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Author Topic: Luck in Magic  (Read 17188 times)
Smmenen
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« Reply #90 on: July 06, 2006, 10:13:29 am »

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.

Your claim is this:

Players cannot consistently top 8 without luck.  Your model is preposterous.

People are getting bogged down here.  Let’s step back and take a look at the situation:

What are we talking about?  We are trying to determine whether luck is a determinate factor in whether people win or lose tournament matches.   That is the issue. 

My position is this:  Luck is NOT a determinate factor, but IS a relevant factor.

Others posit: luck IS a determinate factor.

Now let’s take a look at your model within this context:


Quote


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. 

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.

Your model is HUGELY flawed.

The FIRST mistake is that you assume a constant among wins/and losses.  Here is why that isn’t true:

a) you only play three games in a match.  Thus,
   i) surprises
   ii) psychological tricks
   iii) sb surprises
   iv) design tweaks which surprise
   v) sbing period

all affect the actual results.  Your point may have MORE validity if you played 10,000 games.  But we don’t.

The ONLY thing that matters is: does luck affect tournament match outcome?  If we sat down and played 10,000 games, then it would be a different matter.

b) You don’t even know how many matches need to be won to make top 8!  It takes 6 matches of 8 rounds to make top 8, not 7.  6-0-2 always makes top 8. 

c) You CANNOT have a constant number to reflect all the matchups.  A persons overall win percentage constantly changes depending upon the deck they choose, the matchups they expect to face and actually face, their sb, their skill, etc. 

You are making some extremely crass assumptions and ignoring the actual reality of how tournament matches play. 

The bottom line is this:

There are dozens if not hundreds of variables in tournament magic that end up affecting who won.  Luck is one of those variables.  In Vintage magic, with all of the tutors and other decision making inherent in the format, those factors are multiplied.

For instance, in other formats with no library manipulation, you may just have two decks where the cards on top of the deck are constant.   The only thing that matters then is how those cards are played.  In Vintage, the options a player has are exponentially greater – thus the potential for missing the *optimal* play is exponentially higher.  There is only one optimal play.   

« Last Edit: July 06, 2006, 10:25:29 am by Smmenen » Logged
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« Reply #91 on: July 06, 2006, 10:40:46 am »

Here is my math on the topic:

Assumptions:
-- 6 rounds of swiss with 64 poeple
-- 8 people make top 8 (duh)
-- ALL (4) plavers who have 12 pts at the end of round 4 draw in (and get in with 14 points 4-2-0).
-- 4 players who got a loss in any previous round will make it in with 15 points (5-0-1)

Dangerous Assumptions:
-- No other players make top 8. because...
-- No players draw unless its an ID in rounds 5 and 6.
-- Your game win % does not change based on round, points, or if you've SBed or not.

-----> The now you might ask why no 4-1-1??  well the reason is, in a perfect world there will be 8 people (a total of 4 tables) with 12 points at the end of round 5.  If any 1 table Draws then its up to tigh breakers for that table.  Because you end up with the following possiblites:
12 pts -- 4 - 3 - 2 - 1 - 0
13 pts -- 0 - 2 - 4 - 6 - 8 <--- ***
14 pts -- 4 - 4 - 4 - 4 - 4 [always the same because these are the 4-2-0ers]
15 pts -- 4 - 3 - 2 - 1 - 0

*** anyone with 13 points will be in contention against everyone else with 13 points, 1/2 will make it 1/2 will not.  So lets assume that no one wants to chance it and all the 12 point ppl at the end of round 5 play it out.

------ Definitions ----------
P is defined as probabilty of a Game win.

R is defined as Prob of Match Win = Bin(3;3,p) + Bin(2;3,p)
 --- this is the simplest way to think about it.  Immagin you are forced to play 3 rounds even if you win the frist 2.  This way we can avoid conditional probabilty.  and lots of messy multiplication and division.

T is probabity of a tournament Top 8 = Bin(4;4,R) + Bin(5;6,R)
Edit:  I totally realized I slightly screwed that up... here is what it really is.
T is probabilty of a Top 8 result = Bin(4;4,R) + Bin(5;6,R) - 2(1-R)(R)^5  [ to discount the fact that WWWWLW and WWWWWL are not options ]
or more simply:    = Prob(4 wins out of 4) + Prob( 3 wins out of 4 AND 2 wins out of 2) = Bin(4;4,R) + Bin(3;4,R)*Bin(2;2,R)

Therefore:
[Prob(game = win) -- Prob(Match = win) -- Prob(Top 8)]
-------------------------------------------------------------------------------
 P ------- R ------- T
50% -- 50.0% -- 12.5%
55% -- 57.5% -- 21.6%
60% -- 64.8% -- 33.7%
65% -- 71.8% -- 48.2%
70% -- 78.4% -- 63.4%
75% -- 84.4% -- 77.4%

Edited End result to be more accurate.


« Last Edit: July 06, 2006, 11:39:05 am by Harlequin » Logged

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« Reply #92 on: July 06, 2006, 12:22:53 pm »

I dont see Magic as a game of "strategy and luck", but as one of "strategy and probabilities". Even intentional random mechanics in the cards (die roll, coin flip) can be expressed as 1o6, 1o2, and so.

You have a 50% chance of starting the match. That´s a probability that comes with the game, which should be added as a factor in deck design (as, in questions like how much should I mulligan against a GrimLong deck, on game two, if I dont go first?). But probability is not (IMHO) luck (at least, in a supersticious way  Wink )

All previous examples (the Ancestrall topdecking, the inclusion of tutors to modify the odds, etc.) can be expressed (as some of our mathematical fellows here have shown) in probability percentages.

Then, as deckbuilders, we all are aware of this, and that`s why we spent happy&merry  hours tweaking and playtesting: so we don´t play a 2 land deck and get mana screw and then say "we had bad luck" Very Happy

(in any case, if someone doing some kind of rituals, or carrying an specific lucky charm, DOES in fact draw Ancestral all the time, may be we are all wrong)
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« Reply #93 on: July 06, 2006, 01:59:13 pm »

Your claim is this:

Players cannot consistently top 8 without luck.  Your model is preposterous.

People are getting bogged down here.  Let’s step back and take a look at the situation:

What are we talking about?  We are trying to determine whether luck is a determinate factor in whether people win or lose tournament matches.   That is the issue. 

My position is this:  Luck is NOT a determinate factor, but IS a relevant factor.

Others posit: luck IS a determinate factor.

My position is actually a lot simpler than that: if you're top 8ing more often than your win rate predicts, it's due to luck (aka sampling error).

If someone is top 8ing (or winning) at a rate higher than their game win rate predicts, they're getting lucky.  Since there are some "messy" but plausible arguments about that, the match win rate (though technically a non-linear extension of the true game win rate that I feel can be safely modeled using a generalized game win rate) should be an absolute predictor of top 8 and win rates.  Since I'm pretty sure that nobody is above 65%, consistent top 8s are always statistically unlikely in reasonably large tournaments.



Your model is HUGELY flawed.

The FIRST mistake is that you assume a constant among wins/and losses.  Here is why that isn’t true:

a) you only play three games in a match.  Thus,
   i) surprises
   ii) psychological tricks
   iii) sb surprises
   iv) design tweaks which surprise
   v) sbing period

all affect the actual results.  Your point may have MORE validity if you played 10,000 games.  But we don’t.

The ONLY thing that matters is: does luck affect tournament match outcome?  If we sat down and played 10,000 games, then it would be a different matter.

b) You don’t even know how many matches need to be won to make top 8!  It takes 6 matches of 8 rounds to make top 8, not 7.  6-0-2 always makes top 8. 

c) You CANNOT have a constant number to reflect all the matchups.  A persons overall win percentage constantly changes depending upon the deck they choose, the matchups they expect to face and actually face, their sb, their skill, etc. 

You are making some extremely crass assumptions and ignoring the actual reality of how tournament matches play. 

The bottom line is this:

There are dozens if not hundreds of variables in tournament magic that end up affecting who won.  Luck is one of those variables.  In Vintage magic, with all of the tutors and other decision making inherent in the format, those factors are multiplied.

For instance, in other formats with no library manipulation, you may just have two decks where the cards on top of the deck are constant.   The only thing that matters then is how those cards are played.  In Vintage, the options a player has are exponentially greater – thus the potential for missing the *optimal* play is exponentially higher.  There is only one optimal play.   



I'm saying that gross win rate is a function of those variables.  Sure, they all factor into it.  If you're t8ing or winning tournaments more often that your win rate predicts, it's still luck.  That's the whole reason that the notion of distributions keeps getting used.  Probability is manifesting as "luck" because the sample size is so small.  That's all I'm saying and there's no refuting it.

Probabilistically, it's no different than making a coin that comes up tails 65% of the time and just betting the match on a coin flip.  The fact that you're really flipping 18 different coins doesn't matter, because you can represent the overall probability as a single game probability.  It yields the same result statistically.  I can prove this as a simple mathematical exercise.

As to "You don’t even know how many matches need to be won to make top 8!  It takes 6 matches of 8 rounds to make top 8, not 7.  6-0-2 always makes top 8," that's all about the size of the tournament.  See Harlequin's analysis if you're concerned about my choice of cut-off.
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« Reply #94 on: July 06, 2006, 02:09:41 pm »

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.


See bolded text. My post said that given a situation where there are two outcomes, each of which has a certain probability of happening, if your outcome's result is the lesser likely of the two, then that constitutes being "lucky" FOR THAT SPECIFIC SITUATION.

Let's take a look at the die roll. Given a D-20, each roll value is as likely as another at 1/20 probability. So, given the roll taking place, we can choose any number as the result; let's say that your opponent rolls a 14; that's a pretty good roll because it's above average numerically. Now for your turn. Of the 20 possible rolls, 6 of them (15-20) result in success, 13 (1-13) result in failure, and 1 (14) results in the scenerio repeating itself from the beginning. For your roll, you only have a 30% chance of winning but a 65% chance of losing (and a 5% chance of repeating itself from the beginning). If you win this, then you could be considered lucky. Yes, someone HAD to win, but once enough of the variables are put into place so that odds can be calculated, it can be CLEARLY seen that you are either in a favorable or unfavorable situation.


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« Reply #95 on: July 06, 2006, 02:17:32 pm »

Quote
My position is actually a lot simpler than that: if you're top 8ing more often than your win rate predicts, it's due to luck (aka sampling error).

Or, of couse, it is possible that your "win rate" isn't accurate.
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« Reply #96 on: July 06, 2006, 02:37:56 pm »

Quote
My position is actually a lot simpler than that: if you're top 8ing more often than your win rate predicts, it's due to luck (aka sampling error).

Or, of couse, it is possible that your "win rate" isn't accurate.

Theoretically, your "win rate" would be determined over a few million matches.  A hundred matches would yield a decent approximation.  You'd use matches (as opposed to individual games) to include the psychological and sideboarding effects Steve mentioned.  You'd then derive a game win rate from that, or just keep it as a match rate.  Since the effects Steve mentioned factor into your numbers already, you could safely ignore them.

You're perfectly corrent that accuracy is a concern.  The number that I'd like to hang my hat on is that t8ing 75% of the time requires that you win 75% of your games.  It gets rid of semantic debates about how close vintage decks are to 50-50 because 75-25 is way beyond anything reasonable unless you assume that *most* players (more than 50%)  are outright awful. 

"Duh, I drew Ancestral Recall, Time Walk, Tinker, Force of Will x2, Island, and Mana Crypt.  I really ought to mulligan.  This hand sucks!"  I mean, they'd all almost have to be that stupid.  Or playing Angels.dec, or Sui 1998.
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« Reply #97 on: July 06, 2006, 05:52:58 pm »

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 don't think that anyone is saying that luck will ever completely control a match. Luck never completely controls a poker game. And while I'm happy to admit that Magic is a much more complex game than Poker is, the best of play can still always be unraveled by the turn of a card. It's a lot harder for that to happen in Magic, since players are usually working with 2 or 3 outs in a 60 card deck instead of 15 in a 52 card deck as in Poker (not to mention the number of times that you need to catch runner-runner precisely to not lose), but it can happen and to say otherwise is both foolish and possibly cheating.

The reason why people are arguing with you, Steve, is because your initial argument was that luck cannot affect the game in a significant way. Now, just because it has never happened to you, or just because bad players blame the fates for their bad play, does not mean that it can't happen. The cards are random, so anything can happen. That's the fun of the game. Even the worst player can beat the best player once in a while, but not often enough as to obliterate skill.

It is highly unlikely that you will lose a match due to luck. In Vintage it's even harder given that players don't get as many draw steps to suck out with, though each drawstep is potentially more powerful than in any other format. But to say it's impossible is a gross exaggeration. Your statement was that you cannot lose with Grim Long unless you make a mistake, which is hilariously false. Unless you know the positions of the cards in your deck, you can never be certain that skill alone will keep you from losing.
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« Reply #98 on: July 06, 2006, 07:38:07 pm »

Quote from: Hi-Val
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.


No douchebaggery detected : )

What I was saying was that if the odds are 1/5 (I think I effed up with 1:5 earlier, is that incorrect notation? I think I mean 1:4 like you wrote) then over an n large sample of previous gamestates with exactly the same odds, you'd have results that fit the odds. My point is that we don't remember when things go badly, we remember when HE RIPPED THE HELIX!!! or situations like that. Rolling a die six times and getting each face exactly once isn't going to happen, but on a long enough timeline, you'll have results that mimic the probabilities. I think we're in violent agreement with each other.

There's a book I'm finishing now called "Chances Are: Adventures in Probability" by Kaplan and it's positively fascinating. Not a lot of daunting math problems in it and if nothing else, it has an incredible chapter on insurance and its history and function. I suggest it to people interested in probabilities.

For the record, I don't believe that luck exists at all.
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« Reply #99 on: July 06, 2006, 09:07:15 pm »

There's a book I'm finishing now called "Chances Are: Adventures in Probability" by Kaplan and it's positively fascinating. Not a lot of daunting math problems in it and if nothing else, it has an incredible chapter on insurance and its history and function. I suggest it to people interested in probabilities.
I read that a few weeks ago. It's good, but it covers a whole lot of basic stuff, math-wise.

I think part of the problem here is that people are blaming luck for losses (or wins) instead of looking at it as just setting the parameters of the game. Sure, some games are much easier to win than others, but provided your deck is powerful enough, almost every game is potentially winnable, provided you make no mistakes. Sure, there will be times where you mulligan three times into a duress, but the frequency of such games is extremely low; you can go through tournaments without running into even one such nigh-impossible game. Every other game, if you are good enough, is winnable, and that means every match is winnable, too. Sometimes the game will be so hard that you just give up and lose, but if you had played better, you could have won. No one in this thread is going to convince me that they make less than one real mistake per game, and honestly almost all of us are making multiple mistakes each turn. In a situation like that, claiming that luck has anything to do with the outcome of a match is just silly. We earn all our losses the hard way--by making mistakes in games we could have won (frequently because we're playing the wrong deck, or a misbuilt version of the right deck).
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« Reply #100 on: July 06, 2006, 09:45:18 pm »

That's an interesting way to put it, and certainly something I'd agree with. I simply take exception to a person who uses absolutes. Magic is much more about skill than pretty much any other card game, simply because there are so many mitigating factors, but I've gotten wins that have felt (and been) pretty damn lucky. Better play would have resulted in me having won earlier or not having been in that situation, but that doesn't mean that I didn't get lucky at that moment. Perhaps (not perhaps, absolutely) better play on my opponent's part would have prevented me from getting lucky in these spots, but perhaps I was also able to use all of my skill to put me into a position to get lucky. I don't think that you can completely separate luck from skill in this game. And while you can't rely on luck, sometimes it'll surprise you.

And as a note, the notation for 1/5 or 20% is 4:1 against because you have 4 chances to lose versus 1 chance to win for a total of 5 possible chances. 5:1 would be 1/6 or 18.3333%.
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« Reply #101 on: July 07, 2006, 04:20:59 am »

On this interesting subject, why not let the master say a few words.

Quote from: Richard Garfield
I believe that the standard dichotomy of luck versus skill is misleading. This comparison implies that the more luck there is, the less skill and vice versa. To me, this is not at all true. The reward for skill depends on how much luck there is in a game, but a game that is mostly determined by luck can have an enormous amount of skill.

Quote from: Richard Garfield
The amounts of skill and luck in a game are unrelated, though they have a related influence on the game's outcome. If you want to minimize luck, you should play the game as many times as possible.

If you want to read the whole article, you can find it in The Duelist magazine NO.19 (October 1997). Wink
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« Reply #102 on: July 07, 2006, 05:26:11 am »

A lot of what has been said here relates to the Law of Large Numbers (often called the Law of Averages by non-statisticians), that is:

Quote
The rule or theorem that the average of a large number of independent measurements of a random quantity tends toward the theoretical average of that quantity.

Because Magic is inherently a game of probability (unless one cheats), the Law of Large Numbers applies to it. A lot of statements in this thread are just restatements of the above Law specific to the situation.

Quote from: Richard Garfield
If you want to minimize luck, you should play the game as many times as possible.

Quote
Poker is a game of luck in the short term, but a game of skill in the long run.

So, does Magic have Luck? The answer depends on the definition of the term 'luck'.
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« Reply #103 on: July 07, 2006, 11:26:25 am »

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 it's 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.  You're saying that all of your decisions were perfect and that you played the perfect deck with the perfect sb. 

Thats pretty dangerous too. It is easy to go back after something happened and say, ya I should have vhad this in my board, etc... Thats like folding 2-7 off, and the flopp coming 772. Was that a bad decision? No. In retrospect, sure it was.

I agree that luck plays a small factor. But it still certainly does. You can't decide to mulligan based on an opponents hand. So your decision to keep or mulligam may cause you to lose a game whereas had you done the opposite, you would have likely won. A good example is the control mirror (slaver). On the draw, Library of Alexandria is absoulutely golden. Your opponent on the play may have duresses and or strip in his hand, but cant seriously mulligan to 6 in order to beat a hand with Library. It

In my mind, it is "lucky" when my opponenet draws the one card I can't deal with, and completely owns me. Just like it is lucky when the Grim Long player draws Lotus. As Steve has said before, he RARELY loses when Lotus is in his starting hand. That's not a matter of skill. That is luck. You have to be lucky to be good. Plain and simple.
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« Reply #104 on: July 07, 2006, 12:57:54 pm »

That's an interesting way to put it, and certainly something I'd agree with. I simply take exception to a person who uses absolutes. Magic is much more about skill than pretty much any other card game, simply because there are so many mitigating factors, but I've gotten wins that have felt (and been) pretty damn lucky. Better play would have resulted in me having won earlier or not having been in that situation, but that doesn't mean that I didn't get lucky at that moment. Perhaps (not perhaps, absolutely) better play on my opponent's part would have prevented me from getting lucky in these spots, but perhaps I was also able to use all of my skill to put me into a position to get lucky. I don't think that you can completely separate luck from skill in this game. And while you can't rely on luck, sometimes it'll surprise you.

This can be taken as skilled play.  Lets say you are playing your Aggro RWG deck against, say, a B/W Deck in standard.  Lets say you are falling behind on the board, and for about 3-4 turns, you use your creatures to chump block and sneak in a point whenever possible, and throw any burn you have at their head.  Eventually, it gets to your last turn, lethal on the board against you, opponent on, say, 3 life.  You have to draw a burn spell (of which you run 7 or 8) right now or lose the game.  Turns out, this time you rip it, and everyone declares how lucky that was.  Now, not to say that you didn't beat the odds there, but it was skilled play that even caused that situation to happen.  Had you not planned turns ahead, planned to make this topdeck count, you could have been dead a turn or two ago, or left your opponent out of range.  Similar is T1, where you need to topdeck something for the win.  The better you play, the better your chances.  You can create more and more outs, until eventually you hit one and just win the game because of your skilled play.

I agree that there are very rare games that a player just CANNOT win.  There is almost always some choice you could have made which would have given you an equal shot at every game.  As Jacob said, EVERYONE makes many mistakes, often multiple per turn, especially in Type1 where there are so many chances to mess up every turn.  There is no one here who can claim they built their deck and played their matches perfectly and still lost.

As an empyrical example, take Steve vs. Rich, when Steve won on his first turn of 2 or the 3 games.  Shortly thereafter, Rich was seen with Leylines in his board.  Some would argue Rich had no shot against Steve's hands and his play that match, but that just isn't correct.  It's a great example of where Deckbuilding is a huge part of skill.  Rich did not have enough respect for the speed of Grimlong, and chose not to sideboard Leylines in order to prevent fast kills, so he paid for it.

Steve has said he rarely loses when he draws Lotus.  I agree completely, most hands in Grim with Lotus are not whether I can win, but how to best do it.  However, that is not to say it is academic.  Even with that card, any mistakes the Grim player makes can throw the game away.  Similarly, the opponent can still make plays to slow or stop the Grim player (if Grim is on the draw, you could have chalice or null rod in your deck, for example).  Having Lotus makes the decisions easier for me, because there are many different paths which will lead to victory, so it is much easier to find one (not necessarily the best one, but a good enough one).  The dilemna hands presented all have roads to victory, but all are very difficult to find and VERY difficult to find the absolute best one.  Steve doesn't draw Lotus in his opening hand any more than any other player on earth.  He runs the same number as the rest of us.  Over the course of a match and a tournament, he gets the same number of Lotus starts as any other player there, on average, but it just so happens that his deck is optimized to win on the first turn when it gets one, whereas something like Fish is hardly going to go insane with the card.   That is a function of his skill in building and choosing his deck: he has optimized the deck to win when it draws lotus.  How often do you win when you get turn1 Ancestral in something like Slaver?  Turn1 3sphere in stax?  It is a very similar setup; it doesn't seem as overpowering, like 3sphere, but in Steve's deck its the closest analogue.

I do think there is some luck involved; drawing good opening hands, good topdecks, things like that.  But, much more than that is the skill involved to make the most of it.  Matches are won on skill, not luck.  The better you play, the "luckier" you may seem when you get good topdecks, but those topdecks are only good because you have played to make them good.  Every match in Type1 where I've lost, especially with Grim, there is something I could have done to change things.  I could have run rebuild, I could have gotten Jar instead of DSC, I could have run Force in the board, I could have taken a different card with duress.  All are mistakes that made me lose, and all could ahve been avoided by a higher skill level.  How often can you think of more than one game a tournament that you sincerely could not win?
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