive cards.  You are changing the deck proportions (ie the balance of draw, acceleration, kill, countermagic, etc). 

The statistical difference between 60 and 61 is less relevent than the statistical difference in messing up your deck proportions.  You can't always sit there and compare two cards that serve completely different functions and by default decide to drop one of them. 

Not to mention, some people like the mana balance of a 61 card deck better (which can be as much as .5% mana ratio change).

[dandan]

http://www.themanadrain.com/forums/index.php?topic=21567.0
(from the newbie forum)

I think we need to divide the reasons for going up to 61 (or more cards)

1. More cards because the deck requires more cards. Examples include decks that win by decking, use the number of cards in the library/deck as a resource, need a specific number of cards in the library at a certain time or some other reason due to new cards. I won't go into specific cases like Stasis and argue if it is optimal but so far everyone has agreed that it is at least possible that more than 60 cards could be optimal for such a deck.(think of the old Wheel of Fortune/Black Lotus deck)

2. Going to 61 cards to add a card that is worse or equal in power/utility/'whatever you want to call it' to cards already in your deck (if you don't like that statement, swap the 61st card for the card in your deck that you consider it is better than)
I think we can agree that if the added card is a singleton or merely an additional copy of a card (cards) already in your deck, it increases the chance of drawing it in your opening hand and indeed of drawing it at any time drawing the game. We can also agree that it decreases the chance of drawing all of the other cards in your deck, both in your opening hand and in the rest of the game. We also seem to agree that the increase in probability of drawing the added card is far higher than the decrease in probaility of drawing the other cards.

Given this we can say

1. In Vintage you are reducing the chance of drawing 'bombs', specifically restricted cards that everyone agrees are higher in power level than other cards (talking about restricted cards in good decks, not some of the crap still polluting the B&R list :lol: ). This is a bad thing.
2. The increased chance of drawing a card that is worse or equal to the worst card in your previous 60 card deck is not an advantage if we are considering purely probabilities and statistics.

Purely from a mathematical point of view, it is not a good idea.

However the point that has been made about the number of threats is a valid one. I would put it another way:
Increasing the number of options may be worth slightly decreasing the chance of having the chance to make that choice.
IF one of your 5 'threats' would win the game then a slightly lower chance of deploying that threat might be worth it rather than having 4 threats and the chance that none of the threats is optimal. I prefer to call them 'options' rather than threats as then we can include utility cards/mana etc.

The best example I can think of the highlight this point of view is a SotF deck that wants a utility creature to handle every opportunity but needs a set number of mana/utility cards to function. In this case the added card has a chance of being 'chosen' far higher than merely drawn and although a lower 'power' card than cards already in the deck, would be THE optimal card in some circumstances. Such a case leaves a pile of poo on statistical probabilities as the probability of drawing the additional card vs other cards is not that relevant and the idea of rating the 61st card in power relative to the other cards is also rather hard to judge.

I concede that such a possibility exists although I think that in 99% (and probably higher) of cases, the 61st card is not the right choice and is merely an example of failing to optimise your deck.

I'll call this 'handbagging' because I am sure many of you would appreciate that one of the fundamental differences between men and women is the ability to not carry around stuff that, although very useful some of the time, are not useful often enough to be worth carrying around all of the time. I once had a girlfriend that carried an iron (not the golfing type) in her handbag, although she did not carry around an electricity supply nor unironed clothes. Perhaps she really needed that iron, and perhaps you really need that 61st card.
(I am aware that an iron can be a savage weapon if used to beat off a mugger, just be aware that the sort of person who carries around an iron is the sort of person who also carries around enough other junk to make swinging the handbag a feat beyond most people, although I did see her accidently catch a few unfortunate guys in the groin as it swung by her side on the (presumably) titanium-reinforced shoulder strap)

As the man walking in the hills says "I think I am starting to ramble" so I'll shut up.

[Khahan]

Sure the chances of getting 1 specific card in your opening hand may be minimal. But in combo, when you are looking for multiple cards as early as possible, a 61st card does a lot more damage than most think:

60! (which is the permutation of 60 meaning the number of different orders the cards can be in) =
8.320987112741390144276341183 2234e+81

61! = 5.075802138772247988008568121 7663e+83

For a difference of:
1.982608315404440064116146708 3619e+87

That means if you have a 60 card deck and simply add 1 more card to it, you now have 1.982608315404440064116146708 3619e+87 more ways that deck can be arranged. Which means you have less chances that card A is in any given spot in that order.

(for those of you who are math retarded like I am...cause I had to ask somebody else what all that meant...  the e+87 means you move the decimal point 87 places to the right and that is your number.  As you can see, simply adding 1 card gives your deck:
1,982,608,315,404,440,064,116,146,708,361,900,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000

I don't even know what to call that number.  And while I've done the math myself on a calculator, I've had people who are far smarter at math than me confirm what I was doing. So it should be pretty accurate, give or take a few.

[Geet]

...
For a difference of:
1.982608315404440064116146708 3619e+87

Need to check your math... difference between those 2 numbers is actually:
4.992592267644834086565804709 9338e+83

[Khahan]

Hmm, maybe I didn't put it in the calculator correctly.
Bit of a difference between those 2. But either way, its still a pretty significant jump in permutations.
Basic point: Most decks (especially in T1) have an ideal opening hand. You are not just looking for 1 particular card. You are looking for a combination of cards. Maybe you are looking for combo pieces, or lock pieces, or a specific mana base and spell (like mox sapphire, underground sea, mana drain).
By adding one card you've increased the # of different opening hands you can draw by more than I can count.  And, if that 1 card you added was not a card you want in your opening hand, then you've really hurt your chances.

[warble]

^
|
|
 

Okay math boys, here's the real importance of a 61st card.

Adding 1 card gives the card 62 places in the deck.  The probability of drawing the card is merely 1/61 for the first card, 1/60 for the second, so on and so forth.  So if you assume you'll draw 20 cards during a game your odds for drawing the card are 1/3.

For a card like a black lotus, the difference between a 1/3 chance and a 20/61 change is pretty significant, because you've changed by 20/3661 ~ 1/183.  For a deck that will draw a paltry 15 cards, you've modified your odds by what appears to be smaller, but in fact your total card pool is less so it will be roughly the same.  Meaning giving excessively large numbers with respect to probabilities should be frowned upon (from a comprehension standpoint).

So isolating our assumptions, we're dealing with a 20-card game and have altered the odds of drawing lotus by 1/183.  However, it's not just the lotus, it's every card.  Thus, we look at consistency as the 182/183 where you weren't going to draw the lotus anyway OR did draw the lotus as well as your new card.  We'll term our "altered state" to be the 1/183 where you exchange the lotus for the 61st card.  Thus, for each of our 60 initial cards, we are changing the state with a 1/183 chance that you have exchanged the 61st card for Black Lotus (for example).

Should we change our deck with a 1/183 chance (for the average 20-card game) for exchanging a random card in the deck with our 61st card?  Personally, I would prefer to have that additional 1/183 chance of drawing lotus or ancestral or walk or an additional mox.  Early in the game the odds are significantly lower, but still any chance of drawing a lotus being compromised for a card such as a 3rd Gifts Ungiven would be IMO a bad change.

The whole basis for the argument stems from the significant change that occurs in, say, a 20 card deck changing to a 21-card-deck.  The fact that it is relatively impossible to draw your entire deck in a normal match (without actually winning prior to this) lessens the effect that a 61st card has, but does not make it insignificant because a card game is still inherently based on luck (Lotus+Crypt+Tinker+Walk+Tolarian and every other broken hand not involving card #61 receives a small but still significant hit to it's probability of being drawn).

Am I running card #61?  No, because I believe my deck will be more broken with that small but significant difference in probabilities.  Does this cost me a conditional answer?  Yes.  Does this make me willing to put card #61 in?  Absolutely not.

When considering the Vintage Forum discussion on a 61st card, the argument that tweaking mana ratio's can lead to more consistent draws, I will argue to this point that any inherently luck-based game suffers from a lack of ambiguity in games, so adding consistency in one aspect while reducing brokenness in another aspect inherently weakens the deck.  I'd never sacrifice brokenness for consistency after tuning 60 cards considering how broken my deck is.  For control decks that are consistent and inherently very not-broken it's feasible that there is benefit.  I prefer combo control, however, and for that deck the brokenness is such that it's very much not to my benefit to cut the brokenness.

[Metman]

I really think this debate is dependent on how many Tutors or cards that fix your hands.  All this data is fine and dandy if the 60 and 61 card decks drew one card at a time.  We all know that doesn't happen though.  We also know that there isn't a deck out there, other than maybe mono green, that doesn't use Brainstorm or Tutors.  In the old school Keeper decks built with several silver bullets and loads of Tutors to get those the 61 first card is another bullet.  The math isn't the only argument in this debate in a deck with that doesn't always draw one card each turn. 

Just food for thought...would you play 59 cards if that was the minimum?  If you argue consistancy for playing 60 instead of 61 than I would assume you say yes; and if so would you play 58?  Where do you draw the line for how many the minimum you would play if you could play as few or as many as you could? 

[warble]

The answer is we'd all play decks between 15 and 30 cards large.  Of course there'd be the guy with the 11-card deck but that guy sucketh hard (stupid combo player!)
Less cards, however, would make the game decided before the match was played, which isn't the point of magic.  You have to weigh probabilities with 60 cards, with 15 all you'd have to do is pick the right 15 cards (and win the coin flip of course)

[apoc7k]

I strongly disagree with the choice of a sixty first card. I used to run a version of kobold-clamp that ran 61 cards... it ran decent, but really did get hammered by matchups that are about 50/50 80% of the time. Funny enough, once i dropped down to sixty cards, the 50/50 matchups were in my favor 60% of the time. Considering what khahan said, the insane number of card combinations you can draw, the extra card doesn't help enough to make it plausable (usually...).

That said, i've noticed something. This thread really turned into a hardcore statistic thread! I'm not saying that's bad by any means, but I personally think it's pretty funny.

Metman also has a good point however. The truth is that type 1 has a plethora of tutors and incredibly powerful draw engines that can go off without any forewarning. 61 cards would make a fairly suttle difference, especially with the tutors. You could easily setup your next draw to be whatever the 61st card is. At the same time, there will always be stupid control decks (stupid as in really annoying) that will have the Force of Will in hand waiting to (figuratively speaking) throw a stick in the spokes of your bike as you are riding on your way towards victory.

I guess in all actuallity, everything I just typed out was a waste of time for one very good reason. More than anything, this is a matter of preference. Some people will value another silver bullet, while others outweigh the bullet with the suttle change in consistency.

Anyways, those are my two cents... adios!

[onelovemachine]

The answer is we'd all play decks between 15 and 30 cards large.

I have never tested a deck with 30 cards in it, but I ask you this: how is that even feasible?  We need so many cards to make our decks work it is actually impossible to function with less than like 45 in type one.  Think about slaver.  You could cut out the brainstorms, some of the mana, maybe down to 3 welders and only 1 of the expensive artifacts, but overall I think your deck would suffer if it were any fewer cards than about 48.  I am not sure any of us would be running decks with so few cards.

I strongly disagree with the choice of a sixty first card. I used to run a version of kobold-clamp that ran 61 cards... 

This is really all your post needed to say.  Combo sucks with anything more than 60 cards.  We all want combo to be down in that 45 card region I talked about.  What about CONTROL DECKS.  [/i]  Control decks generally speaking want utility.  If Zherbus' most recent 3cc control list added one and only one card like a gifts ungiven, as an example, would it hurt the deck?  In my opinion the answer is no.  Gifts, or whatever other spell that effectively replaces itself, if anything helps you thin through your deck and fine the cards you want more so than it sacrifices anything.  Those two thousands of a percent I spoke of in my original post can't at all be playing a factor in an individual match.  Playskill will set in long before those odds do.  In my opinion it is possible to have a deck that is so tight that there are no less optimal cards to fit those slots, but at the same time the deck can be lacking one more card that would add versatility. 

  Just food for thought...would you play 59 cards if that was the minimum?  If you argue consistancy for playing 60 instead of 61 than I would assume you say yes; and if so would you play 58?  Where do you draw the line for how many the minimum you would play if you could play as few or as many as you could?

I have been thinking about this, and the answer is, I don't know.  What do you cut from your gifts ungiven list to make it 59 cards?  The first thought that comes to mind is brainstorm.  Brainstorm is in almost every combo deck whether it be drain or ritual based because it allows you to see more cards.  So cut the card that effectively thins your deck right?  Somehow I don't think so.  Brainstorm happens to be an incredibly powerful effect.  Draw 3 is all you need to know.  So if not brainstorm then maybe a mana source?  Great, and get screwed because those two thousandths of a percent weren't good enough to help you hit into the land you still had left in your deck....

Increasing the number of options may be worth slightly decreasing the chance of having the chance to make that choice   

I think this is the most elegant way to put everything I have been trying to say.  Again guys were are talking about control here not combo.  And while maybe a deck like gifts abso-fucking-lutely cannot afford to have a 61st card based on its combo nature we have to assume that not every deck will play out like this one.  What about fish?  Fish runs a LOT of unrestricted cards.  So why limit yourself to 3 null rods instead of four?  Will it really make a difference in that deck whether or not your chances of drawing your one recall decrease by two thousandths of a percent? 

I find myself building mana drain combo-control decks that are so tight that I have already removed things I chose to consider as chaff, like mystical tutor, and yet still desire to have at least one more card in the deck.  Maybe I build terrible decks, but honestly I think that apart from a deck where very specific cards need to be employed in order to win, that extra card could be worth it in some situations.

[forests failed you]

Franklin, do you have any idea how insane a thirty card Oath deck would be.  Oh, god.

[Machinus]

Just food for thought...would you play 59 cards if that was the minimum?  If you argue consistancy for playing 60 instead of 61 than I would assume you say yes; and if so would you play 58?  Where do you draw the line for how many the minimum you would play if you could play as few or as many as you could? 

This is an abysmal argument. Go look up "doomsday" and figure out what it does.

[Imsomniac101]

The answer is we'd all play decks between 15 and 30 cards large.

I have never tested a deck with 30 cards in it, but I ask you this: how is that even feasible?  We need so many cards to make our decks work it is actually impossible to function with less than like 45 in type one.  Think about slaver.  You could cut out the brainstorms, some of the mana, maybe down to 3 welders and only 1 of the expensive artifacts, but overall I think your deck would suffer if it were any fewer cards than about 48.  I am not sure any of us would be running decks with so few cards.

I strongly disagree with the choice of a sixty first card. I used to run a version of kobold-clamp that ran 61 cards... 

This is really all your post needed to say.  Combo sucks with anything more than 60 cards.  We all want combo to be down in that 45 card region I talked about.  What about CONTROL DECKS.  [/i]  Control decks generally speaking want utility.  If Zherbus' most recent 3cc control list added one and only one card like a gifts ungiven, as an example, would it hurt the deck?  In my opinion the answer is no.  Gifts, or whatever other spell that effectively replaces itself, if anything helps you thin through your deck and fine the cards you want more so than it sacrifices anything.  Those two thousands of a percent I spoke of in my original post can't at all be playing a factor in an individual match.  Playskill will set in long before those odds do.  In my opinion it is possible to have a deck that is so tight that there are no less optimal cards to fit those slots, but at the same time the deck can be lacking one more card that would add versatility. 

  Just food for thought...would you play 59 cards if that was the minimum?  If you argue consistancy for playing 60 instead of 61 than I would assume you say yes; and if so would you play 58?  Where do you draw the line for how many the minimum you would play if you could play as few or as many as you could?

I have been thinking about this, and the answer is, I don't know.  What do you cut from your gifts ungiven list to make it 59 cards?  The first thought that comes to mind is brainstorm.  Brainstorm is in almost every combo deck whether it be drain or ritual based because it allows you to see more cards.  So cut the card that effectively thins your deck right?  Somehow I don't think so.  Brainstorm happens to be an incredibly powerful effect.  Draw 3 is all you need to know.  So if not brainstorm then maybe a mana source?  Great, and get screwed because those two thousandths of a percent weren't good enough to help you hit into the land you still had left in your deck....

Increasing the number of options may be worth slightly decreasing the chance of having the chance to make that choice   

I think this is the most elegant way to put everything I have been trying to say.  Again guys were are talking about control here not combo.

You guys are missing the big picture. If the absolute minimum number of cards for a deck were 30 that would mean that draw spells like brainstorm and ancestral recall's power level will increase drastically. That would mean combo decks can win 1st turn consistently; that in turn will have a drastic effect in the way control decks are built; and so on and so forth.

[onelovemachine]

do you have any idea how insane a thirty card Oath deck would be. 

Ok. So here's what we have gone over and over: Combo gets really f-ing good when we remove all the stuff it doesnt need and cut it down to thirty cards.  Good job at restating the obvious Demars. 

How do you play gifts belcher at thirty cards?  Honestly, if someone worked on it long enough it might work.  But the average deck can't cut down to just 55.... it would probably rather have those other cards in there than do that.

[brianb]

In a 55-card format, "average" decks that couldn't be cut five cards would soon find themselves bettered by decks that could.    You really want to play the minimum for all the obvious reasons people have stated.  We've already mentioned two semi-legitimate reasons to break the rule:

1)  Deck strategy necessitates a few (or many) extra cards--stasis, thoughtlash, battle of wits.  The enormous drawback of playing extra cards in type one pretty much sinks these strategies in any case.

2)  Fine-tuning mana ratios.  I've never done this myself, but some people swear that they've determined that 23/60 is too few and 24/60 is too much, but 24/61 is just right for a certain deck's mana curve.  I'm skeptical that the amount of playtesting you can accomplish in this lifetime could determine a correct ratio so precisely to want to play an extra card, but theoretically, you could.

One other good reason is decks that play intuition.  Intuition encourages you to play at least 3 of some cards.  Sometimes this can make it suboptimal to cut to 60.  Not usually (hardly ever really), but sometimes.

Just having a lot of tutors (or survival) does not justify playing a utility card as the 61st card.  I think everybody understands the acid test a card has to pass to be considered as a 61st card in this scenario:

Will having this card in the deck provide me enough utility to overcome the times when I draw it instead of the key cards and broken cards that make the deck work?

Now you may well answer yes in the case of a certain utility card they want to add.  But what most people don't always remember is that in a 61-card deck, every single card has to pass the acid test.  Every card has to be evaluated: am I willing to play this as a 61st card?  I haven't seen a case where I felt they all could.

[forests failed you]

Any deck in Vintage gets better and better as the maximum number of cards required in the deck goes down.  The reason for this is obviously that you increase your chances of drawing your restricted bombs.  Even a deck like Belcher would be significantly more busted at thirty cards.  The reason for this is that you could simply cut all of the four ofs in any given deck down to two ofs, and run half as many land, and statistically have the exact same percentage of drawing those cards when you needed them.  (since the deck is now twice as small).  Force of Will, Mana Drain, Brainstorm, Gifts, land et cetera are still in your hand the same percentage of the time they would normally be;  however the only difference is that Ancestral Recall, Moxes, Lotus, and Will are in your hand twice as much as they would normally be.  However, this really is a stupid thing to be talking about since it is a moot point, we play with sixty card decks.

However, it does reinforce the point, at least in my mind, that in Vintage there is NO reason why one should ever play with a deck that has more than Sixty cards exactly; and, if they ever lowered the minimun deck size that a player should never play with more than that number.  (Barring extreme examples, Battle of Wits, Stasis, et cetera)/   Vintage is different from every other format in Magic because of the power level of certain cards, especially with regards to Mana acceleration.  From my experience, which is extensive, Black Lotus is a fundamentally stupid card.  When I have Black Lotus and an even Mediocre hand and am on the play with any decent deck in the format, I do not lose.  With that kind of advantage in Mana so early on in the game most good players can usually out-play almost any opponent.  Statistically lowering the chance of drawing broken cards, even lowering it only by a little bit, is bad policy in my mind.  If one is truly worried about needing extra slots to deal with specific cards, there is always something that can be cut to make room.  This is what good metagaming is about, deciding what one will need most in a specific tournament.  Not to mention that every control deck in Vintage has at least eight maindeck answers to every non-land threat, 4 Mana Drain, and 4 Force of Will.  Most of the time if one manages his or her resources correctly, plays smart, and does his or her job and thinks things all the way through, that person will have counterspells when he or she needs them.  Yes, broken things happen and sometimes people have turn one Tinker for Colossus with Force of  Will backup (I'm talking about you Mr. Perry!).  However, even in a situation, assuming that there is a 61st card in your deck which is Echoing Truth, the chances of drawing it before being dead are very small.  I'd rather improve my chances of drawing as many bombs as possible over the course of a seven or eight round Swiss style tournament, than lessen my chances in order to play with answers to highly situational gamestates in my maindeck.  In my opinion, that is what Cunning Wish is for.

Lastly, I could build a fifty card version of any Vintage archetype that would have a considerably higher win percentage than its sixty card counterpart.  Even Gifts, and especially gifts.

[dandan]

I'm sorry but I think this thread has been all about people missing the point.

Nobody has argued that adding a card does anything other than reduce the chance of drawing any of the 60 cards in the rest of your deck. Nobody. EVER. I don't think anyone is missing this point and I don't think any serious player cares about the actual probablilities. It lowers the chance of finding the good stuff in your deck and the change is significant. I would appreciate it if we could take this as a universally accepted fact from this point on.

There have been 3 main reasons for adding a 61st card (or more) so far.
1. The deck concept - see the old unrestricted Wheel/Lotus deck. 60 cards is not an option in such a deck. Stasis decks could also lay claim to using the 61st card as a resource. I have seen Dragon players claim that a 61st card allowed Lim-Dul's Vault use to find a particular combination.
In these examples the deck wants to have more than 60 cards in order to have more than 60 cards (or not have mulriples of 3/4/5 cards etc). I also mentioned that cards like Arcslogger use cards as a resource a again care about the number of cards in your deck (having 50 is better than 49 if you opponent is on 10 life). I don't personally think such a deck currently exists in competitive Vintage but I don't really see how anyone can argue against such a deck requiring 61 or more cards.
2. Card balance (mana ratio, threat density)
Some people have suggested using 61 cards for this reason. I can understand that it is possible to get a more exact mana ratio if you are willing to add a land to a 60 card deck, ditto for threats, etc. I am not at all convinced that such a move is ever justified as improving your chance to Ancestral/Brainstorm/tutor/win also have a positive effect on you having the correct mana necessary to win. I concede that in strict ratio terms, adding a card can lead your deck to have the exact mana ratio you desire although I am fairly sure that the difference in ratios is never a large enough advantage to overcome the disadvantage of reducing the chance of drawing the original 60 cards.
3. Some people have suggested that the 61st card is an additional option. Imagine a SotF deck with 5 utility slots - you could get a creature that destroys a creature, an artifact, an enchantment, a land, causes a discard or disrupts the graveyard. That's 6 choices. What if your metagame had 6 decks each one disruptable by one of the above methods. The 6th choice coupled with the tutoring power to find it, might be more worthwhile than running 60 cards and folding to 1/6 decks out there but being slightly better against the rest. Again, I don't think we are talking about any actual current Vintage decks but I can see how this is theoretically possible. (note that the ratio 5/60 or 6/60 isn't the issue, it is the number 5 or 6, this is slightly different to 2 and a completely different application)

I don't think an argument can be made against the theoretical existance of decks that use 61 or more cards for reasons 1 or 6. I'm not convinced by argument 2.

Having said all that I'm sure 99% of decks I see with more than 60 cards should have 60 cards.

[warble]

Nobody has argued that adding a card does anything other than reduce the chance of drawing any of the 60 cards in the rest of your deck. Nobody. EVER. I don't think anyone is missing this point and I don't think any serious player cares about the actual probablilities. It lowers the chance of finding the good stuff in your deck and the change is significant. I would appreciate it if we could take this as a universally accepted fact from this point on.

Really?  I thought I did.  Let me elaborate.

We don't call our decks "random bags filled with good stuff" like you.  Instead, we call them ordered sets that we choose from in a random SEARCH pattern.  Certain cards alter the search pattern, and certain search paths lead to other searches.  A search is complete when the search pattern you have followed and the opposition's search pattern result in a game-winning, game-losing, or game-drawing state.

Knowing that you have to follow a search pattern to get your cards, there is a subset (a large subset in blue's case) from each color that allows you to alter the search pattern, proceed multiple steps down the search, and even with future sight+top or bazaar+dragon, complete the search pattern immediately.  Knowing we have a random search, the subset of cards that alter the search and the subset that alter the game state deserve certain proportions(from France we saw how drastically Bazaar alters the game state).  There are also constraints for cards that drastically alter either the search (ancestral) or the game state (black lotus) in that we can only include one of those cards in our search.

We all realize that there must be a balance between card draw and mana production, and also concede that game-winning cards deserve an appropriate proportion.  For decks like aggro, the game-winning state is usually the result of a threshold of game-winning cards, or your search being suitably tuned such that the opposing search cannot reach it's end before your search finishes (usually 20 damage).  For decks like storm combo, the game-winning state is the result of a threshold of steps taken at once, and the appropriate number of tutors in the deck guarantee that the game-winning step is taken after the threshold of steps.

To now proceed back to everyday terms, putting 4 brainstorms + ancestral + 4 fetchlands in the deck allow for a faster progression through your search.  Putting Black Lotus + 5 Mox + Mana Crypt in your deck allow for a faster progression through the game state.  The issue is that with 60 cards, we cannot only have a search and game-state-acceleration, we have a "control" element with counterspells, "game-altering" states such as bazaar and worldgorger, and aggression against opposing game-state acceleration and game-winning conditions such as null rod.  Now that we have progressed past the "combo-only" view of our game, it becomes extremely difficult to find the proper cards for our deck.  We can no longer just win or lose, we must search through the deck in many cases extremely inefficiently (brainstorm, pop fetch, ancestral into 3 lands for example).  To reduce this inefficiency, we seek repeatability in our search (tutors) but again we must proportion this correctly or we will have all tutors and not enough winning combinations.  Now we have 4 elements to balance, and this is not even considering counterspells.

So here we are, balancing all of these elements in our decks, and the argument is made that a longer, more random search will lead to a faster or more reliable progression to the game's end.  From a game balancing standpoint, the proportions can become "more optimal" but the search length will likely become longer.  This means that a longer, more random but also more repeatable(if only tuning is involved) search is being chosen over a shorter search.  Since we are playing a card game where certain search paths are more preferable then others we prefer the shorter search paths because the decrease in randomization leads to more brokenness.

In other words, card #61 better be a game-winning card or things are bad for your tuning.  Also, cards 1-60 need to

a)have the proper proportions that would be un-altered from a 60 to 61 card deck.
b)be at least 0.5 card-probabilities short of win conditions and
c)be sufficiently "too slow at winning" to justify not playing the 61st card.

The point about the decklists from France is that a) was extremely questionable.  My point is that I don't have a lifetime to make a simulation engine that will optimize a) through c), so sticking to 60 cards is the safe bet(an easier optimization because the conditions are dropped).

For the record, my personal 61st card is vampiric tutor.  I play with 60.

[Brutha]

Over a game in which you see maybe 30 cards. Your chances to see specific card are ~ 1/31 more worse than in an 60 card deck.
If you want to see 5 cards at much as possible(Recall/Timewalk/Black Lotus/Yawamoth Win/Your Silverbullet Xy), and play 7 rounds in a tourment you will see 5*7*1/31= ~1 important card less than a player how plays a 60 card deck.

It is irrelevant to look at a per draw chance to draw a specific card, you have to see the hole picture over a larger time.

[Lunar]

This is one of the most mind numbing threads ive ever encountered.

Math = bad - reallybad to the 10th power / 2i squared

okay so maybe not quite that bad...

Try being a little more focused and build a list with 60 cards....over time any statistical negative against you will hurt you...this could mean losing 1 game out of a 10 round tourney, but what if that happens to be game 3 in a final??? 

It would be like knowing that when flipping a coin it was actually 51:49 in favor of heads, yet you decide to always call tails. (these are the people you love to play against in Vegas)

[xrobx]

Obviously, the subtle differences in the 61st card and 60th card have very little signifigance, mathematically.  We've covered this.

I think a more on topic question, if we were talking about combo and not control, would be how many cards are we allowed to use?  That is to say, that if we were "allowed" to use say 2 vampirics, or 2 imperial seals, would we?  I would have to say that if this were the case in some of my combo decks, I'd simply cut out the suboptimal cards, and replace them with the more broken cards.  Until there is a day where you can't afford NOT to run that extra 1 card in the 60 card deck, it really doesn't make any sense to run the card.

For example, say the optimum mana sources for a given combo deck were 30 (just a number, not suggesting the accuracy of these numbers whatsoever).  The win condition must also have a spot, or two***.  The number of tutors must also be at a maximum, to the best efficiency of the deck.  Obviously, you'd not play a tutor that costs 4 mana, but would very likely play ANY tutor that effectively wins you the game that costs 3 or less mana.  The ***s above would then be the difference, between that 60-61 card deck.  Say that you ran 1 win condition, and that equaled out to 60 cards.  If you could possibly squeeze in an extra card, would you put a win condition, or an EXTRA tutor?  The tutor WOULD have drastic changes in the way the deck plays out, because essentially you're drawing whatever you want, when you draw the extra card.

Hence, in a deck that is already ridiculously solid as a build, and is very efficient, if the possibility of adding a 61st card (say, due to the unrestriction of a tutor....made in portal maybe... ) seemed feasible, I would have no problem trying it out.  However, in todays metagame I think it's pretty hard to say that there isn't a way to make the cards you want fit in the deck, or there is usually no need for that extra 1 card.

[Metman]

Just food for thought...would you play 59 cards if that was the minimum?  If you argue consistency for playing 60 instead of 61 than I would assume you say yes; and if so would you play 58?  Where do you draw the line for how many the minimum you would play if you could play as few or as many as you could? 

This is an abysmal argument. Go look up "doomsday" and figure out what it does.

What part of that made you think it was an argument?  I thought it was clear by stating that it was "Just food for thought."

I really don't think statistics can be used as an argument as to why not play a 61st card.  What if I think 26 mana sources is too much and 25 is too little.  Statistically I could show you how often a mana source in a deck with 60 cards and 26 mana sources comes up.  Maybe that's too often.  How about a 60 card deck with 25 sources...oh that doesn't look like enough.  Wouldn't a 61 card deck with 26 sources be a compromise I'm looking for?

Again, I really think that there are too many search, draw, mana fix, and hand fix abilities in vintage for the argument that the one card will come up more frequently to change the game, even over a long time.

[Machinus]

Just food for thought...would you play 59 cards if that was the minimum?  If you argue consistency for playing 60 instead of 61 than I would assume you say yes; and if so would you play 58?  Where do you draw the line for how many the minimum you would play if you could play as few or as many as you could? 

This is an abysmal argument. Go look up "doomsday" and figure out what it does.

What part of that made you think it was an argument?  I thought it was clear by stating that it was "Just food for thought."

Pronunciation: 'är-gy&-m&nt
Function: noun
Etymology: Middle English, from Middle French, from Latin argumentum, from arguere
2 a : a reason given in proof or rebuttal b : discourse intended to persuade
3 a : the act or process of arguing : ARGUMENTATION b : a coherent series of statements leading from a premise to a conclusion

[dandan]

Nobody has argued that adding a card does anything other than reduce the chance of drawing any of the 60 cards in the rest of your deck. Nobody. EVER. I don't think anyone is missing this point and I don't think any serious player cares about the actual probablilities. It lowers the chance of finding the good stuff in your deck and the change is significant. I would appreciate it if we could take this as a universally accepted fact from this point on.

Really?  I thought I did.  Let me elaborate.

We don't call our decks "random bags filled with good stuff" like you.  Instead, we call them ordered sets that we choose from in a random SEARCH pattern.  Certain cards alter the search pattern, and certain search paths lead to other searches.  A search is complete when the search pattern you have followed and the opposition's search pattern result in a game-winning, game-losing, or game-drawing state.
So here we are, balancing all of these elements in our decks, and the argument is made that a longer, more random search will lead to a faster or more reliable progression to the game's end.  From a game balancing standpoint, the proportions can become "more optimal" but the search length will likely become longer.  This means that a longer, more random but also more repeatable(if only tuning is involved) search is being chosen over a shorter search.  Since we are playing a card game where certain search paths are more preferable then others we prefer the shorter search paths because the decrease in randomization leads to more brokenness.
The point about the decklists from France is that a) was extremely questionable.  My point is that I don't have a lifetime to make a simulation engine that will optimize a) through c), so sticking to 60 cards is the safe bet(an easier optimization because the conditions are dropped).
For the record, my personal 61st card is vampiric tutor.  I play with 60.

OK, OK, I concede the point that although adding a 61 card reduces the probability of drawing any of the other 60 cards IF we view them a pieces of cardboard, if the 61 card is a tutor a longer search chain might still result in an improved chance of finding the desired card [indeed it seems logical that adding a tutor is likely to improve the chance of finding the sort of cards you aim to find]. Bear with me and for the sake of simplicity lets call this a case 2 where the added utility outweighs the 'pure cardboard' decrease in probability of drawing the good stuff.

I haven't seen anyone arguing against the possibilities of case 1 or 3 decks and Warble makes a solid point that I will chose to support the existance of case 2 decks IN THEORY. Both myself and Warble seem to doubt the existance of a optimally-tuned Vintage deck with 61 cards or more. However we are talking about THEORY not the current metagame.

For those of you too lazy (like me to scroll up). The three theoretical cases for 61 (or more) card decks are
1. The deck requires more than 60 pieces of cardboard for some reason (Wheel/Lotus, Dragon/LDV, Stasis, Battle of Wits, Arc-Slogger type cards)
2. The deck requires a certain proportion of some resource (mana, tutoring, kill condition) than it is not possible to achieve using 60 cards. Example a 27/61 mana ratio
3. The deck requires a certain number of resources/options usually silver-bullets but conceivably kill conditions. Example SotF toolbox

All of these cases accept the lower chance of drawing individual cards in order to gain something else and view the gain as greater than the loss. I don't really see how it is possible to number crunch the trade offs and say for certain that 60 cards is better. Clearly we have no current tier 1 decks that are based around deck quantity, I'm not sold on case 2 but I can see the logic and Vintage is far more about active decks than reactive decks so case 3 decks are clearly not currently tier 1.

The only way this thread is going to bear fruit is if we can look at the benefits of the 61st card rather than just the cons of adding it. After all, most difficult choices have pros and cons and I feel that by labelling all decks and decbuilders that even consider using more than 60 cards as bad, we are being rather blinkered.

[xrobx]

The only way this thread is going to bear fruit is if we can look at the benefits of the 61st card rather than just the cons of adding it. After all, most difficult choices have pros and cons and I feel that by labelling all decks and decbuilders that even consider using more than 60 cards as bad, we are being rather blinkered.

You make a solid point, so I guess the question is which decks can we apply this theory to, and who's going to throw the first stone.  Both combo and control should be looked at, as they both have potential with the addition of these cards.  On the combo note, I do not, however, know if this would apply as the conditions set don't really apply to combo in general...

1. The deck requires more than 60 pieces of cardboard for some reason (Wheel/Lotus, Dragon/LDV, Stasis, Battle of Wits, Arc-Slogger type cards) Well, maybe...but I personally don't see it just yet...

2. The deck requires a certain proportion of some resource (mana, tutoring, kill condition) than it is not possible to achieve using 60 cards. Example a 27/61 mana ratio This could be applicable, given a certain manabase where you run something like land grant to fill up spots, and need solid mana producers along with the correct ratio of spells to mana.

3. The deck requires a certain number of resources/options usually silver-bullets but conceivably kill conditions. Example SotF toolbox  Again, the unrestriction of portal may play an important role here.

[Metman]

Just food for thought...would you play 59 cards if that was the minimum?  If you argue consistency for playing 60 instead of 61 than I would assume you say yes; and if so would you play 58?  Where do you draw the line for how many the minimum you would play if you could play as few or as many as you could? 

This is an abysmal argument. Go look up "doomsday" and figure out what it does.

What part of that made you think it was an argument?  I thought it was clear by stating that it was "Just food for thought."

Pronunciation: 'är-gy&-m&nt
Function: noun
Etymology: Middle English, from Middle French, from Latin argumentum, from arguere
2 a : a reason given in proof or rebuttal b : discourse intended to persuade
3 a : the act or process of arguing : ARGUMENTATION b : a coherent series of statements leading from a premise to a conclusion

Again I don't know where you think I'm arguing.  I was intending to spur discussion not make a point.  Therefore, you should refer to your post with the dictionary quote not me. 

Getting back onto topic.  I don't have a lot of experience playing with combo but I think I understand the basic mechanics of numerous combo decks.  Although this is only in theory, I believe that combo puts cards into the deck to simply fill the 60 card void.  I honestly think that many combo decks come down to the point, after the basic combo core has been built, where the deck builder says, "Now, how am I going to get this combo go off?"  Then they add the tutors, extra draw, etc. to ensure that it happens.  So, in theory I'm guessing that combo could be stronger if the minimum weren't 60 cards, therefore I'm assuming that 61 or more wouldn't be any more optimal.

Control I think is a different story, or at least control that utilizes numerous tutors, deck thinners, dig, draw, search, and what ever else you can imagine goes into their tool boxes.  Prime examples are 3/4cc and Keeper esq.  These are decks that don't seem as redundant as others.    When building these decks, I'm often faced with adding another tutor; most often Vampiric Tutor, Mystical Tutor, or Merchant Scroll.  If one of these is the 61 first card you've increased the likelyhood of finding one of the tools in your box during a game right?  I think that as long as the deck is proportionally effective you can't discount the 61st card being added to certain decks.   

[Machinus]

Just food for thought...would you play 59 cards if that was the minimum?  If you argue consistency for playing 60 instead of 61 than I would assume you say yes; and if so would you play 58?  Where do you draw the line for how many the minimum you would play if you could play as few or as many as you could? 

This is an abysmal argument. Go look up "doomsday" and figure out what it does.

What part of that made you think it was an argument?  I thought it was clear by stating that it was "Just food for thought."

Pronunciation: 'är-gy&-m&nt
Function: noun
Etymology: Middle English, from Middle French, from Latin argumentum, from arguere
2 a : a reason given in proof or rebuttal b : discourse intended to persuade
3 a : the act or process of arguing : ARGUMENTATION b : a coherent series of statements leading from a premise to a conclusion

Again I don't know where you think I'm arguing.  I was intending to spur discussion not make a point.  Therefore, you should refer to your post with the dictionary quote not me. 

Since you fail to bring your own reasoning ability to this debate, I will have to spell the correct answer out for you.

The strongest possible deck size is 8 cards. An 8-card deck will goldfish immediately and will not lose to game rules. You might even be able to include anti-hate cards in this deck to deal with spheres or labs. This is an obvious conclusion from the game limits and there shouldn't be uncertainty about it.

[cssamerican]

The only way this thread is going to bear fruit is if we can look at the benefits of the 61st card rather than just the cons of adding it. After all, most difficult choices have pros and cons and I feel that by labelling all decks and decbuilders that even consider using more than 60 cards as bad, we are being rather blinkered.

Here is an example where the small risk might be worth it IN THEORY.
You are going to a tournament and you have a very tight decklist; you play this decklist all the time and feel very comfortable with it. For some reason you find out a few minutes before deck registration that a team is showing up at this tournament piloting a deck that goes 60/40 with your deck as is game 1; however, the deck auto loses to a game 1 hoser. Because of the number of players in this team as compared to the number of players in the tournament, it is likely you will be playing a member of this team once in the swiss and possibly again in the finals. The decided advantage that the hoser card as the 61st card could give you in your 2 games could easily outweigh any statistical mishaps thoughout the course of the tournament. So then you ask why not cut a card for the hoser? Since this is a deck that you are extremely familiar with the contents of, it is possible, although unlikely that cutting a card could create a play mistake, such as casting a tutor to get a card only to realize that it was cut for mythical 61st card. And of course the most obvious reason to just add the 61st card in this situation is it is a spur of the moment decision, you have had no time to playtest to decide what card to cut for it. And in this case it might be better to run the 61st card rather than to cut the wrong card.