Luck in Magic

[Gandalf_The_White_1]

It merely means that I accept the fact that there is only so much one can do before surrendering to chance.

This is where we fundamentally disagree. I don't think there has ever been a player who did not make mistakes, and as long as you are making mistakes, luck is not the determining factor in any game, much less match.

Isn't 'not making mistakes' the same thing as 'making the best decisions/plays'?  And are the 'best decisions/plays' the ones that give one the best chance or highest probability of victory(thus they are NOT CERTAIN to result in victory)?  Not to say that people don't make mistakes, but even the best lines of play can often be foiled by chance.  In an example (hypothetically) where someone makes all of the perfect decisions, they can still lose.  And making a mistake doesn't always cost one the game/match.  Mistakes can often be irrelevant to the outcome of the game anyways, meaning that even though one makes mistakes one can still lose because of luck rather than those mistakes.

[Hi-Val]

This weekend at one point I won a game on what I call luck. Here's the situation

I'm playing vs. Ravager Aggro Stax (which BTW I think was a very good deck, I'm looking forward to a list). I've necro'd down to a very low life total and had to FoW a opposing threat (he then resolved a Chalice for 0). Basically I could play a will at 1 life and then have 8 Black and 1 Blue in pool afterwards. I had Vamp in my yard for tutoring, but that was it. I did have an ancestral however which I played since it was my only out. I calculated my odds of hitting a tendrils or DT and it was about 20% as I had just under 40 cards left in my deck. I hit tendrils and won the game.

Was that luck? I'd say so.

So your odds were 1:5 in that situation. Thus, in the times it has come up last in testing, playing, etc., you probably lost 4 out of 5 times generally. However, do you remember those losses? Our mind tends to edit those things out, and it is a fantastic editor. It's the time that you roll four 6s in a row to determine who starts the game that you remember, not the countless times when you've rolled and it hasn't come up. I don't think your situation is "lucky" at all. I think it's mathematical, and your brain might be tricking you. Your odds were not terrible at all there; remember that people bet on million-to-one odds whenever they play the lottery. We're very happy to take chances when we have little risk, which in your case, was nothing. You drew the Tendrils or DT or you didn't and lost.

This whole thread is going to turn into a determinism debate : \

[Cross]

It seems like this discussion is more about the times when you have a minutia of chance to draw a particulr card or hand, and do.

I would say that chance is optimized by better deckbuilding, so in that sense if you play perfectly you are only as good as the version of the deck you have. In magic it is kind of the ratio of deckbuilding skill, which increases chances of doing well, to actual playing skill which also increase chance.

[AmbivalentDuck]

This whole thread is going to turn into a determinism debate : \

Whenever decision-making comes up that happens.  It shouldn't, really.  It's pretty much a given that solving the entire range of possibilities is impossible, and so you're stuck making imperfectly informed decisions.  The Meandeck stance on play error is ridiculous because it requires information that you *shouldn't* have: otherwise you're playing a game that's not Magic.

Even without a stance on determinism, you're stuck playing probabilities...and trying to read your opponent.  Theoretically, neither of you can "read" the top card of your decks (unless you're cheating).  So, topdecking comes down to probabilities and thereby luck.  That propagates into game wins, match wins, top 8s, and tourney wins.  Sure, you can build a deck that has favorable probabilities, but how many times you have to mull per tourney comes down to luck. 

[benthetenor]

So your odds were 1:5 in that situation. Thus, in the times it has come up last in testing, playing, etc., you probably lost 4 out of 5 times generally.

I hate to be a douchebag, but you can't really infer that. Regardless of past results, every single time that you go into a situation getting 4 to 1 odds against something happening, and that something happens, that's quite lucky. I know that's not quite what you were saying, but you still cannot infer what the test results could have been. It's more than probable that with such a small test batch (i.e., less than a thousand of the same situation) you would have gotten odds of 0% or 100% or anywhere inbetween. It's calculations based upon the actual gamestate that decide whether or not a play is statistically intelligent or not.

Regardless, at 4:1, it was not a good bet to take, but you took it and won. It's a very risky play (and consequently one to be taken only in the direst of situations) specifically because you will lose many more times than you will win. The fact that you happened to win that time doesn't make it the right play, nor should the fact that you've already made the play 4 times and not won factor into your decision to make the play. If you've made the play a hundred times and never lost, the odds of losing are still 4:1. That, by the way, would be very lucky.

Professional poker players call poker a game of short-term luck and long-term skill. With any given play, there is always the chance to lose, even if the play that you've made is 100% correct. Skill manifests itself not through the course of a game but through the course of a tournament or a year's worth of tournaments or a lifetime. Magic is the same. If you've sufficiently randomized your deck, then there is a significant amount of luck present. The fact that bad players use this luck as an excuse for their bad play does not negate the fact that luck exists. But the presence of this luck does not exclude good players from winning against bad players in the long run, even if it can in the short run.

Quick example: Your DCI rating is, in a nutshell, a mathematical aproximation of a player's skill. It's flawed, but it's the closest that we have in this game to an objective measure of skill. When two opponents have an equivalent rating, say two players with an 1800 rating, then each has a 50/50 chance of beating the other. They have each shown themselves to be of equivalent skill (in this flawed, objective measure), and assuming all else is equal, they have an equal chance of winning. The equation used to calculate a DCI rating is a little complex, but it takes into account both the ratings and the k-value of the tournament and spits out what's called a win percentage. For instance, if one player has a rating of 1600 and the other has one of 1800, the percent difference between the two is about 12 percent, meaning that whoever wins will get 12 percent of the other person's rating after accounting for the k-value of the tournament. The equation is built in this way because the better player should win about 88 times out of a hundred, whereas the weaker player should win about 12 percent of the time. In this way, if they play out a hundred games and do as expected, neither player will lose or gain any points. If they overperfom, they will get points from the opponent.

Even the greatest player will not win every time. Not even close. The inkling that pure skill will keep you from losing is flawed. The fact that no one has ever played a flawless game does not mean that playing flawlessly will ensure a win. If you want that, go play freakin' chess, a game where the pieces are not randomized before starting play.

[Smmenen]

Part of the problem is that those of you who disagree are not thinking broadly enough.

You are thinking about luck, ceteris peribus. From that perspective OF COURSE luck will seem to control. If your deck choice, card choices, sb, sbing decisions, and in game decisions are all constant, luck is the ONLY remaining variable and it will ALWAYS appear to determine the outcome of a game.

The problem is that this is the ass backwards way of looking at things.

When I think about all the possible things I could have done:

a) Play a different deck
b) play different card choices
c) play a different sb
d) sb differently
e) mulligan different
f) tutor for different cards
g) make different, earlier, in game decisions

When you put all those things in the mix, how important is luck really? Pretty damned marginal. I acknowledged that its there, but not determinative.

That’s why I say luck is a factor, but never controls. If you disagree with what I just posted, that’s pretty bold. Your saying that all of your decisions were perfect and that you played the perfect deck with the perfect sb.

Although, from your perspective, I agree that luck is a marginal factor, isn't that perspective unnecessarily generalized?  In any particular descriptive model, assumptions are made to simplify it.  Otherwise, you have an endless amount of variables, and hopelessly complicated equations to deal with. 

No.  Let's assume I'm playing Stompy.  Or better yet, Fish.

My opponent opens with turn one Tinker for Darksteel Colossus.  I lose.  Is that luck?  

What if I was playing Grim Long?  IT?  Control Slaver?  Turn one Welder off Stax?  

There are TONS of variables here.  I don't think we should be eliminating variables just for cognitive simplicity.  That's crazy.  Let's ignore factors A, B, and C because they make things complex.  That's just wrong.  

It seems fair that you examine the luck factor, given that:

1) You've made a deck choice
2) You've made card choices within that deck choice
3) You've made SBing decisions based on the metagame
4) You've sideboarded accurately for the match
5) You believe these decisions are correct

While there may be slight variations in the accuracy of these assumptions, they should still be (at a level of play as high as we claim to play at) fair assumptions.  With these in mind, your list looks much more like this:

a) mulligan different
b) tutor for different cards
c) make different, earlier, in game decisions
d) luck

And luck plays a much more important role.  While nothing you said is wrong, (and I believe neither is anything I have said) the macro- view of things seems overly broad.

Again, I don't agree at all.

Deck choice is huge in Vintage.  As is deck design.  Keeping that constant is part of the reason people don't improve.  It assumes that every deck is competitive.  This is false.  

[Smmenen]

a) Play a different deck
b) play different card choices
c) play a different sb
d) sb differently
e) mulligan different
f) tutor for different cards
g) make different, earlier, in game decisions

Each one of these things can still be foiled.

Sure, they can be foiled.  But in total, they are extremely unlikely to be.  The fact that any given one of these can be foiled is not relevant.

My list was also nonexhaustive - it was illustrative of a broader point. 

I could go on and on and on about this subject because the flaws in the opposing view here are enormous. 

a) As an extreme example, you pick a deck that is a bomb in the current metagame and beats everything 70% of the time, except this one deck that like no one ever plays, since it loses to pretty much everything else.  You go to the tournament and of 140 people, 2 are playing that one deck, and you draw them in rounds 1 and 2.  You go 0-2 drop.

This is a ridiculous example simply becuase Vintage doesn't work like that.  Vintage is always 20% random and power is a particuarly important component.   Argments by analogy onloy work if they are analogous.  This is not.

b) You don't draw those cards.

c) You don't draw the sideboard cards.

d) You don't ever draw the sideboard cards.

e) You mulligan bad hands that you cannot keep and end up having to take 4 or 5 cards in the end.  Do you keep an unplayable hand of 7 that has land in fear that you will draw a 6 card hand with no mana, and have to go to 5?

f) and g) are really the only ones you can control here.

As I said, sure, any one of these could fail.

But will they ALL fail?  And will they fail 2/3 games?  Given the dozens of variables, I'd say luck is pretty marginal.  Sure its a factor, but its not detrminative.

The validity of Steve's contention simply depends on the definition of "luck". However, what I see here is that he's trying to operate with a definition that has some practical applications, while others are challenging his statements for the sake of demonstrating that they can be invalidated by altering the definition.

Simply put, the way I'm understanding this is that skill (whether playskill, deck construction skill, ability to predict metagames, analyze test results properly, utilizing efficient methods of testing to maximize the amount of pertinent information that can be extracted etc) can go a very long way in minimizing the luck component in matches. "Luck" is an inherent part of this game and is inescapable; however, many players are not quite at the level yet where they are able to minimize its impact. The fact some top players can perform consistently supports this contention. Furthermore, weaker players have great difficulty in discerning when they lost due to "luck", or when they lost because of their play error. For instance, the fact that they needlessly played a mana source on turn 6, thereby critically weakening their Brainstorm on turn 8, thereby not stopping their opponent's "lucky topdeck" of a game winning YWill on turn 10, can cause a serious misassesment of the impact luck contributed to that game, and propagate this myth that T1 has a very significant luck component.

I am not attempting in any way to downplay the importance of proper play, or to chalk things up to luck.  I'm stating that it is a factor, and to dismiss it as one seems as faulty as to dismiss any other factor.  Yes, you can minimize its impact, but it is always there.  In my experience, the longer the game goes on, the more of a factor playskill becomes.  On the other hand, winning on turn 1 has much more luck involved, be it hitting the right cards in your opening 7, or the right cards in your Draw 7.  Sometimes, it's just ripping Will off the top when you're on the draw.  Is deck construction part of this?  Yes, it is.  But to say it has more of an impact than the luck of the draw in even this situation is flawed reasoning. 

Steven's points, as I said previously, are not incorrect.  They are, from the perspective he has taken, accurate.  I merely contend that this is not necessarily the best perspective from which you can look at the situation.  Your claim is that his view is from a practical standpoint.  Where is the practicality in questioning your deck choice as a function of your opponent winning on turn one? 

It can be VERY practical!  Rich Shay put Leyline of the Void in his sb so he wouldnt lose turn one to Grim Long as frequently.  Then he just stopped playing Slaver, in part, because he wanted a deck that was slightly faster to compete with Grim Long.   He now plays Dragon, a deck that can combo over Grim Long far more than Slaver could and is highly disruptive.  I played Rich last weekend in five games and he beat me with his dragon deck 4-1.  I was surprised.  Rich Shay would have had a much better shot against me with Dragon than Slaver. 

Really, what difference would there be between playing Oath or Gifts in that situation?  Both decks run the same number of Force of Will and enough blue cards to support them, and in this *practical* situation, are functionally identical in all relevant ways. 

Not true not true not true!

MDGifts runs 4 Mechant Scroll and 3 Misdirections.  Thus, a tendrils for precisely 20 could be misdirected (the last one).  Or if you get a turn, turn one Scroll for FoW would help you find the Force.  There are lots of reasons!  It is not functionally identical.  THere are critical differnces. 

Nonetheless, diceman's reply captures the sentiment I'm espousing. 

Let me put it this way.

SOmeone else used this example earlier in the thread:  Topdecking Ancestral.

Both decks are in topdeck mode.  Let's say Dragon v. Control Slaver.   One of the decks topdecks Ancestral and wins the game. 

Now, let's anayze this situation.  One player may say: wow, what a savage lucksack.  However, if we analyzed the game state, we may find that actually there was a 25% chance that the player would topdeck into the win.  For the dragon player, it could have been intution, Demonic Tutor, Ancestral Recall, an Animate spell, etc.  For the SLaver player, it could have been one of four Brainstorms, Yawg Will, Tinker, one of 4 Thirsts etc.

My point is that what one perceives as luck frequently actually was not lucky, but probable or at least not improbable. 

[Smmenen]

yeah, kai budde and jon finkel made top 8s consistently due to luck. 

Yes.  I guess I should let this argument get technical because I can't win it otherwise.  Let's pretend that all tournaments are 8 matches, they need 2/3 to win a match, they need to win 7 matches to top 8, and they win 80% of the time (even against other pros).  Now, I'll write that into computer code (code available upon serious request) and have it play 100000 tournaments so there's no whining about which approximation I choose:

They top 8 about 80% of the time.

Let's change that to what I guessed for you, about 65%: you should top 8 only 30% of the time.

In a series of completely even matches, you against your clone army: you should top 8 only 4% of the time.

Running again assuming you only need 6 matches:
97%, 60%, and 15% respectively.

SOOOOO....if we take stalling into draws into account, and take my 65% guess, you should only be top 8ing between 40-55% of the time.  So, yes I call that luck.  

You realize that no reasonable person is going to listen to what you say now.

If Kai Budde was merely lucky, then we can all accept that you are a quack (get it, duck?).

[Smmenen]

I can't speak for my whole team, but don't think I have ever had a completely unavoidable loss.

Are you including situations in which you made the correct decision to keep a hand, but your opponent kept a hand that is statistically unlikely but foiled yours?

For example: It's game 1 and your opponent is playing dragon on the play.  You're playing say MDG.

You keep a hand of

Force of Will
Ancestral Recall
Chain of Vapor
Mox Pearl
Brainstorm
Fetchland
Fetchland

Your opponent goes

Mox Jet - Duress
Black Lotus
Bazaar
Pitch Dragon
Animate

Even though you kept a great hand, one that is unlikely that you are going to duplicate in power by mulliganing, you still lost despite any action you may have taken once the game began.

Are you saying that these situations haven't ocurred to you, or are you saying that if you mulliganed you may have gotten a hand that could foil this, which would constitute action you could have taken to prevent your loss?

Yes.  It's called Leyline of the Void. 

[Gandalf_The_White_1]

I can't speak for my whole team, but don't think I have ever had a completely unavoidable loss.

Are you including situations in which you made the correct decision to keep a hand, but your opponent kept a hand that is statistically unlikely but foiled yours?

For example: It's game 1 and your opponent is playing dragon on the play.  You're playing say MDG.

You keep a hand of

Force of Will
Ancestral Recall
Chain of Vapor
Mox Pearl
Brainstorm
Fetchland
Fetchland

Your opponent goes

Mox Jet - Duress
Black Lotus
Bazaar
Pitch Dragon
Animate

Even though you kept a great hand, one that is unlikely that you are going to duplicate in power by mulliganing, you still lost despite any action you may have taken once the game began.

Are you saying that these situations haven't occurred to you, or are you saying that if you mulliganed you may have gotten a hand that could foil this, which would constitute action you could have taken to prevent your loss?

Yes.  It's called Leyline of the Void. 

The dragon player could just as easily have gotten a hand including chain of vapor, or whatever.  The point is that I don't think that the gifts player made a mistake in keeping that hand, yet he/she lost just the same.  How is this not an example of losing because of bad luck?  Should the gifts player always assume that the dragon player has a turn 1 kill and mull into leyline (even though this could also be to no avail)?

Sure, they can be foiled.  But in total, they are extremely unlikely to be.

I don't think that anyone is disputing this point.  Of course good players win often, and it's not because they are merely lucky.  It's obvious that there are many factors other than luck, but it is foolish to discount the fact that luck is a factor and can sometimes determine the outcome of a game or match.  If we define the 'luck' component of magic as that outside of one's control, then I can break this down into a rather simple argument:

1: Are there factors which influence what happens during a match outside one's control?

Yes.

2: Can these factors cause one to win or lose?

Yes.

Not meant as an ad hominum argument, but I seriously think that someone would have to be either extremely foolish or conceited to disagree with either of these questions.  It all seems pretty simple and straightforeward to me.

[Moxlotus]

Vintage is always 20% random

Aren't you contradicting yourself by saying this?

Professional poker players call poker a game of short-term luck and long-term skill. With any given play, there is always the chance to lose, even if the play that you've made is 100% correct. Skill manifests itself not through the course of a game but through the course of a tournament or a year's worth of tournaments or a lifetime. Magic is the same

Wow, that was a much more elegant way of saying what I believe. 

[Smmenen]

I can't speak for my whole team, but don't think I have ever had a completely unavoidable loss.

Are you including situations in which you made the correct decision to keep a hand, but your opponent kept a hand that is statistically unlikely but foiled yours?

For example: It's game 1 and your opponent is playing dragon on the play.  You're playing say MDG.

You keep a hand of

Force of Will
Ancestral Recall
Chain of Vapor
Mox Pearl
Brainstorm
Fetchland
Fetchland

Your opponent goes

Mox Jet - Duress
Black Lotus
Bazaar
Pitch Dragon
Animate

Even though you kept a great hand, one that is unlikely that you are going to duplicate in power by mulliganing, you still lost despite any action you may have taken once the game began.

Are you saying that these situations haven't ocurred to you, or are you saying that if you mulliganed you may have gotten a hand that could foil this, which would constitute action you could have taken to prevent your loss?

Yes.  It's called Leyline of the Void. 

The dragon player could just as easily have gotten a hand including chain of vapor, or whatever.  The point is that I don't think that the gifts player made a mistake in keeping that hand, yet he/she lost just the same.  How is this not an example of losing because of bad luck?  Should the gifts player always assume that the dragon player has a turn 1 kill and mull into leyline (even though this could also be to no avail)?

I can construct dozens of examples like this.  But my point was fairly simple: it shouldn't control the match.  In addition, if this gifts player fears Dragon sufficiently, they may sb in Leylines.  If so, there is a chance that they will show up in your opening hand.  I'm not saying they should mullligan, but we must not forget that Leyline can prevent LOTS of turn one wins in this format.  

[Smmenen]

Vintage is always 20% random

Aren't you contradicting yourself by saying this?

Random decks, not random statistical.

For example, in my analysis of the Rochester metagame, I predicted 20% random crap - i.e. not established archetypes.  It was actally higher. 

I was speaking tersely in a way that could easily be misunderstood.  My mistake. 

[Gandalf_The_White_1]

I can construct dozens of examples like this.  But my point was fairly simple: it shouldn't control the match.  In addition, if this gifts player fears Dragon sufficiently, they may sb in Leylines.  If so, there is a chance that they will show up in your opening hand.  I'm not saying they should mullligan, but we must not forget that Leyline can prevent LOTS of turn one wins in this format. 

Just because it SHOULDN'T control the match doesn't mean it wont, and likewise just because leylines CAN prevent lots of turn one wins doesn't mean they will.  I don't want to sound like a broken record (to use a cliché), but despite the fact that you have listed numerous courses of action one could attempt to TRY to influence the outcome of a match, they will not always be successful simply because of luck.

I'm not sure that we're really disagreeing here about what influences the outcome of a match (we both seem to agree that one can make certain decisions and that there are certain probabilities that result based on these decisions that determine whether one wins or loses, correct me if I am mistaken here) but simply perhaps semantics by not attributing the same meaning or definition to certain words.  I define 'luck' in magic as anything outside one's control.  Would you agree with that definition or not?  If not, what so you consider luck to be?

[Smmenen]

Magic is the same.

I disagree.

Poker and magic, while sharing many elements, are still very different games.  Vintage, in some ways, is also a very different game from the game played in standard.  The sheer quantity of options in Vintage present so many possibilities for metagaming, for design, and for impeding opposing strategies that it is almost impossible that luck will actually and completely control the outcome of a match.

I would like to take this opportunity to point out one place I am willing to make something of a concession.  And I must confess that I am shocked no one else has raised this point until now.  It has been at the center of my thoughts on this subject, but I did not say anything until now:

The Die Roll.



If there is ANYTHING in magic that even approximates a critical roll for luck, it is that.  We are on page four of a thread and this hasn't even been brought up.  It's the best argument on the other side!

The die roll is Absolutely critical in Vintage.  Every game I play Grim Long I count my lucky stars when I get favorable rolls.  In every single matchup, the die roll is huge with Grim Long.  The Die Roll is a monster in Vintage, and if luck plays a roll, it is there and there alone.  I think that is where luck most rears its head. 

[TopSecret]

     I understand that blaming a game loss on luck is a very self-destructive habit,
at least in its effect towards an individual's skill at this game.

     I also understand that deck building can be very influential in controlling when
a player draws which cards and when.

     I do not recognize luck in its superstituous sense.

     However, I am inclined to recognize the uncontrollable variable:
simply drawing a "random" card from the library.

     I am not suggesting that this variable is incredibly influential in most games of Magic,
or in general. However, I do recognize that it is there, and it is what some people call "luck".

[Webster]

I would like to take this opportunity to point out one place I am willing to make something of a concession.  And I must confess that I am shocked no one else has raised this point until now.  It has been at the center of my thoughts on this subject, but I did not say anything until now:

The Die Roll.



If there is ANYTHING in magic that even approximates a critical roll for luck, it is that.  We are on page four of a thread and this hasn't even been brought up.  It's the best argument on the other side!

The die roll was brought up multiple times on the first page. Go back and re-evaluate your statements.


Luck. Well, that's a rather ambiguous term right now. So let's see what I can make of it. Luck comes basically down to probability; what is the probability of drawing card X? If it is not card X, what other cards can get to card X with the resources that are available? If a draw spell is drawn, given Y draws, what is the probability of seeing either card X or a card that gets me to X? How many cards left in the deck do not draw more cards, get me to card X, or are card X themself, and thus, dead draws for the desired outcome of the current gamestate? There is 'luck' in every instance of a hidden card being revealed; sometimes, X is the same card, but most of the time it changes because the gamestate changes.

Most people are incappable of evaluating these probabilities because we are human. Humans make mistakes, especially with complex situations like a game of magic, type 1 none-the-less. Most people are bad at magic, and thus, even if they were able to calculate the odds of drawing the optimal card or finding it through a series of cards, the card they chose as optimal has a likelyness of being the wrong card altogether. People will play poorly, making incorrect gamestate evaluations, lose, and label it as another loss to "bad luck" like some mythical beast that cannot be conquered.

Luck is beating the odds. Take the situation where any competant player knows what card they need to draw to win. Take the probabilies of drawing the card, finding the card through a series of draw effects, tutors, etc and weigh them against the draws where that situation does not happen; if the odds are unfavorable for that player yet they manage to find card X, for that particular situation, there was a higher chance that they would fail, yet they succeeded. That is luck. Probability suggested failure, yet victory was achieved.

Not every draw in every game can be as black and white as the example above, but the idea of probabilities of favorable/unfavorable cards does exist in each and every one of them, and thus, shows what "luck's" face looks like.


Web

[Smmenen]

The die roll was mentioned several times in passing, but never given the centrality that it deserves when discussing luck.

Consider:

a) getting drain online

b) being able to play Chalice of the Void

c) turn one duress in the combo mirror followed by threat of turn two kill

d) Stax decks of all stripes


Going first is of enormous importance of vintage. 

I did a sample of Stax games not long ago - Stax won something like 75% of the time it was on the play, pre-board.  The ability of Stax to win matches is dependent upon its performance post board and on the draw. 

Chalice of the Void oscillates in value as a card depending on who was on the play.

[Elric]

The die roll was mentioned several times in passing, but never given the centrality that it deserves when discussing luck.

Going first is of enormous importance of vintage. 

I started a thread a while back to quantify the Importance of winning the coin flip in vintage.  Winning the die roll happens to be an easily quantified measure of luck. 

Chess is a game that would have no luck if players could play perfectly.  In actual play, though, chess players do not play perfectly so there is still some element of luck.  For example, you have Brilliant Move A that will win you the game, but if you make that move and your opponent sees Even More Brilliant Counter-Move B you will lose.  Otherwise the game will be a draw.  Your decision now rests on hidden information...

[Godder]

Before asking if there is, or isn't, luck in Magic, what is the accepted definition of the term 'luck'? Without that definition, this discussion is very difficult. That said, luck does have the connotations of subjective assessment of a given event based on the probability of that event.

As a minor aside, trying to use ratings to quantify skill is difficult when one considers that all the modifications made to the Elo system for Magic have been contrary to the statistical background of the system. That said, a rating that is consistently above 2000 does suggest an exceptional player.

[herbig]

Chess is a game that would have no luck if players could play perfectly.

I disagree with this.  Chess is completely luck free and rests on outplaying your opponent.  If your opponent makes a suboptimal play which causes them to lose while you make no such mistakes you are simply a better player.  The game is just a more complicated version of Tic-Tac-Toe in theory.  When played by two completely error free players the game will always end in a draw.

Magic, on the other hand, has randomness and hidden information which prevents completely optimal plays.  If you could know your opponent's hand, you would have information to make the right play, much like in poker theory, where your betting and calling is determined by what cards your opponents have and the outs either of you could draw.

The closest to optimal play possible then would be making your decisions as if you knew your opponent's hand.  But the element of randomness in topdecking still prevents completely optimal decisions.

Its been alluded to, but bad luck is just a term for losing despite having a statistical advantage at any given moment and good luck the other way around.

Consider players playing a match where each rolls a three sided die.  Player 1 wins on a roll of 1, while Player 2 wins on 2 or 3.  Player 1 may well win a match occasionally, but through thousands of iterations, Player 2 would win out more often than not.  Could Player 1 be carried through 10 rounds of this?  Sure.  But throughout a thousand iterations of this, he would certainly never win more than once.

That said, I believe that a player can get "lucky" versus a vastly superior player to win a round, or even a tournament, especially in Vintage, where the power level of cards are often enough to allow huge mistakes.  But winning more than once suggests divine intervention, which is not something anyone wants to debate here, or cheating.

[Mr. Nightmare]

No.  Let's assume I'm playing Stompy.  Or better yet, Fish.

My opponent opens with turn one Tinker for Darksteel Colossus.  I lose.  Is that luck?

What if I was playing Grim Long?  IT?  Control Slaver?  Turn one Welder off Stax?

Any viable deck should have an answer for Colossus.  In any of those situations, if you knew your opponent had the possibility of turn 1 Colossus, it's your responsibility to have an answer of some sort (or access to it) in hand.  This is where mulligan decisions come in.  Yes, I am aware you know this. 
I'm not saying luck is the determining factor.  I'm saying luck is a factor, much more than deck choice.

There are TONS of variables here.  I don't think we should be eliminating variables just for cognitive simplicity.  That's crazy.  Let's ignore factors A, B, and C because they make things complex.  That's just wrong.

No, thats science.  Coming from completely different educational backgrounds, I kind of thought we'd have this difficulty.  You are very analytical, Steve, but you get caught up in the details.  You can ignore things that are constant in a given model.  Its what allows you to factor in simple mathmatical equations.  Its what allows you to discount drag in a physics problem.  If the variable has a minute enough effect, it's close enough to zero in relation to the other variables that you can set it equal to zero.  This is what is happenning below:

It seems fair that you examine the luck factor, given that:

1) You've made a deck choice
2) You've made card choices within that deck choice
3) You've made SBing decisions based on the metagame
4) You've sideboarded accurately for the match
5) You believe these decisions are correct

While there may be slight variations in the accuracy of these assumptions, they should still be (at a level of play as high as we claim to play at) fair assumptions.  With these in mind, your list looks much more like this:

a) mulligan different
b) tutor for different cards
c) make different, earlier, in game decisions
d) luck

And luck plays a much more important role.  While nothing you said is wrong, (and I believe neither is anything I have said) the macro- view of things seems overly broad.

Deck choice is huge in Vintage.  As is deck design.  Keeping that constant is part of the reason people don't improve.  It assumes that every deck is competitive.  This is false.

We agree on this point.  Not every deck can win a tournament.  But any deck can get lucky and win a game.  You're looking at the tournament.  I'm looking at the game, and that's where our disagreement stems from.

[kombat]

Deck choice is huge in Vintage.  As is deck design.  Keeping that constant is part of the reason people don't improve.  It assumes that every deck is competitive.

No it doesn't, not at all.  "Deck choice" means the selection of a single deck from the pool of competive decks.  Uncompetitive decks are left out of the selection process, and are never considered when making the "deck choice."

And deck choice can still be foiled by random chance.  Say you're going to a large tournament where you expect a particular metagame, so you opt for an appropriate deck that is strong against control decks.  You arrive at the tournament, and you were right.  Drain decks are everywhere.  Round 1 pairings to up.  You get paired against an aggro deck and lose.

No matter how skilled you were in selecting the deck choice, if you get paired against your worst matchup by sheer chance, you can't change that.  Did you make the wrong deck choice?  Or did luck negate your skill in deck selection?

Steve, have you never been combo'd out on on the first turn?  Would you not call that "losing due to luck?"  You talk about playing the perfect game and making 100% correct decisions, but don't you agree that there are actually quite a few games where you do play a perfect game (by virtue of the fact that you were only given 1 or 2 turns, and you didn't actually have many decisions to make, and thus easily made the correct ones) and still lost?

Perhaps I'm misunderstanding how you're defining "playing perfectly."  I think most people here take the term to mean "making the correct decisions to optimize the probability of a win in the general case," whereas it almost seems like you are defining it to mean "making the correct decisions to optimize the probability of a win in the specific case," as in, in that particular matchup.  Are you saying that if there existed certain plays you could have made to win that matchup, even if those plays would have seemed completely counterintuitive and even suicidal at the time, given that you didn't know what your opponent had in hand, then those would have been the "correct" plays in that case?

Hindsight is 20/20.  If you lose the die roll, would you ever keep an opening hand without a Force of Will in it?  If you do, and your opponent proceeds to combo out on you on the first turn, with you never getting a single turn, was not mulliganing the "wrong" play?  How can it be the wrong play if you didn't even know what your opponent was playing?  Surely you don't mulligan into a Force of Will no matter what, whenever you're going second, do you?

[kombat]

I would like to take this opportunity to point out one place I am willing to make something of a concession.  And I must confess that I am shocked no one else has raised this point until now.  It has been at the center of my thoughts on this subject, but I did not say anything until now:

The Die Roll.

If there is ANYTHING in magic that even approximates a critical roll for luck, it is that.  We are on page four of a thread and this hasn't even been brought up.  It's the best argument on the other side!

Maybe you can't see my posts or something, but I brought it up in my very first post in this thread, way back on page 1:

From the opening coin flip to see who goes first to the die roll for the Mana Vault, luck is a major factor in Vintage.  To pretend that it's not is, frankly, a little arrogant, in my opinion.

[Harlequin]

Luck. Well, that's a rather ambiguous term right now. So let's see what I can make of it. Luck comes basically down to probability; what is the probability of drawing card X? If it is not card X, what other cards can get to card X with the resources that are available? If a draw spell is drawn, given Y draws, what is the probability of seeing either card X or a card that gets me to X? How many cards left in the deck do not draw more cards, get me to card X, or are card X themself, and thus, dead draws for the desired outcome of the current gamestate? There is 'luck' in every instance of a hidden card being revealed; sometimes, X is the same card, but most of the time it changes because the gamestate changes.

That is not luck, thats probabilty.  There is a difference.  Winning a single die roll is not lucky.  Someone HAD to win the die roll, and it was going to be you, or them.  Winning all of your die rolls for an entire tournement IS lucky.

If some scrub net-decks a combo.dec list, wins the roll every game, and has a turn 1 win in hand in half his games... then they are lucky.  The hands they were delt were far above the expectation of the deck.  There are only a finite (descrete) number of possible ways to give a unique shuffle to a deck, its roughly 8.3 x 10^81... of all those possible configurations, some number of them are turn 1 wins.  Lets say (for arguements sake) that Combo.deck has a 20% chance to turn 1 win assumeing your opponent doesn't have a FoW or LLotV. and its got lets say 3% chance to power a turn 1 win through a force of will.  So getting 2 or 3 turn one wins durring a tournement is NOT lucky... its statistically satisfying.    If your pushing better than 50% then sure, I'd call you lucky --or your bad at shuffling, or you cheat--.

Conversely lets say that control.dec has about a 1 in 4 mulligan rate.  (so you generally keep 3 out of 4 hands).  If you end up mulliganing 5 times before round 3.  Then I would say your unlucky --or are bad at shuffling--.

[kombat]

There are only a finite (descrete) number of possible ways to give a unique shuffle to a deck, its roughly 8.3 x 10^81.

This is the math nerd in me showing through, but it's far, far less than that.  My permutation theory is a little rusty, but you've assumed each card was unique, and that's not true.  If you take into account that Magic decks typically contain multiple cards in sets of 4 (Brainstorm, for example), and that in each distribution of those 4 cards, there are 24 ways the 4 actual cards could be distributed.  P(n, r) = n!/(n-r)! = 4!/0! = 4! = 24.  However, given that the cards are functionally the same in the context of a Magic game, all 24 of these permutations should be counted as a single element, because if you draw one of the top, it doesn't matter if it's your signed FNM foil Brainstorm or your Korean Mercadian Masques Brainstorm.  It's still a Brainstorm.

If the deck contained 60 different cards, then your number would be correct, because P(60,60) = 60! = 8.32e+81.

[Harlequin]

Not to get into an e-peen measureing contest, but were talking about probabilty.  So taking 60! is actually correct.  It doesnt matter that brainstorm is brainstorm.  So If in my deck I run 2 brainstorms, and you run 1 brainstorm and 1 slight of hand.  I have double the odds of drawing brainstorm as card 1.  For example.  So perhapse "Unique" was the wrong word to use.  But it is still mathematically sound to use itterations = 60!

So Assumeing that each card in your deck is unique, any given permuation of the deck has exactly 1 / 60! probability. 


All in all, this is not the point.  My point was to say there is a descrete number of possible ways to shuffle the deck.  So that means if you took every possible combination and siad: does this stack win on turn 1 "yes" or "no."  Then you could derive what the decks turn 1 win % is without taking play skill into account.  As in if you have an opening hand of X,X,X,X Saphire, Brainstorm.  there is no agruement of "well if you draw Y, and Z on the brainstorm then its a turn 1 win .... because with this method you actaully take into acount ever possible combination of cards you could draw with brainstorm.  And, from a probability stand point.  There are 4* ways to see: Dark Rit, Will, DT And one* way of drawing: Lotus, Will, DT.  why? well because you run 4 rits and only 1 lotus ... hense the need to accknowledge the "uniqueness" of each Ritual.

* - for correctness, there are actually 4 * 50! and 1 * 50! ways to see each hand (considering that there are 50 cards remaining inthe deck after you've draw 7 and brainstromed.  But those other 50! permutations are a wash.

[kombat]

So If in my deck I run 2 brainstorms, and you run 1 brainstorm and 1 slight of hand.  I have double the odds of drawing brainstorm as card 1.

Yes, exactly, because they are functionally the same card.  2 of those 60! permutations are functionally identical, and thus they should only count as one permutation of the deck.  Thus, there are actually fewer than 60! unique ways to randomize the deck, which is precisely what I was saying.

So Assumeing that each card in your deck is unique, any given permuation of the deck has exactly 1 / 60! probability. 

Again, I agreed with this.  But this has nothing to do with the discussion, because your premise is irrelevant.  We're not talking about decks comprised of 60 unique cards.  We're talking about competitive Vintage decks, which always contain at least some degree of duplication.  I can't think of any competitive Vintage deck in which all 60 cards are different.  Combo would be close, but it's off by enough to make your 60! approximation hopelessly inaccurate.

[Harlequin]

Let me just point out that

#1) 60! is correct because we are "talking about" probabily (you should be upset with the word "unique" if you really are going to have a fit, I could remove the word "unique" from my post and I would be correct)
#2) Any number less than 60! actually makes my point stronger.  you can even consider 60! to be the maximum number.  hell what about decks that run 61 cards?  Nate's ran 61 cards.  Lets not get into the preachyness of the situation.  My point was to say that 60! is not infinity.  Its huge, but it is technically measurable.  So saying "oh man its actually way less than that" only HELPS support my theory.

#3) Your not even seeing the real logic flaw, and that is "what happens when you shuffle your library"  if you take into account every permutation of the deck, then every possibly TIME when you shuffle the deck, and for every time you shuffle, you permutated the remaining cards in the deck, then the number would be SIGNIFIGANTLY larger than 60!  But still technically not infinite.  -- Even further more: Now we can get into the Countably Infinte!  There is a non-zero ammount of probabilty that you will draw Lotus Time Twister, and then EVERY time you draw your 7 hand, you draw Lotus, Regrowth, Ritual, Lotus petal 3 lands... out into infinity.  So there... thats your arguement!!  Use that if your trying to disprove my mathematics.

-- This is highly irrelevant to the definition of Luck, and even more irrelevant to "does luck matter in magic"  So I suggest we move on and talk more about the actual topic and not get this thread shut down.  I just get defensive of my numbers =P

** woot 600th post **

[AmbivalentDuck]

You realize that no reasonable person is going to listen to what you say now.

If Kai Budde was merely lucky, then we can all accept that you are a quack (get it, duck?).

Because most reasonable people ignore evidence and instead use name-calling and straw men to make their points.

It's a simple binomial distribution with p=game win percentage, you use that with n=3 to find the percent of matches won, and plug that into a second binomial distribution with p=that and n=8.  You'll see that the brute force numbers match the analytical results.  I used computational brute force so that if anyone called me on it, I could explain it without having to use those words.  There's no doubting that I produced accurate numbers, sorry.

I never said that Kai Budde was *merely* lucky.  That's your choice of words.  I said that even with what I think is the highest real percentage he could actually have against a field of pros (around 65%) he'd only top 8 about half the time, much less win.  With so few tournaments, sampling error makes his win rate look a lot higher.

You're losing this debate from so many angles.  You've lost the game theory angle, the determinism angle, and the stats angle.  I'll be interested to see what you run to next or if you even admit defeat.