Variance is the random nature of the game. You don't know what cards you will draw or what cards your opponent will have. By comparison Chess has zero variance because the pieces are all visible and never change.
Variance is the random nature of the game. You don't know what cards you will draw or what cards your opponent will have. By comparison Chess has zero variance because the pieces are all visible and never change.
Actually, chess also has variance, otherwise whoever goes first would always win. The variance in chess however comes from your opponent, how they play, their skill etc.
But yes, In magic there is a lot of variance. Your seven card opening, the fact you occasionally mulligan, the fact that sometimes a card will just stick and win you a game (The pro tour game when a mono black player played zero spells and reduced his control opponent to 0 life due to a mutavault and the fact his opponent drew no answer or sphinx's revelation).
That said, the game also has reliability built into it during deck construction. Sure you can't guarantee you'll draw a sylvan caryatid, but you can make it really damn likely.
Variance is the random nature of the game. You don't know what cards you will draw or what cards your opponent will have. By comparison Chess has zero variance because the pieces are all visible and never change.
Actually, chess also has variance, otherwise whoever goes first would always win. The variance in chess however comes from your opponent, how they play, their skill etc.
But yes, In magic there is a lot of variance. Your seven card opening, the fact you occasionally mulligan, the fact that sometimes a card will just stick and win you a game (The pro tour game when a mono black player played zero spells and reduced his control opponent to 0 life due to a mutavault and the fact his opponent drew no answer or sphinx's revelation).
That said, the game also has reliability built into it during deck construction. Sure you can't guarantee you'll draw a sylvan caryatid, but you can make it really damn likely.
Have to say, your post seems generally wrong on the points it is making.
Variance is the random nature of the game. You don't know what cards you will draw or what cards your opponent will have. By comparison Chess has zero variance because the pieces are all visible and never change.
Actually, chess also has variance, otherwise whoever goes first would always win. The variance in chess however comes from your opponent, how they play, their skill etc.
But yes, In magic there is a lot of variance. Your seven card opening, the fact you occasionally mulligan, the fact that sometimes a card will just stick and win you a game (The pro tour game when a mono black player played zero spells and reduced his control opponent to 0 life due to a mutavault and the fact his opponent drew no answer or sphinx's revelation).
That said, the game also has reliability built into it during deck construction. Sure you can't guarantee you'll draw a sylvan caryatid, but you can make it really damn likely.
Have to say, your post seems generally wrong on the points it is making.
On what basis? that every game has variance? that Magic's variance is really dependent on draws?
I just would like to hear it explained in mtg words/how it translates to mtg.
Variance is technical term in probability and statistics. By the "method of moments" it is the natural way to describe the spread of a probability distribution. The variance and the standard deviation, which is derived from it, hold a special place in mathematics because they are the basis of the computationally simplest analytic form of linear regression (as in you can use them to find the "line of best fit" by hand).
What is meant by "variance" in MTG is the unpredictable behavior of the game or of a particular deck. High variance indicates that extremely good and extremely bad outcomes are common while low variance indicates that the deck tends to play similarly every time. There are a few things we can mean by variance in MTG. A combo deck might be said to be high variance because its opening hands have little in common but we might also say that the deck is low variance (or "consistent") if most of those hands will lead to a win anyway. In practice it is difficult to quantify the variance of a deck but comparisons are still possible. For instance we can reduce variance by playing many copies of an important card, for instance having four copies of Llanowar Elvesand four copies of Elvish Mystic hugely reduces variance compared to just running a single Elvish Mystic because you will consistently have a 1/1 Elf Druid that taps for mana.
The attached image shows the effects of variance, the higher the line the greater the probability of a result. In red we see low variance, the probability of extremely good or extremely bad outcomes is low. In blue we see high variance, the probability of extreme outcomes is much greater.
Variance is a measure of how far an outcome can differ from predicted.
In the statistical sense, all cards that don't have a luck element (e.g. no coin flips, no clash) have zero variance, because they do exactly the same thing when you cast them, every time. A Lightning Bolt will deal 3 damage every time you cast it, for example. It doesn't sometimes do 2 and sometimes 4.
A hypothetical coin-flip burn spell which deals 4 damage on heads and 2 on tails has variance. Another burn spell which does 6 on heads and 0 on tails has even more variance.
One example of an actual card with variance is Groundswell. Sometimes it gives +2/+2, sometimes it gives +4/+4. Giant Growth, on the other hand, always gives +3/+3.
When is Groundswell better? When you have an evasive 1/1 and you need to deal at least 5 damage to your opponent to win. Giant Growth only gives +3/+3, leaving you 1 damage short. Groundswell may give +2/+2 if you can't turn on landfall, but if you can (with a non-zero probability), then you win.
When is Giant Growth better? When you have an evasive 1/1 and you need to deal at least 4 damage to your opponent to win. Giant Growth is guaranteed to kill, while Groundswell may fail you because you couldn't turn on landfall.
HOWEVER...when people talk about "variance", they mean it in the general sense of "how often is this card good/bad?" Sometimes this depends on your deck (e.g. "how often does my deck end up in situations where I need to deal 5 damage with a 1/1 to win?"), but it can also depend on what your opponent is playing.
Take the example of Keldon Marauders in Burn. If your opponent can't remove or block it, it's very efficient - it deals 5 damage for 2 mana. On the other hand, if your opponent had a removal spell for it, it only deals 2. That's a pretty bad deal when something like Skullcrack does 3.
So Keldon Marauders has a noticeable amount of variance to it - it can do more than a burn spell of the same mana cost, or less, depending on your opponent.
Tournament structure also leads to people choosing "high-variance" decks. Suppose you have the choice of two hypothetical decks, one of which goes 2-2 all of the time, and one which goes 0-4 half the time and 4-0 the other half. If your goal is to 4-0 an event, you should pick the latter deck. Like the Groundswell example above, if you play the guaranteed 2-2 deck, you are guaranteed NEVER to 4-0.
- Take the example of Keldon Marauders in Burn. If your opponent can't remove or block it, it's very efficient - it deals 5 damage for 2 mana. On the other hand, if your opponent had a removal spell for it, it only deals 2.
Obv, something is amiss here, the 1 card that opponent used (but still do 2 dmg). An mtg player understands that this matter, so context matters.
I think we can conclude that lower variance has nothing to do with increasing the skill-factor of the game, in fact the reality is the opposite.
For any pair of events (original event and subsequent event), "variance" is the term that describes the distribution of subsequent events.
Variance is a measure of consistency. If event B always follows event A, then the series of events has low variance (alternatively, it's very consistent). For most things that don't have a determined outcome, there are usually a bunch of different subsequent events that can follow the original one. This creates a probability distribution, which is a measure of how likely an event is.
As an example, imagine that you roll a single 6-sided die. These are the odds at which you get each possible sum:
1: 1/6
2: 1/6
3: 1/6
4: 1/6
5: 1/6
6: 1/6
Notice that there is a 100% chance of getting an outcome (the sum across all of the probabilities is 1). In this case, there is an equal probability of getting any number.
Now imagine that you roll two dice. These are the odds at which you get each possible sum:
2: 1/36
3: 2/36
4: 3/36
5: 4/36
6: 5/36
7: 6/36
8: 5/36
9: 4/36
10: 3/36
11: 2/36
12: 1/36
What you'll notice, is that there is still a 100% chance of getting an outcome (the sum across all of the probabilities is 1). The most likely outcome is 7 (it has the maximum probability in the spread).
Variance is the measure of how narrow the probability distribution is. When you rolled the one die, it had high variance, relative to the time that you rolled two die. This is because the two-die case had a concentration of the outcomes was weighted around a single, most likely point.
High variance means an event happens inconsistently. Low variance means that the same event tends to happen consistently. That event can either happen, not happen, or have a fixed-percent chance of happening; variance only cares that the outcome doesn't easily change.
In Magic, variance is still a measure of consistency. People will use the word in a variety of different contexts, but the idea is that "low variance" tends to be good. If you need your deck to perform consistently, for a long period of time (for example, in a big tournament), then you want your deck to be low variance. If your deck is high variance, then it will perform well in some games, and poorly in others.
For individual cards, variance tends to refer to how useful an individual card is in any given match. Cards like Lightning Bolt tend to be useful in every match, so they're thought of as low variance. For cards like Stony Silence, the card will be excellent in certain matchups (and formats), but terrible in others. Generally, cards that are low variance tend to get maindecked, and cards that are high variance end up in a sideboard (and then used when they're good).
For players, variance tends to refer to how consistent your playstyle is. This is pretty hard to measure, but the idea is that certain players perform more consistently than others (consistently good, bad, or anything in between). In general, you want to have a low variance playstyle, and you want to play well.
I think we can conclude that lower variance has nothing to do with increasing the skill-factor of the game, in fact the reality is the opposite.
In a technical sense, you can be bad, and still consistent. So variance is, technically, independent of skill.
However, the way that most people use the term "variance", the more skilled you are, the better you are at reducing variance. The idea is simple: the better you are as a player, the more likely you are to be able to reduce the randomness in your games. There will always be things that are outside of your control (like what cards you draw). But highly skilled players build low variance decks, and make low variance play decisions. Consequently, good players tend to have low variance, relative to other players.
Playing millions of cards every turn... Slowly and systematically obliterating any chance my opponent has of winning... Clicking the multitude of locking mechanisms into place... Not even trying to win myself until turn 10+ once I have nigh absolute control... Watching my opponent desperately trying to navigate the labyrinthine prison that I've constructed... Seeing the light of hope fade and ultimately extinguished in an excruciatingly slow manner... THAT'S fun Magic.
We have 2-3 users that are dramatically making this thread incomprehensible and non-productive for anyone else to possibly join in the discussion. This needs to change.
Every time I see [ktkenshinx] post in here, I get the impression of a stern dad walking in on a bunch of kids trying to do something dumb and just shaking his head in disappointment.
Near Mint: The same as Slightly Played, but we threw some Altoids in the box we stored it in to cover up the scent of dead mice. Slightly Played: The base condition for all MTG cards. This card looks OK, but there’s one minor annoying ding in it that will always irritate and distract you whenever you draw it. Moderately Played: This card looks like it survived the Tet Offensive tucked inside the waistband of GI underwear. It may smell like it, too. Heavily Played: This card looks like the remains of Mohammed Atta’s passport after 9/11. It may be playable if you double-sleeve it to stop the chunks from falling out. The condition formerly known as "Washing Machine Grade" Damaged: This card is the unfortunate victim of a Mirrorweave/March of the Machines/Chaos Confetti/Mindslaver combo.
[M]aking counterfeit cards is the absolute height of dishonesty. Ask yourself this question: Since most people...are totally cool with the use of proxies...what purpose do [high] quality counterfeit cards serve?
Variance is often also used to refer to mechanics or even an entire environment. For instance, Suspend is a high-variance mechanic. An Errant Ephemeron in your opening hand is WAY better than one drawn on turn 5 or so.
Other high-variance mechanics are Clash and Bloodthirst. Mechanics can also be high variance if they require multiple things to work together. For instance, a heroic deck in Theros limited requires some number of heroic creatures and some number of heroic enablers, and is AMAZING if you get just the right ratio, but can just do stone nothing if you don't. Compare that to a deck that is just full of individually powerful cards, where any draw is just about as good as any other draw (barring mana issues, which of course affect every kind of deck).
Similarly, a limited format which encouraged you to play lots of colors but didn't offer very good color support could be high variance if the best strategy was to end up with a shaky mana base and a very powerful deck. All the shaky mana bases mean more games decided by mana issues, thus increasing the variance.
Gamble 2, get back 4 or 0. This is the one with least variance.
Gamble 3, get back 6 or 0, Gamble 7, get back 0 or 14..... Variance gets higher and higher.
I get the point, but I must point out that it requires more to describe the reality of happens in mtg.
What some people describe as a high/low variance situation is really just a wrongly calculated situation.
You go for the one with least variance and gamble 1 to hopefully get 2, when the situation in fact is so that
if you had gambled 3 you would have the chance to get back 7 (and not 6), in this choice it is wrong to gamble 1(unless you only need to win 2 in order to win the whole game). Choosing low variance in situation where the high variance choice is of equal ratio (1:2 and 4:8) has the advantage that you
get to do it more times, and that means a greater chance for the opponent to make mistakes (assuming the first player expects he is better at the game (routines) than the opponent(especially thinking of not 'slipping up' in this case)).
Being aware of what choices (gambles) that are available is the key mtg ability I think.
The ability to adapt is important in this.
Actually, chess also has variance, otherwise whoever goes first would always win. The variance in chess however comes from your opponent, how they play, their skill etc.
MTG also has this sort of variance, as different people respond differently to the same situation. This is a different kind of variance because collectively the players have complete control (as opposed to games with actual variance like dice or shuffled cards). Another type of variance comes from games where game theory is required for optimal play (randomizing your moves), but I won't get into that!
Also, it has never been proved that a perfectly played game of chess should go to white. It's theoretically possible that chess should always be a draw, or even that the game starts in zugzwang!
A deck of 60 basic forests would have 0 variance, it does what it does all the time 100%.
A deck with 30 basic forest and 30 grizzly bears would be pretty low on variance aswell.
Burn for example has a low level of variance, as many cards more or less do the same.
A combo deck would have a giant amount of variance, but trys to reduce it with card draw spells and especially tutors to increase consistency and reduce variance.
Same is true for a mana base. If you play 2 colors and you have to play basics, your variance is quite big, as you have many draws in which you miss a color. If you can build your manabase out of lands that all produce both colors, the variance is equal to a mono-colored deck again.
Even a 5-color deck can have a variance like a mono-colored deck, if all its lands produce every color ; which was at least semi-true for the Vivid lands, as decks could play Cloudthresher, Cryptic Command, Cruel Ultimatum in the same deck.
In Limited especially you would try to reduce variance by playing as mana 2-3-4 frops as you can, and avoid the 5+ drops , so your deck can operate with the usual 3-4 lands you will "guaranteed" to see (as you can keep a hand with them allready).
I think we can conclude that lower variance has nothing to do with increasing the skill-factor of the game, in fact the reality is the opposite.
I disagree. A deck that has less variance means you have to know when to mulligan and what you need in an opener of 7 cards, 6 cards.. and so on. It is harder to play a deck with less variance so its pilot needs more skill to recognize what needs to be done when.
I think we can conclude that lower variance has nothing to do with increasing the skill-factor of the game, in fact the reality is the opposite.
I disagree. A deck that has less variance means you have to know when to mulligan and what you need in an opener of 7 cards, 6 cards.. and so on. It is harder to play a deck with less variance so its pilot needs more skill to recognize what needs to be done when.
What is a deck that has less variance ?
And what does a high variance deck that doesn't need mulligan decisions look like ?
I think we can conclude that lower variance has nothing to do with increasing the skill-factor of the game, in fact the reality is the opposite.
I disagree. A deck that has less variance means you have to know when to mulligan and what you need in an opener of 7 cards, 6 cards.. and so on. It is harder to play a deck with less variance so its pilot needs more skill to recognize what needs to be done when.
What is a deck that has less variance ?
And what does a high variance deck that doesn't need mulligan decisions look like ?
Burn in most formats is a low variance deck that doesnt need mulligans too often. Most single color properly curved decks have low variance. Of course that doesnt mean it never will need a mulligan, but they are less then say a 3 color deck or 5 color deck. In a multicolor deck even with the proper curve will need certain lands in the opener to play things on turn. You can have a perfect mana base and you will mulligan more then a single color deck.
Thats not to say single color decks are less skill intensive, just a different set of skills. SIngle color decks rely heavy on drawing correctly and that is a variance you just can not control. Even with cheap efficent draw spells, you can hit all lands when you dont need them or spells you cant play.
One thing that is a variance that differs from player to player is certain players can play certain decks better then other players. So play style comes into play with variance. You can give a burn deck to 10 different players and have the deck stacked the exact same way for each player, and you will get 10 different ways to play out the game. Same for a 2 color deck, and 3 color.
There are so many variances in the game its really hard to pinpoint just one. From decks, to play style, to format, to match ups, to deck bulding, to mana bases. I am sure I missed something.
I think you are looking for a deck that requires little to no thinking and the way the game is made, there just isnt any. You can play a deck perfectly and still lose, on the other hand you can play a match and make some glaring mistakes and still win. That is just the way the variance works in this game.
Variance is the random nature of the game. You don't know what cards you will draw or what cards your opponent will have. By comparison Chess has zero variance because the pieces are all visible and never change.
Actually, chess also has variance, otherwise whoever goes first would always win. The variance in chess however comes from your opponent, how they play, their skill etc.
But yes, In magic there is a lot of variance. Your seven card opening, the fact you occasionally mulligan, the fact that sometimes a card will just stick and win you a game (The pro tour game when a mono black player played zero spells and reduced his control opponent to 0 life due to a mutavault and the fact his opponent drew no answer or sphinx's revelation).
That said, the game also has reliability built into it during deck construction. Sure you can't guarantee you'll draw a sylvan caryatid, but you can make it really damn likely.
Have to say, your post seems generally wrong on the points it is making.
On what basis? that every game has variance? that Magic's variance is really dependent on draws?
No I think your wrong here, Chess has no variance, there is no "Random Factors" and victory is determined solely by out playing your opponent. Ultimately chess can be solved solely from board state and why being able to see sufficient moves ahead is the key to winning. I have a vague quote in mind of something like the victor is the one who makes the next to last mistake.
I think we can conclude that lower variance has nothing to do with increasing the skill-factor of the game, in fact the reality is the opposite.
I disagree. A deck that has less variance means you have to know when to mulligan and what you need in an opener of 7 cards, 6 cards.. and so on. It is harder to play a deck with less variance so its pilot needs more skill to recognize what needs to be done when.
What is a deck that has less variance ?
And what does a high variance deck that doesn't need mulligan decisions look like ?
Okay. Talking about variance in mtg can lead to confusion at times because people will say "variance" without labeling the important part: variance of what. On the card level, we could be talking about the dispersion on that cards performance. On the deck level, it could be about the dispersion of how the deck may perform in a game. We could even talk about it as the dispersion of how a player plays the game. Making matters worse for using the term "variance," it isn't really worth the time to make a map and represent each possible outcome with a number to actually calculate variance.
Then, people (particularly in Legacy) say "low variance" decks, but most often they're not referring to Burn. They're referring to decks with Brainstorm, Ponder, Green Sun's Zenith, or Sensei's Divining Top which allows the deck to find what it's looking for more often. People often say that better players will pick decks with less variance, but that isn't really what is is going on. As pointed out, Burn is a deck with very low variance, but a lot of players stay away from it. I'd say that more skilled players tend towards decks that allow them to make more meaningful decisions (or more accurately that less skilled players tend towards decks with less meaningful decisions, lowering the number of times they "screw up" over a tournament). It just so happens that many of the variance reducing cards also happen to be cards that force you to make a lot of decisions. Thus, the answer to whether or not lower variance in decks increases the skill factor of a game is really..."it depends."
[quote=Dinofish]A deck that has less variance means you have to know when to mulligan and what you need in an opener of 7 cards, 6 cards.. and so on.
I'm not convinced. Mulligans decisions are tough (when they are not obvious) because we have to weight the potential risk with the against the potential reward. A high variance deck by definition offers higher risks and bigger rewards - you have more to gain and more to lose. When variance is lower, you have less to gain and less to lose - meaning it doesn't matter as much either way.
An interesting point - there are to ways to measure the role of skill in a game. The first asks how big an advantage one gets from optimal play (vs merely good play); the second asks how difficult it is to play optimally (regardless of the size of the advantage so gained).
Imagine we play chess, but agree that after the game we roll a die,and call the game a draw on a result of 1-5. This (silly) variant reduces the advantage gained by skill, but does not actually reduce the skill level required to play the game well.
Are you saying low variance makes it harder to play optimally, or offers bigger rewards for optimal play?
[quote from="Mistermind »" url="http://www.mtgsalvation.com/forums/magic-fundamentals/magic-general/596453-what-is-variance?comment=2"]Actually, chess also has variance, otherwise whoever goes first would always win
there is a demostration for this?
anyway, think as variance as "the numbers of different scenarios that could happen", high variance means a lot of escenarios, and low variance means few.
for example, other than deck variance there is also meta game variance, standard have a lot less variance than modern for example
Ultimately chess can be solved solely from board state
There's currently no evidence that chess can be solved.
Currently chess requires a great deal of information not available on the board, mainly how the other player will react, which is how human-vs-computer games are currently approached.
No I think your wrong here, Chess has no variance, there is no "Random Factors" and victory is determined solely by out playing your opponent. Ultimately chess can be solved solely from board state and why being able to see sufficient moves ahead is the key to winning. I have a vague quote in mind of something like the victor is the one who makes the next to last mistake.
I think there are some subtle ways in which there is variance in Chess. For instance, there might be some rock-paper-scissors in the pairings... one chess player is an expert at the endgame but poor at the beginning game, so might do better or worse depending on the skills of his opponent.
You could also argue that the fact that the same two players can play 10 games and NOT have identical results each time suggests that there is some level of variance... kind of in the purest definition of the word.
Back to magic, it's definitely the case that a low-variance deck is easier to mulligan. You can see this by taking it to an extreme... a deck of 20 mountains and 40 lightning bolts is very easy to mulligan, because you'd only mulligan if you had too few or too many lands. Which can possibly still be tricky, but a lower variance deck will still have to make those too few/too many decisions, plus all the other more complicated decisions that come from having more than one unique spell in the deck.
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I just would like to hear it explained in mtg words/how it translates to mtg.
Actually, chess also has variance, otherwise whoever goes first would always win. The variance in chess however comes from your opponent, how they play, their skill etc.
But yes, In magic there is a lot of variance. Your seven card opening, the fact you occasionally mulligan, the fact that sometimes a card will just stick and win you a game (The pro tour game when a mono black player played zero spells and reduced his control opponent to 0 life due to a mutavault and the fact his opponent drew no answer or sphinx's revelation).
That said, the game also has reliability built into it during deck construction. Sure you can't guarantee you'll draw a sylvan caryatid, but you can make it really damn likely.
On what basis? that every game has variance? that Magic's variance is really dependent on draws?
Variance is technical term in probability and statistics. By the "method of moments" it is the natural way to describe the spread of a probability distribution. The variance and the standard deviation, which is derived from it, hold a special place in mathematics because they are the basis of the computationally simplest analytic form of linear regression (as in you can use them to find the "line of best fit" by hand).
What is meant by "variance" in MTG is the unpredictable behavior of the game or of a particular deck. High variance indicates that extremely good and extremely bad outcomes are common while low variance indicates that the deck tends to play similarly every time. There are a few things we can mean by variance in MTG. A combo deck might be said to be high variance because its opening hands have little in common but we might also say that the deck is low variance (or "consistent") if most of those hands will lead to a win anyway. In practice it is difficult to quantify the variance of a deck but comparisons are still possible. For instance we can reduce variance by playing many copies of an important card, for instance having four copies of Llanowar Elves and four copies of Elvish Mystic hugely reduces variance compared to just running a single Elvish Mystic because you will consistently have a 1/1 Elf Druid that taps for mana.
The attached image shows the effects of variance, the higher the line the greater the probability of a result. In red we see low variance, the probability of extremely good or extremely bad outcomes is low. In blue we see high variance, the probability of extreme outcomes is much greater.
In the statistical sense, all cards that don't have a luck element (e.g. no coin flips, no clash) have zero variance, because they do exactly the same thing when you cast them, every time. A Lightning Bolt will deal 3 damage every time you cast it, for example. It doesn't sometimes do 2 and sometimes 4.
A hypothetical coin-flip burn spell which deals 4 damage on heads and 2 on tails has variance. Another burn spell which does 6 on heads and 0 on tails has even more variance.
One example of an actual card with variance is Groundswell. Sometimes it gives +2/+2, sometimes it gives +4/+4. Giant Growth, on the other hand, always gives +3/+3.
When is Groundswell better? When you have an evasive 1/1 and you need to deal at least 5 damage to your opponent to win. Giant Growth only gives +3/+3, leaving you 1 damage short. Groundswell may give +2/+2 if you can't turn on landfall, but if you can (with a non-zero probability), then you win.
When is Giant Growth better? When you have an evasive 1/1 and you need to deal at least 4 damage to your opponent to win. Giant Growth is guaranteed to kill, while Groundswell may fail you because you couldn't turn on landfall.
HOWEVER...when people talk about "variance", they mean it in the general sense of "how often is this card good/bad?" Sometimes this depends on your deck (e.g. "how often does my deck end up in situations where I need to deal 5 damage with a 1/1 to win?"), but it can also depend on what your opponent is playing.
Take the example of Keldon Marauders in Burn. If your opponent can't remove or block it, it's very efficient - it deals 5 damage for 2 mana. On the other hand, if your opponent had a removal spell for it, it only deals 2. That's a pretty bad deal when something like Skullcrack does 3.
So Keldon Marauders has a noticeable amount of variance to it - it can do more than a burn spell of the same mana cost, or less, depending on your opponent.
Tournament structure also leads to people choosing "high-variance" decks. Suppose you have the choice of two hypothetical decks, one of which goes 2-2 all of the time, and one which goes 0-4 half the time and 4-0 the other half. If your goal is to 4-0 an event, you should pick the latter deck. Like the Groundswell example above, if you play the guaranteed 2-2 deck, you are guaranteed NEVER to 4-0.
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Big Johnny.
Obv, something is amiss here, the 1 card that opponent used (but still do 2 dmg). An mtg player understands that this matter, so context matters.
I think we can conclude that lower variance has nothing to do with increasing the skill-factor of the game, in fact the reality is the opposite.
Variance is a measure of consistency. If event B always follows event A, then the series of events has low variance (alternatively, it's very consistent). For most things that don't have a determined outcome, there are usually a bunch of different subsequent events that can follow the original one. This creates a probability distribution, which is a measure of how likely an event is.
As an example, imagine that you roll a single 6-sided die. These are the odds at which you get each possible sum:
1: 1/6
2: 1/6
3: 1/6
4: 1/6
5: 1/6
6: 1/6
Notice that there is a 100% chance of getting an outcome (the sum across all of the probabilities is 1). In this case, there is an equal probability of getting any number.
Now imagine that you roll two dice. These are the odds at which you get each possible sum:
2: 1/36
3: 2/36
4: 3/36
5: 4/36
6: 5/36
7: 6/36
8: 5/36
9: 4/36
10: 3/36
11: 2/36
12: 1/36
What you'll notice, is that there is still a 100% chance of getting an outcome (the sum across all of the probabilities is 1). The most likely outcome is 7 (it has the maximum probability in the spread).
Variance is the measure of how narrow the probability distribution is. When you rolled the one die, it had high variance, relative to the time that you rolled two die. This is because the two-die case had a concentration of the outcomes was weighted around a single, most likely point.
High variance means an event happens inconsistently. Low variance means that the same event tends to happen consistently. That event can either happen, not happen, or have a fixed-percent chance of happening; variance only cares that the outcome doesn't easily change.
In Magic, variance is still a measure of consistency. People will use the word in a variety of different contexts, but the idea is that "low variance" tends to be good. If you need your deck to perform consistently, for a long period of time (for example, in a big tournament), then you want your deck to be low variance. If your deck is high variance, then it will perform well in some games, and poorly in others.
For individual cards, variance tends to refer to how useful an individual card is in any given match. Cards like Lightning Bolt tend to be useful in every match, so they're thought of as low variance. For cards like Stony Silence, the card will be excellent in certain matchups (and formats), but terrible in others. Generally, cards that are low variance tend to get maindecked, and cards that are high variance end up in a sideboard (and then used when they're good).
For players, variance tends to refer to how consistent your playstyle is. This is pretty hard to measure, but the idea is that certain players perform more consistently than others (consistently good, bad, or anything in between). In general, you want to have a low variance playstyle, and you want to play well.
In a technical sense, you can be bad, and still consistent. So variance is, technically, independent of skill.
However, the way that most people use the term "variance", the more skilled you are, the better you are at reducing variance. The idea is simple: the better you are as a player, the more likely you are to be able to reduce the randomness in your games. There will always be things that are outside of your control (like what cards you draw). But highly skilled players build low variance decks, and make low variance play decisions. Consequently, good players tend to have low variance, relative to other players.
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Other high-variance mechanics are Clash and Bloodthirst. Mechanics can also be high variance if they require multiple things to work together. For instance, a heroic deck in Theros limited requires some number of heroic creatures and some number of heroic enablers, and is AMAZING if you get just the right ratio, but can just do stone nothing if you don't. Compare that to a deck that is just full of individually powerful cards, where any draw is just about as good as any other draw (barring mana issues, which of course affect every kind of deck).
Similarly, a limited format which encouraged you to play lots of colors but didn't offer very good color support could be high variance if the best strategy was to end up with a shaky mana base and a very powerful deck. All the shaky mana bases mean more games decided by mana issues, thus increasing the variance.
Gamble 3, get back 6 or 0, Gamble 7, get back 0 or 14..... Variance gets higher and higher.
I get the point, but I must point out that it requires more to describe the reality of happens in mtg.
What some people describe as a high/low variance situation is really just a wrongly calculated situation.
You go for the one with least variance and gamble 1 to hopefully get 2, when the situation in fact is so that
if you had gambled 3 you would have the chance to get back 7 (and not 6), in this choice it is wrong to gamble 1(unless you only need to win 2 in order to win the whole game). Choosing low variance in situation where the high variance choice is of equal ratio (1:2 and 4:8) has the advantage that you
get to do it more times, and that means a greater chance for the opponent to make mistakes (assuming the first player expects he is better at the game (routines) than the opponent(especially thinking of not 'slipping up' in this case)).
Being aware of what choices (gambles) that are available is the key mtg ability I think.
The ability to adapt is important in this.
MTG also has this sort of variance, as different people respond differently to the same situation. This is a different kind of variance because collectively the players have complete control (as opposed to games with actual variance like dice or shuffled cards). Another type of variance comes from games where game theory is required for optimal play (randomizing your moves), but I won't get into that!
Also, it has never been proved that a perfectly played game of chess should go to white. It's theoretically possible that chess should always be a draw, or even that the game starts in zugzwang!
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A deck with 30 basic forest and 30 grizzly bears would be pretty low on variance aswell.
Burn for example has a low level of variance, as many cards more or less do the same.
A combo deck would have a giant amount of variance, but trys to reduce it with card draw spells and especially tutors to increase consistency and reduce variance.
Same is true for a mana base. If you play 2 colors and you have to play basics, your variance is quite big, as you have many draws in which you miss a color. If you can build your manabase out of lands that all produce both colors, the variance is equal to a mono-colored deck again.
Even a 5-color deck can have a variance like a mono-colored deck, if all its lands produce every color ; which was at least semi-true for the Vivid lands, as decks could play Cloudthresher, Cryptic Command, Cruel Ultimatum in the same deck.
In Limited especially you would try to reduce variance by playing as mana 2-3-4 frops as you can, and avoid the 5+ drops , so your deck can operate with the usual 3-4 lands you will "guaranteed" to see (as you can keep a hand with them allready).
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I disagree. A deck that has less variance means you have to know when to mulligan and what you need in an opener of 7 cards, 6 cards.. and so on. It is harder to play a deck with less variance so its pilot needs more skill to recognize what needs to be done when.
And what does a high variance deck that doesn't need mulligan decisions look like ?
Burn in most formats is a low variance deck that doesnt need mulligans too often. Most single color properly curved decks have low variance. Of course that doesnt mean it never will need a mulligan, but they are less then say a 3 color deck or 5 color deck. In a multicolor deck even with the proper curve will need certain lands in the opener to play things on turn. You can have a perfect mana base and you will mulligan more then a single color deck.
Thats not to say single color decks are less skill intensive, just a different set of skills. SIngle color decks rely heavy on drawing correctly and that is a variance you just can not control. Even with cheap efficent draw spells, you can hit all lands when you dont need them or spells you cant play.
One thing that is a variance that differs from player to player is certain players can play certain decks better then other players. So play style comes into play with variance. You can give a burn deck to 10 different players and have the deck stacked the exact same way for each player, and you will get 10 different ways to play out the game. Same for a 2 color deck, and 3 color.
There are so many variances in the game its really hard to pinpoint just one. From decks, to play style, to format, to match ups, to deck bulding, to mana bases. I am sure I missed something.
I think you are looking for a deck that requires little to no thinking and the way the game is made, there just isnt any. You can play a deck perfectly and still lose, on the other hand you can play a match and make some glaring mistakes and still win. That is just the way the variance works in this game.
Decks where nearly each card does the same thing.
Burn is the closest. lightning bolt, chain lightning, etc.
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No I think your wrong here, Chess has no variance, there is no "Random Factors" and victory is determined solely by out playing your opponent. Ultimately chess can be solved solely from board state and why being able to see sufficient moves ahead is the key to winning. I have a vague quote in mind of something like the victor is the one who makes the next to last mistake.
Then, people (particularly in Legacy) say "low variance" decks, but most often they're not referring to Burn. They're referring to decks with Brainstorm, Ponder, Green Sun's Zenith, or Sensei's Divining Top which allows the deck to find what it's looking for more often. People often say that better players will pick decks with less variance, but that isn't really what is is going on. As pointed out, Burn is a deck with very low variance, but a lot of players stay away from it. I'd say that more skilled players tend towards decks that allow them to make more meaningful decisions (or more accurately that less skilled players tend towards decks with less meaningful decisions, lowering the number of times they "screw up" over a tournament). It just so happens that many of the variance reducing cards also happen to be cards that force you to make a lot of decisions. Thus, the answer to whether or not lower variance in decks increases the skill factor of a game is really..."it depends."
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It's the first definition
I'm not convinced. Mulligans decisions are tough (when they are not obvious) because we have to weight the potential risk with the against the potential reward. A high variance deck by definition offers higher risks and bigger rewards - you have more to gain and more to lose. When variance is lower, you have less to gain and less to lose - meaning it doesn't matter as much either way.
An interesting point - there are to ways to measure the role of skill in a game. The first asks how big an advantage one gets from optimal play (vs merely good play); the second asks how difficult it is to play optimally (regardless of the size of the advantage so gained).
Imagine we play chess, but agree that after the game we roll a die,and call the game a draw on a result of 1-5. This (silly) variant reduces the advantage gained by skill, but does not actually reduce the skill level required to play the game well.
Are you saying low variance makes it harder to play optimally, or offers bigger rewards for optimal play?
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Most low variance decks you can play perfectly and still lose. Low variance decks are much more forgiving so there is less reward in most cases.
there is a demostration for this?
anyway, think as variance as "the numbers of different scenarios that could happen", high variance means a lot of escenarios, and low variance means few.
for example, other than deck variance there is also meta game variance, standard have a lot less variance than modern for example
There's currently no evidence that chess can be solved.
Currently chess requires a great deal of information not available on the board, mainly how the other player will react, which is how human-vs-computer games are currently approached.
I think there are some subtle ways in which there is variance in Chess. For instance, there might be some rock-paper-scissors in the pairings... one chess player is an expert at the endgame but poor at the beginning game, so might do better or worse depending on the skills of his opponent.
You could also argue that the fact that the same two players can play 10 games and NOT have identical results each time suggests that there is some level of variance... kind of in the purest definition of the word.
Back to magic, it's definitely the case that a low-variance deck is easier to mulligan. You can see this by taking it to an extreme... a deck of 20 mountains and 40 lightning bolts is very easy to mulligan, because you'd only mulligan if you had too few or too many lands. Which can possibly still be tricky, but a lower variance deck will still have to make those too few/too many decisions, plus all the other more complicated decisions that come from having more than one unique spell in the deck.