No Mulligans for Any Reason, Win Rate Shot through the Roof

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So if you've followed any of my other posts you'd know the top 3 things I lose to are mana issues, opponent bombs and mulligans. Upwards of 90% of the games I lose involve at least one of those factors and I'm winning upwards of 90% of the games where none of them do. Up until very recently I followed a basic mulliganing strategy of keeping almost all 2-4 land hands, dumping all 0, 6 and 7 land hands, dumping most 1 land hands and thinking very carefully about the 5 landers.

But recently I've been conducting an experiment on the shuffler (results to be posted in the Online Forums) which required me not to mulligan, at all for any reason for the last 57 games. Yet remarkably, rather than my win rate going down, it shot through the roof. I started stringing together 6-0 and 3-0 finishes like I never have in this set before, and my pattern for every other set has been to see my win rate go down the longer the set is out.

I am very curious if anyone else has tried this. I mean, most of the time it feels insane keeping a 1 lander with a high curve, or any 6 lander, but at least for the last 57 games they've all been working out. The last time I got really mana screwed was keeping a 2 lander I wouldn't have mulliganed anyway.
57 games is an insanely small sample size that you can't really draw any conclusions from.  I don't doubt that a zero mulligan policy could lead to better results for some players, though.  It's really difficult to calculate mulligan ranges accurately in limited, where individual cards, deck archetype and mana curve are all factors.  I think a lot of players have a mulligan range that is too wide and end up mulling 7 card hands that are better than an average 6 too often.  I, for one, feel I punt games way too often due to loose mulligans, especially from 6 to 5.
So if you've followed any of my other posts you'd know the top 3 things I lose to are mana issues, opponent bombs and mulligans. Upwards of 90% of the games I lose involve at least one of those factors and I'm winning upwards of 90% of the games where none of them do. Up until very recently I followed a basic mulliganing strategy of keeping almost all 2-4 land hands, dumping all 0, 6 and 7 land hands, dumping most 1 land hands and thinking very carefully about the 5 landers.

But recently I've been conducting an experiment on the shuffler (results to be posted in the Online Forums) which required me not to mulligan, at all for any reason for the last 57 games. Yet remarkably, rather than my win rate going down, it shot through the roof. I started stringing together 6-0 and 3-0 finishes like I never have in this set before, and my pattern for every other set has been to see my win rate go down the longer the set is out.

I am very curious if anyone else has tried this. I mean, most of the time it feels insane keeping a 1 lander with a high curve, or any 6 lander, but at least for the last 57 games they've all been working out. The last time I got really mana screwed was keeping a 2 lander I wouldn't have mulliganed anyway.



Those are probably the three main reasons your opponent slose as well...I'm not sure what this study is trying to prove...other than you think a 7 card no land hand is somehow better than ataking a shot at a six card hand.
bulletd Guidelines: 5.0: I will take this card no matter what. Creature 1 or playable 1 or hate 1.Archangel of Thune 4.5: Bomb and splashable. Creature 1-2, playable 1-2, removal 1. Jace, Memory Adept 4.0: Excellent first pick first pack, will sway me into same colors. Creatures 1-4, removal 1. Haunted Plate Mail 3.5: Excellent first pack pick two, will confirm colors or possibly sway into second color. Doom Blade 3.0: Good in-color addition, or splashable removal/creature. Creatures 3-9, removal 1-3. wall of Frost 2.5: Solid pick in-color; creatures 5-12, removal 3-5. Dark Favor 2.0: Creatures 10-16; removal 6-7. Elvish Mystic 1.5: My 23rd or 22nd card, depending on removal. Act of Treason 1.0: 23rd card if I don't maindeck an additional land. Lay of the Land 0.5: This card will sometimes be sideboarded in. Brave the Elements 0.0: I will shred this card for counters. Darksteel Forge
Small sample size (ie lucky streak)

I tend to mulligan less than I should and I also tend to regret it. I can remember several times where not mulliganing (ie 5 land slow hand, or 1 land on the draw "surely I'll draw that second land") resulted in a quick loss.

Are you really saying you won't mulligan a no-land hand, and expect to win?
Limited formats are much slower than constructed ones so having bad hands of say lands and stuff that will take a while to cast are much easier to keep than do nothing hands in constructed. I'll keep a do nothing hand in limited all day if it has all my colors need to cast the spells in the deck and you'll usually come out fine. 

Your basic mulligan strategy is just that; basic. Each hand is different and needs individual analysis to see if it is good or not. You cannot just say, oh, I'll keep all hands with 2-4 lands because your hand still might be bad and you need to mulligan. If you're in three colors and have 4 lands of one color and 3 spells you can't cast are you going to keep that? The other thing that is basic about your study is your inability to understand the meaning of the word variance. This isn't the place to complain about the MODO shuffler so I don't even see why you are posting this. 

What is your conclusion? Mulligans suck? You still haven't be able to prove that any of your proposed systems are better than the current one or that your systems will mitigate any of the current "problems" you've been recording. 

Quite frankly, instead of using this forum as your live journal why don't you actually make a live journal and blog about stuff. Making threads about nothing is not constructive to anybody except yourself.  
What do you mean by skyrocketed? Your win percentage seems high if you win over 90% of games when you don't mulligan, have mana problems, or opponent plays a bomb. Just wondering what percentage change you observed. 

Not mulliganing means you're more likely to have mana problems. If you keep a 6 or 7 land hand, you're definitely going to have too much mana in a game. Keeping a 0-1 land hand also leads to mana problems.   Winning games when you keep hands like this shows luck more than it shows that mulliganing loses games.

I also feel that I lose more games keeping 7 card hands that are below average than I lose games by mulliganing down to 6. I feel that making smart calculated mulligan decisions will help decrease the amount of games you lose to mulligans. Always assigning losses to mulligans is a bad idea.    

  

"This list much made Niche barf a lil' in his mouth, so I can be proud of that." -rstnme

One thing to note here is that people misinterpret their own misplays.

I hardly believe that bobus goes misplay or opponent beats them without a bomb only 10 % of the time. If so then he's superman of magic
bulletd Guidelines: 5.0: I will take this card no matter what. Creature 1 or playable 1 or hate 1.Archangel of Thune 4.5: Bomb and splashable. Creature 1-2, playable 1-2, removal 1. Jace, Memory Adept 4.0: Excellent first pick first pack, will sway me into same colors. Creatures 1-4, removal 1. Haunted Plate Mail 3.5: Excellent first pack pick two, will confirm colors or possibly sway into second color. Doom Blade 3.0: Good in-color addition, or splashable removal/creature. Creatures 3-9, removal 1-3. wall of Frost 2.5: Solid pick in-color; creatures 5-12, removal 3-5. Dark Favor 2.0: Creatures 10-16; removal 6-7. Elvish Mystic 1.5: My 23rd or 22nd card, depending on removal. Act of Treason 1.0: 23rd card if I don't maindeck an additional land. Lay of the Land 0.5: This card will sometimes be sideboarded in. Brave the Elements 0.0: I will shred this card for counters. Darksteel Forge
This is also the end of a format, when a lot of players are "over it" or are trying new builds out of boredom or are saving $ for Gatecrash. Hell, last week I drafted three stab wounds over five picks from pack 2. This shouldn't be happening.

I found Carmen Sandiego before you were born unless you're Zlehtnoba.

I would have to guess that he is also throwing out any games where he had too few or too many lands through the game.  This just helps to increase the number of games he gets to throw out of his study.

I would have to guess that he is also throwing out any games where he had too few or too many lands through the game.  This just helps to increase the number of games he gets to throw out of his study.




I've never seen bobus shy away from talking about mana screw...

I found Carmen Sandiego before you were born unless you're Zlehtnoba.

1:  Give me numbers for "shot through the roof".  If you don't have statistics on this, I'm just going to call confirmation bias.  If you do have statistics, I'm going to call Niche.
2:  What mulligan criteria did you use before?  Obviously, if you were taking mulligans on good hands, your winrate will go up if you stop doing so, even if you miss making a few obvious mulligans.  That doesn't mean keeping 0 and 1 landers (in most cases) is a good idea, nor is keeping 0 or 1 spellers. 

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139359831 wrote:
I hope all this helps you to see things in a greater light—and understand that Magic: the Gathering was really created by extraterrestials using Richard Garfield as a medium. The game itself reflects the socio-psycho realtivity between living beings, and the science that takes precedence over them—to define reality for them all (like telekinesis, weather, scientific reaction, phenomenon, ingenuity, how the brain works, etc.). I'd also bet there is an entity floating thousands of miles above us, looking down on the current state of game, shaking its fist like... "Wtf are you doing?! You're getting it all screwed up!". Awkward—to be evolved, and yet still subject to the ladder that is the concepts of the game. In this case, misconception, corruption, and deception. With the realities of each color becoming distorted (through oblivious designers), leading the game to reflect a false state of reality that warps the understanding that other people have about those things. For example, people thinking that white could be anything except pure good. This shouldn't be too far off though, I mean...Magic is designed based on reality after all, so that entity (those entities) should be subject to those things. Anyways, I guess when you're busy doing space stuff you can't always be around to ensure quality control. It's no wonder they choose Garfield, they're so much alike; that's exactly what happened to him and Magic.
166199665 wrote:
omg snortng so much febbdelicious /intocixated in rl
"Those are probably the three main reasons your opponent slose as well...I'm not sure what this study is trying to prove...other than you think a 7 card no land hand is somehow better than ataking a shot at a six card hand."

Looking back on the starting hands I was getting during that 57 game span, it appears that I didn't get any 0, 6 or 7 land starting hands. So effectively what my forced no mulligan policy meant is that I was keeping 1 and 5 land hands I wouldn't have kept normally (it is extremely rare for me to toss 2, 3 or 4 landers) I agree that in the majority of games the losing player has mulliganed his starting hand, hit mana issues or his opponent has played a bomb. Glad to see you're on board with this.

"What is your conclusion? Mulligans suck?"

My conclusion is that it appears that the 1 and 5 land starting hands I had been mulliganing previously should not have been mulliganed at all. Prior to the test I had been dumping approximately 90% of 1 landers, approximately 30% of 5 landers, and it appears I would have been better off dropping none of them. (Certainly there some of the 1 landers and 5 landers that should be dropped, but the criteria I was using to pick them previously could not have been correct if a blanket 'keep all' strategy outperformed it)

"What do you mean by skyrocketed?"

Skyrocketed for this set. For most sets I can usually maintain a record where I'm getting primarily 2-1s, but significantly more 3-0s than 1-2s. In a good set I can often go for stretches where I am going 3-0 on average every other tournament. For this set however I've been getting mostly 2-1s, and more 1-2s than 3-0s. For the 57 game stretch my match records were all 3-0s and 2-1s and nearly as many 3-0s as 2-1s. There were some 6-0 game records in there too.

"Always assigning losses to mulligans is a bad idea."

As I stated in an earier post, from the previous sets where I employed standard mulliganing strategy I found that all 7 card hands I kept were winning approximately 65% of games, while hands with 6 cards or less were winning in the 50% range. So while taking a mulligan certainly isn't an autoloss, it's much less likely to be a win.

"I hardly believe that bobus goes misplay or opponent beats them without a bomb only 10 % of the time. If so then he's superman of magic"

Looking at the previous sets, I am already winning 80-85% of the games where I:
A) Keep my starting 7 cards
B) Hit my first 3 land drops (no mana short)
C) Draw at least as many spells as lands over the course of the game (no mana flood)

So a game win rate of 80-85% just for avoiding mana issues and mulligans. Removing the losses were my opponent played bomb(s) pushes that up further.
I would have to guess that he is also throwing out any games where he had too few or too many lands through the game.  This just helps to increase the number of games he gets to throw out of his study.




No, my study was for the shuffler. To conduct it I had to keep every starting hand and include the data from every game. Hence why there were no mulligans allowed. Here is a link to my preliminary results: community.wizards.com/go/thread/view/758...
Keeping one land hands is going to be a mistake upwards of 80% of the time. You may hit a mana rush but not likely.

Many of the cards we need to win are 3-6 converted mana cost. On a one land hand its pretty common for the first two draws to be spells. That means turn 4 probably second land and maybe, maybe turn six for third land, I hope I play you at a GP when you use this "no mulligan" strategy!
bulletd Guidelines: 5.0: I will take this card no matter what. Creature 1 or playable 1 or hate 1.Archangel of Thune 4.5: Bomb and splashable. Creature 1-2, playable 1-2, removal 1. Jace, Memory Adept 4.0: Excellent first pick first pack, will sway me into same colors. Creatures 1-4, removal 1. Haunted Plate Mail 3.5: Excellent first pack pick two, will confirm colors or possibly sway into second color. Doom Blade 3.0: Good in-color addition, or splashable removal/creature. Creatures 3-9, removal 1-3. wall of Frost 2.5: Solid pick in-color; creatures 5-12, removal 3-5. Dark Favor 2.0: Creatures 10-16; removal 6-7. Elvish Mystic 1.5: My 23rd or 22nd card, depending on removal. Act of Treason 1.0: 23rd card if I don't maindeck an additional land. Lay of the Land 0.5: This card will sometimes be sideboarded in. Brave the Elements 0.0: I will shred this card for counters. Darksteel Forge
Per definition, having access to the mulligan is a bonus. If your win rate continues to stay this high, you should seriously examine your mulligan processing as it were before. You most likely have been mulliganing hands that were worth keeping. I would hold out for several hundred more games before considering this a likely conclusion to.
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Isn't this more about SilentBob's growth as a player, not Limited and sealed? Bob, If you want people to take you seriously, don't lead with "while I was testing the MTGO shuffler." That's like saying "I found the unified field solution while I was disproving the moon landings."
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oh my god, AWESOME! Then changing the Slivers was your idea! haha lol
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What exactly is wrong with testing the MTGO shuffler? I've been keeping records of draws and the common thread behind all of them was that online clumps of lands come up considerably more often than one would expect by chance. Some of the people on the online forum were upset I was keeping a record of cards drawn during Limited games, they were convinced that I was only seeing the results I was seeing because each game stopped with a different number of cards drawn. So I decided to try a new experiment where I kept every hand and drew out all of the remaining cards from the deck at the end of it and recorded everything. The results were the same as the original tests, LL clumps come up more often than would be expected by chance.
What exactly is wrong with testing the MTGO shuffler? I've been keeping records of draws and the common thread behind all of them was that online clumps of lands come up considerably more often than one would expect by chance. Some of the people on the online forum were upset I was keeping a record of cards drawn during Limited games, they were convinced that I was only seeing the results I was seeing because each game stopped with a different number of cards drawn. So I decided to try a new experiment where I kept every hand and drew out all of the remaining cards from the deck at the end of it and recorded everything. The results were the same as the original tests, LL clumps come up more often than would be expected by chance.



That's the thing about chance...you can't have too many expectations about it

bulletd Guidelines: 5.0: I will take this card no matter what. Creature 1 or playable 1 or hate 1.Archangel of Thune 4.5: Bomb and splashable. Creature 1-2, playable 1-2, removal 1. Jace, Memory Adept 4.0: Excellent first pick first pack, will sway me into same colors. Creatures 1-4, removal 1. Haunted Plate Mail 3.5: Excellent first pack pick two, will confirm colors or possibly sway into second color. Doom Blade 3.0: Good in-color addition, or splashable removal/creature. Creatures 3-9, removal 1-3. wall of Frost 2.5: Solid pick in-color; creatures 5-12, removal 3-5. Dark Favor 2.0: Creatures 10-16; removal 6-7. Elvish Mystic 1.5: My 23rd or 22nd card, depending on removal. Act of Treason 1.0: 23rd card if I don't maindeck an additional land. Lay of the Land 0.5: This card will sometimes be sideboarded in. Brave the Elements 0.0: I will shred this card for counters. Darksteel Forge

That's the thing about chance...you can't have too many expectations about it



Heh, heh. Really, that's going to be your line? If you flipped a coin dozens of times you wouldn't expect heads and tails to come up with equal frequency? If you rolled two six-sided dice dozens of times you wouldn't expect to roll a 7 more often than any other number?
Ok, I'd like the following data:
1:  The number of games in which you would ordinarily mulligan, but chose not to in this case.
2:  Your win % in those games.
3:  Your win % in the same format on single mulligans.
Exclude the first 2 weeks of the set being out in your data, as the quality of both your play/drafting and that of the average opponent will fluctuate greatly. 

Why does everyone think I'm phantom lancer? QFT:

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139359831 wrote:
I hope all this helps you to see things in a greater light—and understand that Magic: the Gathering was really created by extraterrestials using Richard Garfield as a medium. The game itself reflects the socio-psycho realtivity between living beings, and the science that takes precedence over them—to define reality for them all (like telekinesis, weather, scientific reaction, phenomenon, ingenuity, how the brain works, etc.). I'd also bet there is an entity floating thousands of miles above us, looking down on the current state of game, shaking its fist like... "Wtf are you doing?! You're getting it all screwed up!". Awkward—to be evolved, and yet still subject to the ladder that is the concepts of the game. In this case, misconception, corruption, and deception. With the realities of each color becoming distorted (through oblivious designers), leading the game to reflect a false state of reality that warps the understanding that other people have about those things. For example, people thinking that white could be anything except pure good. This shouldn't be too far off though, I mean...Magic is designed based on reality after all, so that entity (those entities) should be subject to those things. Anyways, I guess when you're busy doing space stuff you can't always be around to ensure quality control. It's no wonder they choose Garfield, they're so much alike; that's exactly what happened to him and Magic.
166199665 wrote:
omg snortng so much febbdelicious /intocixated in rl

That's the thing about chance...you can't have too many expectations about it



Heh, heh. Really, that's going to be your line? If you flipped a coin dozens of times you wouldn't expect heads and tails to come up with equal frequency? If you rolled two six-sided dice dozens of times you wouldn't expect to roll a 7 more often than any other number?



Obviously yes, but I would not consider the dice or coin broken if the result was not the exact median result. In fact, a "wrong" result is very likely (individually more unlikely than the "right" result but together far more likely). You roll a 7 only something like 1/6th of the time.
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What exactly is wrong with testing the MTGO shuffler? I've been keeping records of draws and the common thread behind all of them was that online clumps of lands come up considerably more often than one would expect by chance.



What's your sample size here?  If you haven't recorded at least 10,000+ (preferably 100,000+) draws, you're not going to get anything statistically significant.  This reminds me of people trying to prove that the RNGs at online poker sites are rigged.

Good to know this

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What exactly is wrong with testing the MTGO shuffler? I've been keeping records of draws and the common thread behind all of them was that online clumps of lands come up considerably more often than one would expect by chance.



What's your sample size here?  If you haven't recorded at least 10,000+ (preferably 100,000+) draws, you're not going to get anything statistically significant.  This reminds me of people trying to prove that the RNGs at online poker sites are rigged.




If you want to read about the test you can go over to the Online forum where the results are posted.

As for sample size, there are no Magic numbers in statistics. Not 10,000, not 100,000. If you had a particular p value you were looking for you could calculate the minimum number of samples required observe that value, but that number is not going to be anywhere near 10,000.

If you observe a small deviation from the expected results over a large number of samples, that can be statistically significant, as can a large deviation from the expected results over a small number of samples. Sample size is built into every test.
Oh look, another one of these topics.

Why do you spend so much time complaining about bad luck and researching online shuffler and/or mulligan statistics?  How does this make you a better player?  I complain sometimes.  Stupid crap happens.  But many times, you have to put a significant amount of stock in skill, both your's and your opponent's.  At the RtR pre-release, I went 5-2, losing in the final two rounds.  I was frustrated (my last opponent's deck was an insane Selesnya deck with multiple Grove of the Guardians with tons of populate) and ended up missing top 8, despite having the highest tiebreakers of all the 5-1s going into the final round.

Later on, knowing more about the format, I thought about my deck selection.  I chose Selesnya as my guild and ran blue alongside those colors with a light splash of black, which I thought I could do very easily because of my two Chromatic Lanterns.  I had removal and tricks up the wazoo.  On the other hand, my pool was STACKED.  I had three Annihilating Fires that were seeing no use due to guild alignment not working.  I had plenty of playable Selesnya cards that I eschewed for the third and fourth colors adding more removal.  I easily could have ran straight-up g/w with that pool and ended up with a more consistent, cohesive deck.  But I didn't.  Instead, I fell to the luck of the tiebreakers, and although I'm still puzzled how I fell so far (seriously, did all of my opponents lose their matches or something?), I can't just blame it on luck.  I made mistakes.

Although you know much more about a format as time passes, so does everyone else.  Stop worrying about mulligans and become a better player.
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Well actually his data may be showing that his prior mulligan algorithm was flawed.

As for the MTGO shuffler, people have long said that it seems harsher because IRL people shuffle imperfectly. Personally I don't know about such things, not having played IRL Magic for many, many years. 
I'm not sure why everyone is jumping on silentbob here. He just realized that he was mulliganing too much before. Now he's learned that a lot of hands are worth keeping even though they don't look good at first glance. It's a good lesson.
I'm not sure why everyone is jumping on silentbob here. He just realized that he was mulliganing too much before. Now he's learned that a lot of hands are worth keeping even though they don't look good at first glance. It's a good lesson.




A reasonable person would have come to those conclusions. However, Bobus is using this as a way to say the modo shuffler is flawed and imply that the mulligan rules should be changed. If you're not fed up with him you've obviously not endured that much of his mindless drivel.
I'm not sure why everyone is jumping on silentbob here. He just realized that he was mulliganing too much before. Now he's learned that a lot of hands are worth keeping even though they don't look good at first glance. It's a good lesson.



A reasonable person would have come to those conclusions. However, Bobus is using this as a way to say the modo shuffler is flawed and imply that the mulligan rules should be changed. If you're not fed up with him you've obviously not endured that much of his mindless drivel.



The MtGO shuffler flaw and mulliganing strategy are too separate things. In order to test the shuffler I needed to not mulligan for several games. In doing so I realized that I did better not mulliganing any 1 or 5 land hands than I had making decisions based on the cards (and generally dumping most 1 landers) Which I thought was an interesting result in itself.
I'm not sure why everyone is jumping on silentbob here. He just realized that he was mulliganing too much before. Now he's learned that a lot of hands are worth keeping even though they don't look good at first glance. It's a good lesson.



A reasonable person would have come to those conclusions. However, Bobus is using this as a way to say the modo shuffler is flawed and imply that the mulligan rules should be changed. If you're not fed up with him you've obviously not endured that much of his mindless drivel.



The MtGO shuffler flaw and mulliganing strategy are too separate things. In order to test the shuffler I needed to not mulligan for several games. In doing so I realized that I did better not mulliganing any 1 or 5 land hands than I had making decisions based on the cards (and generally dumping most 1 landers) Which I thought was an interesting result in itself.


How does not mulliganing test the shuffler again?

Why does everyone think I'm phantom lancer? QFT:

Show
139359831 wrote:
I hope all this helps you to see things in a greater light—and understand that Magic: the Gathering was really created by extraterrestials using Richard Garfield as a medium. The game itself reflects the socio-psycho realtivity between living beings, and the science that takes precedence over them—to define reality for them all (like telekinesis, weather, scientific reaction, phenomenon, ingenuity, how the brain works, etc.). I'd also bet there is an entity floating thousands of miles above us, looking down on the current state of game, shaking its fist like... "Wtf are you doing?! You're getting it all screwed up!". Awkward—to be evolved, and yet still subject to the ladder that is the concepts of the game. In this case, misconception, corruption, and deception. With the realities of each color becoming distorted (through oblivious designers), leading the game to reflect a false state of reality that warps the understanding that other people have about those things. For example, people thinking that white could be anything except pure good. This shouldn't be too far off though, I mean...Magic is designed based on reality after all, so that entity (those entities) should be subject to those things. Anyways, I guess when you're busy doing space stuff you can't always be around to ensure quality control. It's no wonder they choose Garfield, they're so much alike; that's exactly what happened to him and Magic.
166199665 wrote:
omg snortng so much febbdelicious /intocixated in rl
I wanted to record every draw from a 40 card deck from start to finish. That means no mulligans and no shuffle effects.
Well actually his data may be showing that his prior mulligan algorithm was flawed.

As for the MTGO shuffler, people have long said that it seems harsher because IRL people shuffle imperfectly. Personally I don't know about such things, not having played IRL Magic for many, many years. 



Part of the problem with the MTGO shuffler may be that it is damn hard to make anything computer-based actually "random".  The appearance of randomness is easy, but actual randomization is almost impossible to code for.  Which creates all sorts of problems with anthing that relies on randomization.

That said, I don't play MTGO.  Just an outside thought.
I know a lot of people are calling for a larger sample size of data, but I have to say you generally have to do some minimal research from a smaller pool of data before launching into a full-on investigation. I'm not saying I want more threads on MTGO shuffling, but I've heard enough about it to feel like it could, to certain concerned parties, warrant some sort of investigation that would be outside the scope of bobus's abilities.

I found Carmen Sandiego before you were born unless you're Zlehtnoba.

If you flipped a coin dozens of times you wouldn't expect heads and tails to come up with equal frequency?



No, I wouldn't. Anyone who would has a seriously flawed understanding of statistics.
If you flipped a coin dozens of times you wouldn't expect heads and tails to come up with equal frequency?



No, I wouldn't. Anyone who would has a seriously flawed understanding of statistics.



Now if you flipped it hundreds of times, it should start to even out however.  Key word is *should*. 
If I flipped 60 coins, and 1/5 of them were a special kind of coin (assuming theat 1/5 of those hands you would have normally mulliganned) and then I, without recording any statistics, got the feeling that I was getting more heads than tails, I wouldn't assume that the special coins were rigged towards heads.  Now, add to this the fact that you did all of your drafts in a new format, which will change your winrate, and you have statistically nothing.

Why does everyone think I'm phantom lancer? QFT:

Show
139359831 wrote:
I hope all this helps you to see things in a greater light—and understand that Magic: the Gathering was really created by extraterrestials using Richard Garfield as a medium. The game itself reflects the socio-psycho realtivity between living beings, and the science that takes precedence over them—to define reality for them all (like telekinesis, weather, scientific reaction, phenomenon, ingenuity, how the brain works, etc.). I'd also bet there is an entity floating thousands of miles above us, looking down on the current state of game, shaking its fist like... "Wtf are you doing?! You're getting it all screwed up!". Awkward—to be evolved, and yet still subject to the ladder that is the concepts of the game. In this case, misconception, corruption, and deception. With the realities of each color becoming distorted (through oblivious designers), leading the game to reflect a false state of reality that warps the understanding that other people have about those things. For example, people thinking that white could be anything except pure good. This shouldn't be too far off though, I mean...Magic is designed based on reality after all, so that entity (those entities) should be subject to those things. Anyways, I guess when you're busy doing space stuff you can't always be around to ensure quality control. It's no wonder they choose Garfield, they're so much alike; that's exactly what happened to him and Magic.
166199665 wrote:
omg snortng so much febbdelicious /intocixated in rl
The chance of hitting exactly 50:50 heads:tails is largest at exactly two throws (a 50% chance). Increasing the number of throws makes it more likely to end closer to the average, but less likely to hit spot on average. With four tosses, the chance is 6/16, or roughly 38%. With six tosses, the chance is 20/64, or about 31%. Increasing the amount of throws even more further dilates the chance of hitting a ratio of exactly 50:50 - on the other hand, the risk of hitting "all heads" or "all tails" (which is 2/4 with two throws, or 50%) is also mitigated; at six throws, it's 2/64, or about 3,1%. At eight throws, it drops below 1%.
Preparing for the M14 Prerelease - New article up! IN THE TANK - my very own blog for rambling about Magic!
In this scenario one would expect to observe a proportion that is close to the expected proportion. In a normal distribution every step away from the expected proportion is increasingly less likely.

As for this experiment, I am hitting some of the bad draws now. You know, kept a single land, never drew a third type stuff. But it does have me intrigued enough to start a mulliganing theory thread.