Muliganing Stats

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I tried asking this in the General forum, but the people there believe that this information does not exist for paper Magic, but might exist Online.

I'd like to know how big a handicap muliganing to 6 cards is, both in the realm of Constructed and Limited play. Specifically I'd like to know how often a player keeping their initial 7 card wins vs a player keeping 6, and how often a person keeping their initial 7 wins against a person keeping 5.

I'd also like to know how often players end up Muliganing to 6 and 5 in both Limited and Constructed games.

Does anyone have these statistics, or know where these statistics might be found?

I guess it could be found out some way.


But the problem with magic is that it is so diverse. If you set two exact same decks against each other then you could probably get some good stats on that after a few hundred games. But once you change the deck lists you would get other results. If you change the land count…


It’s like trying to guess who wins the game by starting first on Monopoly, Chess, jeopardy all together…


The most crucial part to mulliganing is by identifying your plays. If you know how your deck performs you know if the hand is worth to keep. If you know your opponents deck you can be even better at this.


But trying to get  numbers on this you are asking for is something I don’t understand why it would be even interesting if possible.


Even if you find out theres a say 51 % chance winning with 7 cards vs 5. What would you do with it?


I have mulliganed down to 3 and still won and I have lost with 7.

Anything but nuts is crazy. - We need moar command helemet!

Labelling a mulligan to 6 as a 'handicap' reveals the bias in your thinking. Many tournament players will aggressively mulligan to get a better hand rather than keep an ok 7, and so think of the 6 as a potential improvement.
Labelling a mulligan to 6 as a 'handicap' reveals the bias in your thinking. Many tournament players will aggressively mulligan to get a better hand rather than keep an ok 7, and so think of the 6 as a potential improvement.



Back before the play/draw rule was put into place one of the best predictors of which player would win the match was the player who won the coin-flip and got to go first, so having even one additional card over your opponent is certainly an advantage. In constructed it isn't as much of a handicap as it is limited, but players keeping 7 cards are certainly winning over 50% of their games over players keeping 6. I'm curious to see if it is a subtle difference like 55%, or much higher than that. In limited I can see it is a huge advantage to start wth 7 cards as opposed to 6, just from my own records, but I would like to know what the averages are. If other peoples records are consistant with my own, people keeping 7 cards are winning 65% of their games against people keeping 6, and near 100% of their games against people keeping 5. (At least in the most recent set)
It’s like trying to guess who wins the game by starting first on Monopoly, Chess, jeopardy all together…



 Yes, it is quite a bit like trying to answer those questions. And the way I want to answer it is to look at the results from a lot of Monopoly, Chess and Jeopardy games and record how often the person playing first won. I'm not trying to figure out how often they should win based on the mechanics of the game.
 
Even if you find out theres a say 51 % chance winning with 7 cards vs 5. What would you do with it?



In limited, people keeping 7 card hands are winning the vast majority of their games against people keeping 5 card hands, it's not even close to 51%

As for what I'm planning to do with this information, I'm going to combine these percentages with the liklihood players will hit a muliganable starting hand in limited (based on the number of lands, which is the primary determinant of when to muligan in limited) I am primarily interested in the effect of muliganing on limited matchups.

I really don't think there is going to be a meaningful answer. To get a statistically relevant number, you would have to pair two players of exceedingly close skill playing the exact same 75 (or 40 in limited) and they would both have to follow strict rules on mulliganing so they are each doing for the same reasons each time. Even if you got those 2 players to do this and follow the rules precisely and play hundreds of games, the number would only be relevant to those parameters.

An example of why this approach seems to go no where: If I have a pool in limited (draft or sealed) with 2 pack rats, there is good reason to believe that mulliganing into a pack rat will give an increased chance of victory, even down to 2 cards.

Another point: What is a keepable hand varies wildly by deck and person. LSV famously kept a no-land hand instead of mulligan because he reasoned - correctly - that no 6 card hand would be better.

This information could be useful if mulliganning was always a statistically determinable option. There are simply too many variables, some of which are not measurable, to make an useful measure. I say useful here because everyone knows that in a vacumn a 6 card unknown hand is worse than a 7 card unknown hand, so finding the statistically representation of such would largely just be a "Duh" moment.

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It is unclear why people keep interpreting this as an attempt to find out how often a person keeping 7 cards should win against a person keeping 6. What I want to know is how often a person keeping 7 cards does win against a person keeping 6, and against a person keeping 5 and so forth.

Ideally there would be a table somewhere with game results I could use along the lines of:

P1 Starting Cards, P2 Starting Cards, Winner
7, 7, P1
7, 6, P1
6, 7, P2
6, 5, P1
7, 6, P2
....

Then I could put that data into a spreadsheet, ignore all of the results where P1 and P2 started with the same number of cards and find out how big an advantage starting with 7 cards actually is over someone starting with 6 cards. And how big an advantage 6 is over 5 and 7 is over 5.

I can make rough estimates based on my own game win % after keeping 7 cards vs keeping 6 and 5, but I don't have a lot of results from 5 card games that I can use.
It is unclear why people keep interpreting this as an attempt to find out how often a person keeping 7 cards should win against a person keeping 6. What I want to know is how often a person keeping 7 cards does win against a person keeping 6, and against a person keeping 5 and so forth.

Ideally there would be a table somewhere with game results I could use along the lines of:

P1 Starting Cards, P2 Starting Cards, Winner
7, 7, P1
7, 6, P1
6, 7, P2
6, 5, P1
7, 6, P2
....

Then I could put that data into a spreadsheet, ignore all of the results where P1 and P2 started with the same number of cards and find out how big an advantage starting with 7 cards actually is over someone starting with 6 cards. And how big an advantage 6 is over 5 and 7 is over 5.

I can make rough estimates based on my own game win % after keeping 7 cards vs keeping 6 and 5, but I don't have a lot of results from 5 card games that I can use.

What would be the point if you were not using it to see who should win? If you just want the number, as I said it will just be a pretty obvious, hey look more cards equals higher chance to win.

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Another point: What is a keepable hand varies wildly by deck and person. LSV famously kept a no-land hand instead of mulligan because he reasoned - correctly - that no 6 card hand would be better.



Out of curiosity, does anyone know which event this occurred in?

 

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Another point: What is a keepable hand varies wildly by deck and person. LSV famously kept a no-land hand instead of mulligan because he reasoned - correctly - that no 6 card hand would be better.



Out of curiosity, does anyone know which event this occurred in?

 


I tried to google it but I was unable to find it. LSV was playing a mono-blue Grand Architect deck and kept a hand with no land, 2 gitaxian probes and other strong stuff, iirc.

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Yes, it is quite a bit like trying to answer those questions. And the way I want to answer it is to look at the results from a lot of Monopoly, Chess and Jeopardy games and record how often the person playing first won. I'm not trying to figure out how often they should win based on the mechanics of the game.



What you're doing is not trying to answer three separate questions by recording three separate lists of "starting player results", as you seem to suggest here. You're lumping the stats from all three games together and then try to figure out if, absolutely speaking, "going first is always advantageous".

The thing is that for some games it inherently is, and for some it isn't. In nim, for example, whoever goes first loses. There are also games where you always win if you start (four-in-a-row, for example). Obviously, if you added the nim and four-in-a-row stats together, all you would be figuring out is which of the games you counted more. You would be saying nothing meaningful about the advantage of going first.

What we're trying to tell you (and I suspect you know this, no-one is this obtuse) is that your approach is just as pointless, for similar reasons. You're treating apples and pears (as well as bananas) as a single fruit.
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I think I would be inclined to treat Monopoly, Chess and Jeopardy as three separate games. Of those three I think Monopoly is the best example, because it contains a non-deterministic element. It seems obvious that going first would be an advantage, but you could argue all day over conceptually how much of an advantage you thought it should be. When it would be easy enough to just have players play out a number of games, to look at records from existing games or to simulate a large number of games with computer players following various rules to figure out how much an advantage going first actually was.

Since no one has been gathering stats for this I decided to go back over the draft stats I had gathered from the previous 3 sets. Using those statistics to approximate the likelihood that a player keeping 7 cards wins against a player muliganing his initial starting hand, I found that the person keeping 7 wins 58.4% of the time against someone who muligans their starting hand. Or alternatively, the muliganing player is winning 41.6% of the time against the player keeping 7. Not quite the wide gulf I expected, but I think it is a wide enough gap to justify tweaking the muliganning rules for limited.
I think I would be inclined to treat Monopoly, Chess and Jeopardy as three separate games. Of those three I think Monopoly is the best example, because it contains a non-deterministic element. It seems obvious that going first would be an advantage, but you could argue all day over conceptually how much of an advantage you thought it should be. When it would be easy enough to just have players play out a number of games, to look at records from existing games or to simulate a large number of games with computer players following various rules to figure out how much an advantage going first actually was.

Since no one has been gathering stats for this I decided to go back over the draft stats I had gathered from the previous 3 sets. Using those statistics to approximate the likelihood that a player keeping 7 cards wins against a player muliganing his initial starting hand, I found that the person keeping 7 wins 58.4% of the time against someone who muligans their starting hand. Or alternatively, the muliganing player is winning 41.6% of the time against the player keeping 7. Not quite the wide gulf I expected, but I think it is a wide enough gap to justify tweaking the muliganning rules for limited.



Why? Don't you consider mulliganing correctly to be an important skill to learn?

Winter.Wolf (ugh at this new forum with the ridiculous double login)

I think I would be inclined to treat Monopoly, Chess and Jeopardy as three separate games. Of those three I think Monopoly is the best example, because it contains a non-deterministic element. It seems obvious that going first would be an advantage, but you could argue all day over conceptually how much of an advantage you thought it should be. When it would be easy enough to just have players play out a number of games, to look at records from existing games or to simulate a large number of games with computer players following various rules to figure out how much an advantage going first actually was.

Since no one has been gathering stats for this I decided to go back over the draft stats I had gathered from the previous 3 sets. Using those statistics to approximate the likelihood that a player keeping 7 cards wins against a player muliganing his initial starting hand, I found that the person keeping 7 wins 58.4% of the time against someone who muligans their starting hand. Or alternatively, the muliganing player is winning 41.6% of the time against the player keeping 7. Not quite the wide gulf I expected, but I think it is a wide enough gap to justify tweaking the muliganning rules for limited.



Why? Don't you consider mulliganing correctly to be an important skill to learn?


10% difference!!! I would say that is quite conclusive that mulliganing once is NOT detrimental to the game. How many other factors have a much higher effect on the game like mistakes, flodding, mana screws, bombs, general bad draws, etc? I think your studies have shown that magic is a game where luck is a very big factor. What your studies have not shown you, which I think is the problem, is that luck is one of the things that makes it very successful.
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Why? Don't you consider mulliganing correctly to be an important skill to learn?




The problem is that even when you muligan correctly there is no way around the fact that drawing your starting hand, seeing 0, 1, 6 or 7 lands in limited generally means you must muligan, and muliganing even once puts you at a measurable disadvantage compared to a player who saw 2-4 lands in their starting hand. Prior to the play-draw rule correctly guessing the outcome of the initial coinflip had a huge effect on the eventual winner of the match. And yet no one talked about coin-flip guessing as being a learnable skill. Since the majority of muligans in limited are forced muligans (muligans where there is a general consensus among all players) it is effectively a random chance to start the game with 1 less card.
Do you remember back before Paris when we had one potential mulligan if we had 7 or 0 lands in our hand? I do. Magic was still fun then but it was imho less fun. Paris caused the art (read: skill) of decision making start at the opening hand instead of waiting to see if fate dealt you a decent hand. I was always a good shuffler and as a result often had very random hands in paper magic. Most often to my detriment. I know from flood/screw.

However what I didn't know at the time was how to properly build to avoid that. I still have some trouble building decks that minimize the potential for flood/screw. (Though I find that ones that screw a lot, will tend to flood just as much.) It seems to me you are minimizing importance of the skill set that factors into why some people mulligan a lot.

As many people have pointed out this is a) something that happens to everyone. If you find that it happens to you more online than off, first question your randomization methods offline. b) something that makes the game more interesting (not less) since even a good player such as your self can fall prey to a bad deck that is luckier than you. c) Games of chance are inherently about luck. You can't write rules that work to minimize the luck in the game without changing the very nature of the game.

I really think Bobus, that you mean well but that you are ignoring some very valuable advice here when people tell you to give it a rest. Your crusade is fruitless and somewhat disheartening though I do admire your singleminded tenacity in the face of such utter opposition.

And I think ultimately if you want to change the game to be more the way you want to you need to start playing it differently then convince others to do it your way. Trying to gather support on these forums before you've even come up with a proof of concept is just asking to be ridiculed and belittled needlessly. I have seen you make some very sage observations when not engaged in this ludicrous endeavor so I expect more from you.

Get out there, make your variant. Show us how it is done. Do it with paper magic then figure out how to do it online if you can. Then demonstrate it. THEN come here and let us know how your project progresses.

Winter.Wolf (ugh at this new forum with the ridiculous double login)

Paris caused the art (read: skill) of decision making start at the opening hand instead of waiting to see if fate dealt you a decent hand. I was always a good shuffler and as a result often had very random hands in paper magic. Most often to my detriment. I know from flood/screw.



As I said in my previous post, the issue I have with 'the art/skill' of Paris muliganing is that in limited 95% of the time the decision is made for you, based on the number of lands in your starting hand, which means it isn't so much skill at all, but rather arbitrary luck. You could say that if you constistantly make good decisions regarding the muliganing of your opening hand that you'll do better than a player who simply tosses all 0, 1, 6 and 7 land hands, keeps all 2-4 hands and flips a coin for 5 landers, and I'll buy that. But the level of improvement over the default, land-based approach is depressingly limited in limited. I guess I just don't see the need to arbitrarily handicap either player at the start of the match, it's not like in constructed where it gives both player the opportunity to search for a game-winning combo. In limited the majority of cards deal with each other on a 1 for 1 basis.
Paris caused the art (read: skill) of decision making start at the opening hand instead of waiting to see if fate dealt you a decent hand. I was always a good shuffler and as a result often had very random hands in paper magic. Most often to my detriment. I know from flood/screw.



As I said in my previous post, the issue I have with 'the art/skill' of Paris muliganing is that in limited 95% of the time the decision is made for you, based on the number of lands in your starting hand, which means it isn't so much skill at all, but rather arbitrary luck. You could say that if you constistantly make good decisions regarding the muliganing of your opening hand that you'll do better than a player who simply tosses all 0, 1, 6 and 7 land hands, keeps all 2-4 hands and flips a coin for 5 landers, and I'll buy that. But the level of improvement over the default, land-based approach is depressingly limited in limited. I guess I just don't see the need to arbitrarily handicap either player at the start of the match, it's not like in constructed where it gives both player the opportunity to search for a game-winning combo. In limited the majority of cards deal with each other on a 1 for 1 basis.



If it was simply about the moment you draw and look at 7 I would be at least partially in agreement with you. But there is more. How many copies of a particular land are you running? How often do you need to draw that land? How does your land to cmc ratio work? If you draft all 1cmcs and 2cmcs you obviously wont need as much land in your deck as if your curve averages around 3-4 and you might need many more if your is averaging at 6+. Or even if you have cards in your deck that go that high and maybe require multiple colors.

Flood can occur when you build a deck with too many lands in it. Screw when you build a deck with too few. Both can occur just randomly. It is a random game after all in some senses. You can build your deck with thinners and shufflers and draw cards that are super efficient and mana enhancers. Ways to use lands stuck in your hand. And so on and so forth, ad nauseum.

Winter.Wolf (ugh at this new forum with the ridiculous double login)


If it was simply about the moment you draw and look at 7 I would be at least partially in agreement with you. But there is more. How many copies of a particular land are you running? How often do you need to draw that land? How does your land to cmc ratio work? If you draft all 1cmcs and 2cmcs you obviously wont need as much land in your deck as if your curve averages around 3-4 and you might need many more if your is averaging at 6+. Or even if you have cards in your deck that go that high and maybe require multiple colors.

Flood can occur when you build a deck with too many lands in it. Screw when you build a deck with too few. Both can occur just randomly. It is a random game after all in some senses. You can build your deck with thinners and shufflers and draw cards that are super efficient and mana enhancers. Ways to use lands stuck in your hand. And so on and so forth, ad nauseum.



Right I agree with that, but what I'm saying is that in limited, once you get past the obvious mistakes that players typically make early on, that there is not much room for additional improvement. Even if you know your deck would benefit from a particular card or mana sink there's no guarentee you'll actually have that card in your pool, and even if you do get one and include it in your deck there's no guarentee you'll actually draw it. One of the worst floods I've had in limited was drawing out 14 lands to 7 spells in a deck with 2 Nivix Guildmages. Ironically the reason I didn't draw one of the guildmages to utilize my extra land is that I only drew 7 spells in total. The majority of mana issues, past the point when players can properly draft decks, count mana symbols and conceptualize which plays they need to make on which turns, will just be random, unavoidable handicaps.

While some players find random unavoidable handicaps add interest and depth to the game, I am not one of those players.
Some 1 and 6 land hands are keepers.  That's where the skill comes into play.  We keep harping on skill because you make it obvious you don't understand that. You're idea of mulliganing is so incredibly crude that it is laughable.  There is so much more to it than the number of lands in your hand.  Only a 0 or 7 land hand is a 100% throw-back, and those happen infrequently enough.

Additionally, even though you found 10% with your data...I could be wrong, but I don't think you were recording your opponent's hand sizes for those experiments.  These were the ones directed at determining the whole likelihood of drawing a land given X number of lands in your starting hand, right?  Or perhaps it was your test of your skill by labeling games as flood/screw.  I didn't think you were collecting data on your opponent's opening hand...

If that is indeed the case, then you certainly have the info for your own hand size, but you don't have your opponents, right?  That'd change the numbers slightly, some of the times you mulliganed to 6, so did your opponent.  So, if you lost that game, it wasn't because you were down a card.  If you didn't keep track of this, I wouldn't be surprised if that changed your numbers by a couple of percentage points or more.

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Some 1 and 6 land hands are keepers.  That's where the skill comes into play.  We keep harping on skill because you make it obvious you don't understand that. You're idea of mulliganing is so incredibly crude that it is laughable.  There is so much more to it than the number of lands in your hand.  Only a 0 or 7 land hand is a 100% throw-back, and those happen infrequently enough.



Certainly I've kept 1 landers so I know that some 1 landers are keepable.

Once again, my issue isn't that there's no skill associated with muliganning , my issue is that even if you made the correct decision 100% of the time (the probabilistic correct decision, not the deterministic correct one) that you wouldn't significantly improve your chances of avoiding a mana/muligan influenced loss vs the crude muliganing model where your decision was based solely on the number of lands. At least in the sphere of limited games which is where I feel muliganing rules should be changed.

I *could* see them change it to one free mulligan for limited events. Then if you get two unkeepable 7 hands the problem lies in your deck contruction and not luck.

Maybe you should stop talking about why it should be fixed and start showing how it could be fixed and then test that extensivly. Show the results of your changed rules. See if it's better and if it effects the game in any other negitive way (for combo decks in contructed a free mulligan would make them an advantage in regards to other type of decks etc.).
So, what about the skill of deciding whether to go first or second? This is quite important in sealed. In draft, your deck should hang together, and mulligans should be much less frequent than in sealed. But in sealed, you play what you're given, and your first decision is play or draw. This connects with the mulligan question, since many hands which should be mulliganed if you go first can be kept if you go second.

I guess my advice is: if mulligans bother you, play one land more, play control and go second. This way, you'll get statistical advantage over people who don't do this. It's always better to game the system than to change it; certainly you have a better chance of success this way, than hoping to change the mulligan rule. I think the rule is just fine, as the amount of decision making and opportunities for good play it adds to the game outweighs the times you draw three bad hands in a row and lose the game before it starts.

Go draft, young man, go draft!

I've looked at the results from the top 8 matches for all limited GPs for 2012. And in those matches the players keeping their initial 7 are winning 69.2% of their games when their opponents mulligan. That's nearly 7 games for every 3 that their opponents win, even at the highest levels of play. So no, I do not believe the current muliganing rules are 'fine as is'. Not for limited anyway.
I've looked at the results from the top 8 matches for all limited GPs for 2012. And in those matches the players keeping their initial 7 are winning 69.2% of their games when their opponents mulligan. That's nearly 7 games for every 3 that their opponents win, even at the highest levels of play. So no, I do not believe the current muliganing rules are 'fine as is'. Not for limited anyway.



So, it's game two, I know what my opponent is playing, and I know that my first seven are just not good enough to beat it. I mulligan, not because my hand is bad as such, but because it can't win against what I'm facing. And then I lose the match, contributing to the statistics above, not because I had to mulligan, but because some matchups are just bad.

I believe you are really bothered by the effect the randomness of the opening hand has on the game, and are currently looking at possible changes to mulligan system that would decrease this effect. However, this randomness benefits you just as often as your opponent, so your play results would not change by a change to the mulligan rule. On the other hand, many players cherish the occasional game where they pull a win against all odds; in fact, some play Magic just for that feeling.

This is really a matter of personal preference; I fell that the amount of randomness inherent in a Magic game, under the current rules, contributes to my enjoyment of the game; you obviously feel otherwise. I don't want to play limited events where the winner is determined by what cards they open. Sure I'm frustated sometimes; but I prefer the swing to the uniformity.

Go draft, young man, go draft!


So, it's game two, I know what my opponent is playing, and I know that my first seven are just not good enough to beat it. I mulligan, not because my hand is bad as such, but because it can't win against what I'm facing. And then I lose the match, contributing to the statistics above, not because I had to mulligan, but because some matchups are just bad.



This has a lot to do with player psychology. While some players have the tendacy to mulligan more in the face of strong opposition, others will mulligan less. The way I generally look at a strong matchup where I lost game 1 is "I didn't beat this deck game 1 with 7 cards, there's no way I'm beating this game 2 with 6". While against a weaker matchup I will say "I can beat this deck with cards to spare, better mull this 1 land hand because the only way my opponent is winning is if I get stuck under 3 lands" Which should produce the opposite of the effect your are describing.

I believe you are really bothered by the effect the randomness of the opening hand has on the game, and are currently looking at possible changes to mulligan system that would decrease this effect. However, this randomness benefits you just as often as your opponent, so your play results would not change by a change to the mulligan rule. On the other hand, many players cherish the occasional game where they pull a win against all odds; in fact, some play Magic just for that feeling.



No the randomness doesn't benefit all players equally. The changes I've proposed regarding mulligan rules benefit players who draft strong decks, make good play decisions and have a good understanding of probability. The main overall effect is that the player most likely to win any given matchup becomes more likely to win it. I do cherish the feeling of the occassional game where I win against all odds, but I would trade all of those wins for a mulligan system under which I wasn't forced to mulligan a 0167 land hand into a 0156 lander into either a probable mana issue lost or an unwinnable 5 card hand.

This is really a matter of personal preference; I fell that the amount of randomness inherent in a Magic game, under the current rules, contributes to my enjoyment of the game; you obviously feel otherwise. I don't want to play limited events where the winner is determined by what cards they open. Sure I'm frustated sometimes; but I prefer the swing to the uniformity.



The winner in a limited environment will always be somewhat detmined by the cards they open and I don't believe that the proposed changes will alter that significantly. The main effect will be removing the "coin-flip" wins, the wins where one player wins because their opponent doesn't play anything at all for long stretchs of time due to mana short, mana flood or mulliganing to oblivion. Without exception the best games I've played have involved both me and my opponent playing large number of game swinging spells, where the eventual winner was in question with every play. Without exception the worst games I've played have all involved either me or my opponent playing almost nothing at all.
I've been thinking about this some more, and I believe that the arguments against the current mulliganing system come down to 3 essential points:

1) The purpose of a having a mulligan system at all is to prevent the inevitable random losses that would come from players being forced to keep 0, 1, 6 and 7 card hands (as well as 2-4 land hands with land/spell color mismatches and the like) But with mulliganers winning only 27% of their games against players of roughly equal skill keeping 7 cards, most of these loses are happening anyway, regardless of whether the person with a questionable hand mulligans it or not.

2) Even with a properly constructed limited deck, some percentage of drawn hands will contain 0, 1, 6 or 7 lands, and the majority of these hands will be unplayable. In a typical limited deck running 17 lands, 12.1% of draws will end up as having 0, 1, 6 or 7 lands by chance. In a well constructed limited deck these 0167 mulligans will account for the majority of total mulligans.

3) Without a real opportunity to improve hands as well as the majority of draws leading to mulligans being unavoidable (even with proper deck construction,) the current mulligan system does not effectively mitigate random losses predicated on starting hands. These 'blind luck' losses are no better than using a coin flip to determine every nth game.

In addition to these three points I did some introspection regarding the best and worst Magic games I have played.

4)  Without exception the best games I've played have involved both me and my opponent playing large number of game swinging spells, where the eventual winner was in question with every play. Without exception the worst games I've played have all involved either me or my opponent playing almost nothing at all. A mulliganing system that results in a higher overall quality of starting hands will replace a number of worst Magic games with a number of best Magic games. For that reason alone I believe it warrants consideration.
I disagree
For a great source of information on the Pauper format check out Pauper's Cage!
I disagree



Wow, that's deep Gabo
Its to prove a point. When I write a long and detailed rationalization, you just ignore the arguments I make and repeat the same incomplete and wild logical leaps you already wrote. It makes no sense to go any further than to just show the fact that I disagree.

For example, many of us have explained that the 27% number you keep repeating is invalid because there are  too many variables to make any kind of analysis useful but you keep going back to it. We've also explained that for many of us, the feel of the game IS good and yet you deny it and insist that its not as if nobody said anything.

So... I disagree. 
For a great source of information on the Pauper format check out Pauper's Cage!
Its to prove a point. When I write a long and detailed rationalization, you just ignore the arguments I make and repeat the same incomplete and wild logical leaps you already wrote. It makes no sense to go any further than to just show the fact that I disagree.

For example, many of us have explained that the 27% number you keep repeating is invalid because there are  too many variables to make any kind of analysis useful but you keep going back to it. We've also explained that for many of us, the feel of the game IS good and yet you deny it and insist that its not as if nobody said anything.

So... I disagree. 



The only thing I see on this thread, aside from this message and the "I disagree" itself is:

"10% difference!!! I would say that is quite conclusive that mulliganing once is NOT detrimental to the game. How many other factors have a much higher effect on the game like mistakes, flodding, mana screws, bombs, general bad draws, etc? I think your studies have shown that magic is a game where luck is a very big factor. What your studies have not shown you, which I think is the problem, is that luck is one of the things that makes it very successful."

As I've stated before, the issue I have with the current mulligan system is for Limited, not Constructed. In Constructed an empirical analysis found that players mulliganing their starting hands were winning 38% of the time against players keeping their starting 7, which is a 12% drop from 50% and "feels about right" In Limited the same empirical analysis (counting the number of wins and losses for people keeping 7 vs players mulliganing) found that mulliganers were winning 27% of the time against people keeping 7, a 23% drop from 50%. Given that the drop in Limited is nearly twice as much as the drop in Constructed it seems unlikely the same set of mulliganing rules work equally well for Limited as they do for Constructed. While it is the same 1 card penalty in each, that penalty clearly has a greater effect in determining game outcomes in Limited than it does in Constructed. If it "feels about right" for one it isn't going to be for the other.
Now you're just acting naive or something.

We both know there is another thread that's discussing the same thing where I explained everything:
community.wizards.com/go/thread/view/758...

We both know that particular paragraph I wrote that you quoted to isn't even talking about constructed (the word "bomb" should be a good indicator since in constructed bombs aren't really a thing) 

And you just did what I mentioned again.. you just repeated the same thing.. this number bla bla bla and this other number bla bla bla even though we've already explained why those numbers aren't valid and that your subjective interpretation of them is basically a feeling.
For a great source of information on the Pauper format check out Pauper's Cage!
Now you're just acting naive or something.

We both know there is another thread that's discussing the same thing where I explained everything:
community.wizards.com/go/thread/view/758...

We both know that particular paragraph I wrote that you quoted to isn't even talking about constructed (the word "bomb" should be a good indicator since in constructed bombs aren't really a thing) 

And you just did what I mentioned again.. you just repeated the same thing.. this number bla bla bla and this other number bla bla bla even though we've already explained why those numbers aren't valid and that your subjective interpretation of them is basically a feeling.



I observed 85 games from the Top 8 Limited GPs from 2010-2012 where one player mulliganed and their opponent kept their initial 7. Of these 85 games the players muliganning collectively won 23 of them. Explain how the assertion: Players keeping less than 7 cards won 27% of their games against players keeping their starting 7 is a "subjective interpretation" or "a feeling"

I haven't seen any posts from you where you've analyzed actual game results. The majority of your posts are abstract musings over whether you feel mulliganing should place the mulliganing player at a significant advantage and whether or not you feel this is helpful to Magic overall. In one post you wrote 877 words where every numerical reference, with the exception of "two players of equal skill will, on average, win 50% of the time against each other" was something that you made up.

The reason I never wrote back regarding those arguments is because I don't want to get into any of that. I don't care about feelings, how much of a disadvantage mulliganing is in the abstract sense, or how many games are decided by mulligans compared to other elements of randomness like bombs, sealed pool strength or any of the other arbitrary factors that dictate the eventual winners and losers of games. I am interested only in how much of a disadvantage mulliganing actually is, as determined empirically by how often players who mulligan win vs players keeping their starting 7.

If you feel there is another factor that explains the result that I observed, let's say "Players wearing blue shirts", then analyze the results from 2010-2012 Limited Top 8 GPs, use those results to write out a statement in the following form: "After controlling for [players wearing blue shirts] mulliganing players are winning x% of their games against players keeping their starting 7" and then I'll evaluate your finding to see if they are correct.

But please, no more:

"It feels right."
"At least anecdotal evidence makes me think that it works quite well."
"It just makes no sense to try to come up with the actual values"

You will never persuade me with feelings, anecdotal evidence or non-actual values. People are entitled to their own opinions, but not their own facts.
I observed 85 games from the Top 8 Limited GPs from 2010-2012 where one player mulliganed and their opponent kept their initial 7. Of these 85 games the players muliganning collectively won 23 of them. Explain how the assertion: Players keeping less than 7 cards won 27% of their games against players keeping their starting 7 is a "subjective interpretation" or "a feeling"

I already have and so have a few others. This stat does not take into account all the other variables in the game. If you naively assume and continue to stubornly believe that there is a perfectly even distribution of all these other variables such that you can dismiss them, then it doesn't make sense to discuss this any longer. 

You will never persuade me with feelings, anecdotal evidence or non-actual values. People are entitled to their own opinions, but not their own facts.

Then your argument has nothing to stand on because the whole base of it is that you feel that 27% (a number which we just decided is invalid) is too little. You see, if you say "27% of mulligans win" that might be the statement of a fact (a wild generalization, but a statement nevertheless), but saying that its too little... that's an opinion. So for all your hand waving, you seem to be using the same tools you are trying to put down.

For a great source of information on the Pauper format check out Pauper's Cage!
Just to be really clear:

"If you feel there is another factor that explains the result that I observed":

Here they are:

Difference of skills
Random Mistakes
Bomb in the sealed pool of one player but not another
Lack of removal
Mana Screw
Mana Flood
 
For a great source of information on the Pauper format check out Pauper's Cage!
This stat does not take into account all the other variables in the game.



The stat does not take into account all of the other variables in the game, it takes into account only the liklihood that the mulliganing player will win against someone who keeps their starting 7. Which is what I set out to determine when I started cataloging the results from the Limited Top 8 GPs. Regardless of any other factors that statistic still stands on its own. The only thing you could argue at this point is that the 27% isn't meaningful because it is correlated with another factor that better explains the variance, but neither you nor anyone else has looked at actual game results to prove this.


"If you feel there is another factor that explains the result that I observed":

Here they are:

Difference of skills
Random Mistakes
Bomb in the sealed pool of one player but not another
Lack of removal
Mana Screw
Mana Flood



The problem with asserting that any of these factors explain away the variance explained by 7vsNot7 is that the primary reason for mulilganing a starting hand in the tournament reports was that the hand contained the wrong number of lands. Further, the vast majority of players were running 17 lands. Which means that that the rates of drawing starting hands with 0, 1, 6 or 7 lands should be roughly consistant across all decks. Unless you want to imply that some players are better shufflers than others it is going to be difficult to prove a correlation between mulliganing rates and anything else.

But what the heck, why don't you give it a shot. All of the Limited  GP Top 8 tournament reports are easily accessible online. I look forward to seeing what you come up with using actual tournament results.
I think one of the biggest flaws in your analysis is the assumption that there is a 50% chance either player will win a game.

Yes, if you have Player A and Player B and neither mulligan.  50% of the players with 7 cards win and 50% lose.

However, if those two players, with those two decks played 100 times (non-mulligan games), you could find that 75% of the time, player A won, for example.  This can introduce a bias in the results.

None of your numbers can account for this, because you aren't doing a controlled experiment, you are just observing a small sampling of numbers without any controls.


You could attempt to make the assumption that the probability of needing to take a mulligan is equal for each player.  So that if the player that generally loses mulligans, they still are going to lose but also that the player that generally wins can mulligan and still win, because he or his deck is just that much better.  However, that only works for extreme examples.


To extrapolate, you're trying to find a number that will describe the disadvantage of a mulligan.  Let's say that that number is 10%.

Now, if we have a player/deck that will win 55% of the time against one that wins 10% of the time, the above counter to the bias assumption I brought up no longer works.

Yes, when the 45% player mulligans, he goes down to 35% chance to win, but he was already more likely to lose.
When the 55% chance player mulligans, he goes down to 45%, making him no longer a favorite.
In a case such as this, there is an unequal effect of the mulligan, so I believe it introduces a bias within the data such that you would not get 10% when you ran numbers of games of these two opponent's with a limited sample size.



As an aside, all of this basically hinges on being -1 in card advantage.  If it is true that you get something like a 20%+ advantage for that one card, then shouldn't playing something such as Mind Rot or (even better) Stupor give that player a extremely large advantage?  That would seem to indicate that these effects are much more powerful than they are given credit for (I don't think mind rot was ever an auto-include in any format...)?

My forever unfinished blog of the 2010 MTGO Community Cup: if you're ever bored...
If you cast Inspiration your winning odds jump from 50% to 104% givving you an assured win. They should ban that card imidiatly since its a game braker

When you cast Thoughtflare your winning chances go up to 158% but when you discard the two lands you go back to 104%

When your opponent plays a Runewing it's better to let it live and kill you since you don't want to give your opponent a 27% better chance at winning

I'll stop for now although this was fun I must say.
Kristijan and Koloshin just made some awesome counterpoints.

I'll just stop since Bobus just takes what I say and repeats what he already said. We're not getting anywhere with that. Bobus, good luck in making your point and winning. I think I'll take a break to do something more constructive. 
For a great source of information on the Pauper format check out Pauper's Cage!
While I agree that any two players have a non 50% chance of winning against each other after keeping 7 going into the match, the implicit assumption is that the players in the Top 8 Limited GPs will be roughly equal in skill level and that any differences in skill levels will cancel out over 85 games. This is also the assumption for mulliganing rate, the vast majority of players are fielding 17 card decks, which mean they hit 0167 lands 12.1% of the time on average and mulligans of 0167 land hands constituted the majority of mulligans. Whatever good or bad luck a particular player had on a particular hand should cancel out after looking at 85 games.

Doing a controlled experiment wouldn't be nearly as helpful as looking at actual game results because actual game results are what I care about, I'm not interested in finding out what the handicap is in the abstract sense, and I'm not certain there is even a practical way to do this.

Once again the uniformity in deck composition (over 80% played 17 lands) and mulliganing decisions (the majority of mulligans were due to players picking up 0167 land hands) means that players are mulliganing at the roughly the same rates. Which makes it just as likely that the player who initially had an over 50% chance of winning with 7 cards was selected as the person to start with less cards as the person with an under 50% chance of winning. There's certainly nothing in the tournament reports to suggest a correlation between 0167 mulliganing rates and player skill and if there were that would be a matter requiring DCI investigation. The drop in win rates due to mulliganing isn't anywhere close to 10%, there's nothing to suggest that the damage done to your chance of winning due to mulliganing isn't the drop from 50% to 27% that I observed.

As for Mind Rot, if it always got 2 spells from your opponent for 3 CMC it would be an exceptional card, an easy first pick. Let's say that it was printed as saying "Target opponent discards 2 cards and misses their next 2 draw steps. For each non-land discarded 1 less draw step is skipped." No one would want to be on the receiving end of that card. The only thing that balances Mind Rot out is that it is a terrible top-deck.

As for cards like Inspiration, they main issue is that you still have to use mana to play the cards that you've drawn and after a certain point drawing additional land does you no good at all. If Inspiration was written as "Exile cards from the top of your deck until you've exiled 2 non-lands, you may play those spells at no cost" Then that would be broken as well.

One good analogy I have left, since I've already used the football team with 10 players analogy, is to imagine a war that is being fought initially by 6 soldiers against 7. At the end of every hour both sides get an additional soldier and the two sides fight until all soliders on one side are dead. It's certainly possible the side with 6 soldiers could use better tactics, or be better shots, or find a way to stall out their opponent until enough reinforcements arrive. But under normal circumstances the army that's starting with 6 soliders is a huge underdog against the one starting with 7. If all soliders were of roughly equal strength they wouldn't be expected to lose by just 1 soldier, they would be massacered.
What if the 7 soldiers had no weapons while the 6 had wapons? What happens then? You are fighting an unwinable battle here. We all agree with you that mulligan in general gives you less chances to win. What that percentage is probably cannot be determined. Mulligan rules are widely accepted by the vast majority of high and low skilled players. Could the mulligan rule be improved? Probably. Will they change the rule simple because some individuals want it to change? Not a chance.

I'll ask you this. Out of all the tournaments where you gathered your data was the winner always the person which did not mulligan or mulliganed the least times out of the top 8 players? I'm assuming no.

There was a tournament where Gerry Thomson was playing while dreased in a dress. Not sure how he did but I'm prety sure he didn't win that tournament. Does that makes us believe that a person wearing a dress cannot win a magic tounrament? Should female magic players wear pants on tournaments so they actually have a shot at winning? The data we have shows that you cannot win in a dress so...
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