8 rifles is less efficient than (example) 2 rifles, 1 pile , 2 rifles, 1 magician, 2 rifles. The number of rifles is less than 8, yet the outcome of randomization is much bigger.
Well if you do find that study, please do let me know. In order to keep my OP airtight I've been trying to only put material there that I can either cite in a scientific journal or extrapolate from such a citation.
If you find the article I'll be more than happy to dig through it and see what I can add to the OP.
Quote from Razzzp »
Does riffle shuffle damage cards or just a myth?
From what people have been saying, if you "riffle smart," ie only riffle the corners and then mash (like they do in casinos), sleeve or even double-sleeve your cards, don't bridge after riffling, etc., then you should be fine.
If you ask me, it's better to go to extra lengths to make riffling work than to simply give up on riffling altogether and be complacent with a non-random (ie stacked) deck.
One thing I wanted to clarify. When I say I "mash" shuffle, I'm not exactly sure that's what I'm doing.
If by mashing shuffling you're referring to that overhand shuffle where they take the cards from the back and using an overhand shuffling motion, mix them into the middle of the deck, that's not what I do.
I divide the deck into 2 equal piles. I line them up, side by side, tall ends up, and kind of "mash" the 2 piles into each other, trying to make them evenly distributed throughout.
Maybe this is actually closer to rifle shuffling without the rifle part. I don't know. It's so hard to visually describe shuffling methods. I guess I could make a video, put it up on YouTube so you could see exactly how I shuffle.
A properly randomized deck will still have land clumps.
Your poor shuffling technique will cause you to get mana screwed less often than you're intended to, even if you still have no idea what order the cards are in.
Your poor shuffling technique therefore gives you an unfair advantage over someone who has a properly randomized deck, even if you're not trying to cheat.
Also, just because there's no apparent pattern with one iteration of your poor shuffling technique doesn't mean that there's no long-term trend for certain (sometimes subtle) patterns.
It was just a study done in his free time, not a published white paper I doubt it would fit your criteria. However, the judge lists (I think at that time we were still under one list only, not sure) used it heavily.
Still, if you find it, do let me know. Even if it's not a published article, if it's by a reputable guy who knows what he's talking about I'll still probably be able to get some use of it.
I just want to see it before I use it, understandably, because I want the this thread to be an actual "truth and maths" thread, with verifiable truths and maths, that can be used as a genuine resource in the future.
I couldn't have summarized it better myself. The one thing you left out is that poor shuffling is not only unintentional cheating, it can even be exploited and manipulated to become intentional cheating in a manner that would be much more challenging to pull off with more sound shuffling practices.
A properly randomized deck will still have land clumps.
Your poor shuffling technique will cause you to get mana screwed less often than you're intended to, even if you still have no idea what order the cards are in.
Your poor shuffling technique therefore gives you an unfair advantage over someone who has a properly randomized deck, even if you're not trying to cheat.
Also, just because there's no apparent pattern with one iteration of your poor shuffling technique doesn't mean that there's no long-term trend for certain (sometimes subtle) patterns.
The problem with all this is you're talking relative, ambiguous and meaningless terms.
"Properly randomized?"
"Poor shuffling?"
What the hell does that even mean? Can you quantify those two statements? No, you can't because they're so ambiguous.
Your properly randomized is one person's overkill and another person's "sorry, that's not good enough for me."
Your poor shuffling is one person's "better than it needs to be in practice" and another person's "that's beyond poor."
I am sufficiently confident that if I sat down in front of any Magic player in the entire world and shuffled my cards the way I shuffle them that they'd be more than satisfied that they are "properly randomized."
But like so what? What does any of this even prove in a real life situation short of somebody sitting there and prearranging his deck? Sure, if you do nothing but pile shuffle and present your deck, your opponent can call a judge and there WILL be consequences because it says right in rules that pile shuffling alone is not allowed.
But anything over and above that is just fine regardless of how anybody feels about how "properly randomized" that deck may be.
So what exactly is the point of all this?
To find the precise number of times to do a particular shuffle so that you take the least amount of time and make the most random pile of cards possible?
Great we get it. I'll file that under my list of things that I'll probably never need to know when it comes to playing practical Magic.
I have no doubt that some folks might care. In fact, some might take this bit of info as the gospel and not only shuffle their deck in that manner forevermore, but work to perfect the technique. I've seen stranger.
But in the grand scheme of things, for the average schmo playing Magic, this isn't going to change the game as we know it.
What the hell does that even mean? Can you quantify those two statements? No, you can't because they're so ambiguous.
Yes, actually, we can. Have you been paying attention at all to the math that has been discussed in my OP and on the previous pages?
"Properly randomized" means that the total variation norm has been minimized via shuffling to to the point that any further shuffles will not reduce it by more than a negligible amount. The total variation norm is a related concept to the number of sequences or runs; the less random you are, the more runs you have, akin to a "mana weave."
"Poor shuffling" refers to any shuffling technique which either achieves inefficiently (e.g. overhand shuffling, which may take anywhere from 1000 to 3000 shuffles to achieve proper randomization) or never achieves (e.g. pile shuffling) randomness.
How random you want to be is ultimately your decision. If you want to be less-than-perfectly randomized so your deck is stacked, that's your choice. But you should understand that inferior shuffling methods are indeed stacking your deck, and that they do make a noticeable difference on gameplay, and not fall into the delusion of thinking that you're achieving "pretty random" or "random enough" with anything other than riffling/mashing 7+ times.
But in the grand scheme of things, for the average schmo playing Magic, this isn't going to change the game as we know it.
If even just a handful of people read this thread and come out of it with their misconceptions corrected regarding the nature of shuffling and randomness, then that's already made it worthwhile to write. Ideally the whole world should be more educated about this, but these things take time and continued effort, not a defeatist or apathetic approach like the one you're taking.
Thanks for this. I know I've been insufficiently shuffling for a while now, but it was difficult to put my finger on the exact problem. Now, at least, I have mathematical evidence for what good shuffling is, and can just do that.
Yes, actually, we can. Have you been paying attention at all to the math that has been discussed in my OP and on the previous pages?
"Properly randomized" means that the total variation norm has been minimized via shuffling to to the point that any further shuffles will not reduce it by more than a negligible amount. The total variation norm is a related concept to the number of sequences or runs; the less random you are, the more runs you have, akin to a "mana weave."
"Poor shuffling" refers to any shuffling technique which either achieves inefficiently (e.g. overhand shuffling, which may take anywhere from 1000 to 3000 shuffles to achieve proper randomization) or never achieves (e.g. pile shuffling) randomness.
How random you want to be is ultimately your decision. If you want to be less-than-perfectly randomized so your deck is stacked, that's your choice. But you should understand that inferior shuffling methods are indeed stacking your deck, and that they do make a noticeable difference on gameplay, and not fall into the delusion of thinking that you're achieving "pretty random" or "random enough" with anything other than riffling/mashing 7+ times.
If even just a handful of people read this thread and come out of it with their misconceptions corrected regarding the nature of shuffling and randomness, then that's already made it worthwhile to write. Ideally the whole world should be more educated about this, but these things take time and continued effort, not a defeatist approach like the one you're taking.
Okay, if you read my first post on how I shuffle my deck, it is random. It is NOT stacked and I do NOT use your method.
There are other ways to randomly shuffle a deck without having to do 8 rifle shuffles. If you claim that is the only way, you are wrong.
The most efficient way? Maybe. Who cares? Is anybody going to take my head off if I take an extra minute or two to shuffle. I'm allowed 3 minutes to present my deck for cutting and I can get my deck randomly shuffled in that time. Again, read how I shuffle. It is random. In fact, it may be more random than your method.
In short, there is more than one way to skin a cat.
"Properly randomized" means that the total variation norm has been minimized via shuffling to to the point that any further shuffles will not reduce it by more than a negligible amount. The total variation norm is a related concept to the number of sequences or runs; the less random you are, the more runs you have, akin to a "mana weave."
That's not exactly a good explanation of what the variation norm is For one thing, the variation norm is a property of the shuffling procedure, not a statistic of the final distribution of cards in the deck like run count is.
Also, I agree that the variation distance from the uniform distribution is a good way to measure the randomness of a shuffle, but even then people will not agree on what variation distance is required for "sufficiently randomized". It is clear that a variation distance of 1 is not sufficient, and that a variation distance of (say) 0.01 is, but where is the cutoff?
I divide the deck into 2 equal piles. I line them up, side by side, tall ends up, and kind of "mash" the 2 piles into each other, trying to make them evenly distributed throughout.
That's what I define as mash shuffling in the OP.
As I've said countless times already, if you're doing this, and your "mashes" just tight enough but not too tight to effectively emulate a riffle shuffle (which is challenging, but possible), and you're not cheating while you do it, then you are essentially performing a riffle shuffle without the riffle.
If you do this eight times, you have essentially riffled eight times, and your deck is fully random.
In other words, mashing properly 8 times is not any more or less inferior to riffling 8 times; if you're mashing properly 8 times, you ARE riffling 8 times.
Quote from TheLizard »
Also, I agree that the variation distance from the uniform distribution is a good way to measure the randomness of a shuffle, but even then people will not agree on what variation distance is required for "sufficiently randomized". It is clear that a variation distance of 1 is not sufficient, and that a variation distance of (say) 0.01 is, but where is the cutoff?
As you know, it's tough to explain the variation norm to a general audience, particularly without showing the formula to calculate it and without explaining what a uniform distribution is; making a connection to card sequences and the effects on gameplay is something people can grasp more readily.
That said, the cutoff Bayer and Diaconis use in the 1992 article, which set the precedent for most if not all of the articles published in the future, uses a cutoff of 0.5 as shown in this graph to define "sufficiently" or "properly randomized." The 7th shuffle of a 52-card deck is the one that brings the total variation norm below 0.5.
I suppose it can indeed be argued that a more stringent value than 0.5 should be used, but that's really beyond the scope of this FAQ-primer-thing. I'm trying to go off of only what's in the literature to keep things as airtight as possible.
If even just a handful of people read this thread and come out of it with their misconceptions corrected regarding the nature of shuffling and randomness, then that's already made it worthwhile to write. Ideally the whole world should be more educated about this, but these things take time and continued effort, not a defeatist or apathetic approach like the one you're taking.
The public in general needs better eduction in math and probability anyway. This is that - applied to a game that many people like.
As I've said countless times already, if you're doing this, and your "mashes" just tight enough but not too tight to effectively emulate a riffle shuffle (which is challenging, but possible), and you're not cheating while you do it, then you are essentially performing a riffle shuffle without the riffle.
If you do this eight times, you have essentially riffled eight times, and your deck is fully random.
In other words, mashing properly 8 times is not any more or less inferior to riffling 8 times; if you're mashing properly 8 times, you ARE riffling 8 times.
As you know, it's tough to explain the variation norm to a general audience, particularly without showing the formula to calculate it and without explaining what a uniform distribution is; making a connection to card sequences and the effects on gameplay is something people can grasp more readily.
That said, the cutoff Bayer and Diaconis use in the 1992 article, which set the precedent for most if not all of the articles published in the future, uses a cutoff of 0.5 as shown in this graph to define "sufficiently" or "properly randomized." The 7th shuffle of a 52-card deck is the one that brings the total variation norm below 0.5.
I suppose it can indeed be argued that a more stringent value than 0.5 should be used, but that's really beyond the scope of this FAQ-primer-thing. I'm trying to go off of only what's in the literature to keep things as airtight as possible.
So then if we are adding pile shuffling and overhand shuffling to this then is that overkill?
As you know, it's tough to explain the variation norm to a general audience, particularly without showing the formula to calculate it and without explaining what a uniform distribution is; making a connection to card sequences and the effects on gameplay is something people can grasp more readily.
Yeah, but I think the difference between a sample statistic and a property of the shuffling method itself is important. Otherwise* people will be under the impression that there are certain arrangements of the deck that are "more random" than others.
*Okay, to be fair, some people probably will be under this impression no matter what we do.
As for the variation distance that is acceptable, I would agree that 0.5 is a good start, but on the other hand I can riffle shuffle my deck 11 times in one minute (I just timed it), which would give a variation distance of about 0.03 or less in a very reasonable amount of time. So I guess I don't have a ton of empathy for those who complain that sufficient randomization is too time-consuming.
Quote from "LandBoySteve" »
So then if we are adding pile shuffling and overhand shuffling to this then is that overkill?
Probably, yes. The pile shuffling and overhand shuffling isn't going to have too much of an effect, if any, but it won't hurt either.
But as has been pointed out, if pile shuffling allows you to count your cards and make sure you're playing with the whole deck, it may be worthy of your time despite not randomizing the cards.
Let me start by throwing in a quick statement in support of pile shuffling as a fast way to count your deck (and nothing else):
G1 of my last match last night saw me, due to a error when un-sideboarding before, sitting at 37 cards. Even if I hadn't been caught, those 3 cards were my frontline medic and two mountains I was using for my red splash. Thank heavens.
That being said... I dislike the term "mash", since it promotes doing it roughly. A good side-shuffle doesn't need to be heavy handed, and as long as you make sure that the top quarter or so of the bottom half of the deck is over the top half (and vice versa) moves the top card. You can do this a good 20 times really, really quickly.
In any case... yes, "less" random would be better for us. We don't get that luxury. If you allow what you want your deck to do to bias your attempts to randomize it, you're cheating.
I don't like to bend my cards with a riffle so like most others I use a mash. It took a bit to get right but what I do is grab approximately the middle half of my deck, put the rest together, and mash it. I've found if I mash in the middle with a loose grip rather than corner to corner I get 3 to 4 clumps of 2-3 cards in the shuffle, and there will be some on the top or bottom (usually bottom) not mashed at all depending on how accurate my grab of half the cards was. Then I cut the deck and put the bottom half on top. This way I ensure that my top and bottom cards which may have seen no mashing are now in the middle of the deck and end up in the group I grab out of the middle for the next mash. It's not as good as a well done riffle since I don't get as many clumps, but I do that 12-14 times before games and usually 3-4 for a shuffle in the middle of a game due to time concerns.
I've never sat down and figured out the exact number I should do but it seems to work alright.
What would be helpful is if there were video of a properly done mash.
A properly done riffle would also be very useful to show in a video. It seems most people don't know how to riffle magic cards. To be fair, it is a little more complex than riffling a standard deck of cards.
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Unfortunately I possess neither the time nor the resources to make videos right now.
That said, many people (myself included) have offered explanations of various proper riffling/mashing techniques throughout this thread--there is more than one right answer.
If you really need a visual aid, there are plenty of videos on youtube that can be found with a quick and simple search showing:
How to casino riffle -- where you only riffle the edges and then mash, with no bridge. It's slightly more challenging with sleeved/double-sleeved cards, but once you get the hang of it the technique is really the same.
How to mash shuffle -- though some videos don't focus explicitly on the tightness of the mashing, after reading this thread you should know to stay vigilant about keeping your mashes nice and tight, not loose, trying to emulate a riffle.
It might help to riffle a deck you're comfortable riffling for practice, like a 52-card deck, or personally I'd recommend gathering up the magic cards you would feel comfortable riffling, like your cheap two-cent commons, and riffle those to get the feel of riffling magic cards, since the cards themselves are slightly thicker than regular 52-card playing cards and you have to get the hang of how they feel. When you perform your riffle (casino riffle or otherwise), before you slide the cards together, observe how they're distributed from each split half of the deck: if you did it right, the "clumps" from each half will be mostly 1 and 2 cards, rarely 3. That distribution right there is what you're trying to emulate during a mash, such that your mashes essentially function as riffles.
I don't like to bend my cards with a riffle so like most others I use a mash. It took a bit to get right but what I do is grab approximately the middle half of my deck, put the rest together, and mash it. I've found if I mash in the middle with a loose grip rather than corner to corner I get 3 to 4 clumps of 2-3 cards in the shuffle, and there will be some on the top or bottom (usually bottom) not mashed at all depending on how accurate my grab of half the cards was. Then I cut the deck and put the bottom half on top. This way I ensure that my top and bottom cards which may have seen no mashing are now in the middle of the deck and end up in the group I grab out of the middle for the next mash. It's not as good as a well done riffle since I don't get as many clumps, but I do that 12-14 times before games and usually 3-4 for a shuffle in the middle of a game due to time concerns.
Even though your mashing method isn't perfectly ideal, if you're doing it "nearly right" 12-14 times instead of the regular 7-8 times, you're probably fine. The additional shuffles compensate. Again, though, I'd recommend riffling a deck of Magic cards you don't care about (like 60 crap commons) or at least a deck of 52-cards, paying close attention to how a riffle actually distributes the cards from each pile, and then shoot for that same distribution as your "gold standard" every time you mash in the future.
Between casino riffling (for people who have faith in the fact that, with proper protection, riffling doesn't damage cards) and mashing done in emulation of riffling (for sticklers who insist their cards remain straight at all times), and considering that both of these techniques can easily be performed at least 9 or 10 times in a minute, there's really no excuse to use any method of shuffling other than mashing or riffling, with the sole exception of maybe one pile shuffle at the beginning of the game to quality-control your deck (ensure you're using the right number of cards, make sure your sleeves are all good, etc.).
I'm in the process of adding some relevant, helpful pictures to the OP since people seem to like pictures to give them something to look at besides big blobs of text.
Just wanted to say thank you to the OP and everyone else that has made a positive contribution to this thread. I think it's good for everyone to understand some of the basic concepts presented here for three important reasons:
To help understand what "randomization" is and what are the quickest and easiest ways to make sure your deck is sufficiently randomized.
To help spot opponents who may try to cheat by intentionally not randomizing their deck sufficiently.
To help players better understand that "chaotic" and "random" are not the same thing.
Even though your mashing method isn't perfectly ideal, if you're doing it "nearly right" 12-14 times instead of the regular 7-8 times, you're probably fine. The additional shuffles compensate. Again, though, I'd recommend riffling a deck of Magic cards you don't care about (like 60 crap commons) or at least a deck of 52-cards, paying close attention to how a riffle actually distributes the cards from each pile, and then shoot for that same distribution as your "gold standard" every time you mash in the future.
I practice shuffling on a stack in my spare time. I'm pretty bad at it though so I get fairly large clumps. I'm always looking to improve it, but the way I do it now seems to work fairly well. I can end a game and pile up all my cards (including a big pile of lands if I'm playing control) and shuffle and not have that clump remain. There's still streaks of land/no land, but that's what there's supposed to be. I don't get a giant block of 10 lands though.
Thanks for the informative post! I am definitely going to try doing 8 riffles in the future. I hope people who read your post know the difference between randomization and a stacked deck.
Well if you do find that study, please do let me know. In order to keep my OP airtight I've been trying to only put material there that I can either cite in a scientific journal or extrapolate from such a citation.
If you find the article I'll be more than happy to dig through it and see what I can add to the OP.
From what people have been saying, if you "riffle smart," ie only riffle the corners and then mash (like they do in casinos), sleeve or even double-sleeve your cards, don't bridge after riffling, etc., then you should be fine.
If you ask me, it's better to go to extra lengths to make riffling work than to simply give up on riffling altogether and be complacent with a non-random (ie stacked) deck.
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Casual: WB [[Primer]]Clerics Tribal; BU Affinity
EDH: ...U [[Primer]]Arcum Dagsson; BG Legal Stax; B Illegal Stax
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Other stuff: [[Official]]Shuffling, Truth + Maths
If by mashing shuffling you're referring to that overhand shuffle where they take the cards from the back and using an overhand shuffling motion, mix them into the middle of the deck, that's not what I do.
I divide the deck into 2 equal piles. I line them up, side by side, tall ends up, and kind of "mash" the 2 piles into each other, trying to make them evenly distributed throughout.
Maybe this is actually closer to rifle shuffling without the rifle part. I don't know. It's so hard to visually describe shuffling methods. I guess I could make a video, put it up on YouTube so you could see exactly how I shuffle.
In fact, I just might do that.
The rules require you to randomize your deck.
A properly randomized deck will still have land clumps.
Your poor shuffling technique will cause you to get mana screwed less often than you're intended to, even if you still have no idea what order the cards are in.
Your poor shuffling technique therefore gives you an unfair advantage over someone who has a properly randomized deck, even if you're not trying to cheat.
Also, just because there's no apparent pattern with one iteration of your poor shuffling technique doesn't mean that there's no long-term trend for certain (sometimes subtle) patterns.
Older Magic as a Board Game: Panglacial Wurm , Mill
Still, if you find it, do let me know. Even if it's not a published article, if it's by a reputable guy who knows what he's talking about I'll still probably be able to get some use of it.
I just want to see it before I use it, understandably, because I want the this thread to be an actual "truth and maths" thread, with verifiable truths and maths, that can be used as a genuine resource in the future.
I couldn't have summarized it better myself. The one thing you left out is that poor shuffling is not only unintentional cheating, it can even be exploited and manipulated to become intentional cheating in a manner that would be much more challenging to pull off with more sound shuffling practices.
Legacy: GWR Enchantress <--That's my banner! (lol tinypic removed it)
Casual: WB [[Primer]]Clerics Tribal; BU Affinity
EDH: ...U [[Primer]]Arcum Dagsson; BG Legal Stax; B Illegal Stax
Proxy: .WX TriniStax
Other stuff: [[Official]]Shuffling, Truth + Maths
The problem with all this is you're talking relative, ambiguous and meaningless terms.
"Properly randomized?"
"Poor shuffling?"
What the hell does that even mean? Can you quantify those two statements? No, you can't because they're so ambiguous.
Your properly randomized is one person's overkill and another person's "sorry, that's not good enough for me."
Your poor shuffling is one person's "better than it needs to be in practice" and another person's "that's beyond poor."
I am sufficiently confident that if I sat down in front of any Magic player in the entire world and shuffled my cards the way I shuffle them that they'd be more than satisfied that they are "properly randomized."
But like so what? What does any of this even prove in a real life situation short of somebody sitting there and prearranging his deck? Sure, if you do nothing but pile shuffle and present your deck, your opponent can call a judge and there WILL be consequences because it says right in rules that pile shuffling alone is not allowed.
But anything over and above that is just fine regardless of how anybody feels about how "properly randomized" that deck may be.
So what exactly is the point of all this?
To find the precise number of times to do a particular shuffle so that you take the least amount of time and make the most random pile of cards possible?
Great we get it. I'll file that under my list of things that I'll probably never need to know when it comes to playing practical Magic.
I have no doubt that some folks might care. In fact, some might take this bit of info as the gospel and not only shuffle their deck in that manner forevermore, but work to perfect the technique. I've seen stranger.
But in the grand scheme of things, for the average schmo playing Magic, this isn't going to change the game as we know it.
Yes, actually, we can. Have you been paying attention at all to the math that has been discussed in my OP and on the previous pages?
"Properly randomized" means that the total variation norm has been minimized via shuffling to to the point that any further shuffles will not reduce it by more than a negligible amount. The total variation norm is a related concept to the number of sequences or runs; the less random you are, the more runs you have, akin to a "mana weave."
"Poor shuffling" refers to any shuffling technique which either achieves inefficiently (e.g. overhand shuffling, which may take anywhere from 1000 to 3000 shuffles to achieve proper randomization) or never achieves (e.g. pile shuffling) randomness.
How random you want to be is ultimately your decision. If you want to be less-than-perfectly randomized so your deck is stacked, that's your choice. But you should understand that inferior shuffling methods are indeed stacking your deck, and that they do make a noticeable difference on gameplay, and not fall into the delusion of thinking that you're achieving "pretty random" or "random enough" with anything other than riffling/mashing 7+ times.
If even just a handful of people read this thread and come out of it with their misconceptions corrected regarding the nature of shuffling and randomness, then that's already made it worthwhile to write. Ideally the whole world should be more educated about this, but these things take time and continued effort, not a defeatist or apathetic approach like the one you're taking.
Legacy: GWR Enchantress <--That's my banner! (lol tinypic removed it)
Casual: WB [[Primer]]Clerics Tribal; BU Affinity
EDH: ...U [[Primer]]Arcum Dagsson; BG Legal Stax; B Illegal Stax
Proxy: .WX TriniStax
Other stuff: [[Official]]Shuffling, Truth + Maths
Okay, if you read my first post on how I shuffle my deck, it is random. It is NOT stacked and I do NOT use your method.
There are other ways to randomly shuffle a deck without having to do 8 rifle shuffles. If you claim that is the only way, you are wrong.
The most efficient way? Maybe. Who cares? Is anybody going to take my head off if I take an extra minute or two to shuffle. I'm allowed 3 minutes to present my deck for cutting and I can get my deck randomly shuffled in that time. Again, read how I shuffle. It is random. In fact, it may be more random than your method.
In short, there is more than one way to skin a cat.
Also, I agree that the variation distance from the uniform distribution is a good way to measure the randomness of a shuffle, but even then people will not agree on what variation distance is required for "sufficiently randomized". It is clear that a variation distance of 1 is not sufficient, and that a variation distance of (say) 0.01 is, but where is the cutoff?
That's what I define as mash shuffling in the OP.
As I've said countless times already, if you're doing this, and your "mashes" just tight enough but not too tight to effectively emulate a riffle shuffle (which is challenging, but possible), and you're not cheating while you do it, then you are essentially performing a riffle shuffle without the riffle.
If you do this eight times, you have essentially riffled eight times, and your deck is fully random.
In other words, mashing properly 8 times is not any more or less inferior to riffling 8 times; if you're mashing properly 8 times, you ARE riffling 8 times.
As you know, it's tough to explain the variation norm to a general audience, particularly without showing the formula to calculate it and without explaining what a uniform distribution is; making a connection to card sequences and the effects on gameplay is something people can grasp more readily.
That said, the cutoff Bayer and Diaconis use in the 1992 article, which set the precedent for most if not all of the articles published in the future, uses a cutoff of 0.5 as shown in this graph to define "sufficiently" or "properly randomized." The 7th shuffle of a 52-card deck is the one that brings the total variation norm below 0.5.
I suppose it can indeed be argued that a more stringent value than 0.5 should be used, but that's really beyond the scope of this FAQ-primer-thing. I'm trying to go off of only what's in the literature to keep things as airtight as possible.
Legacy: GWR Enchantress <--That's my banner! (lol tinypic removed it)
Casual: WB [[Primer]]Clerics Tribal; BU Affinity
EDH: ...U [[Primer]]Arcum Dagsson; BG Legal Stax; B Illegal Stax
Proxy: .WX TriniStax
Other stuff: [[Official]]Shuffling, Truth + Maths
Older Magic as a Board Game: Panglacial Wurm , Mill
So then if we are adding pile shuffling and overhand shuffling to this then is that overkill?
*Okay, to be fair, some people probably will be under this impression no matter what we do.
As for the variation distance that is acceptable, I would agree that 0.5 is a good start, but on the other hand I can riffle shuffle my deck 11 times in one minute (I just timed it), which would give a variation distance of about 0.03 or less in a very reasonable amount of time. So I guess I don't have a ton of empathy for those who complain that sufficient randomization is too time-consuming. Probably, yes. The pile shuffling and overhand shuffling isn't going to have too much of an effect, if any, but it won't hurt either.
But as has been pointed out, if pile shuffling allows you to count your cards and make sure you're playing with the whole deck, it may be worthy of your time despite not randomizing the cards.
G1 of my last match last night saw me, due to a error when un-sideboarding before, sitting at 37 cards. Even if I hadn't been caught, those 3 cards were my frontline medic and two mountains I was using for my red splash. Thank heavens.
That being said... I dislike the term "mash", since it promotes doing it roughly. A good side-shuffle doesn't need to be heavy handed, and as long as you make sure that the top quarter or so of the bottom half of the deck is over the top half (and vice versa) moves the top card. You can do this a good 20 times really, really quickly.
In any case... yes, "less" random would be better for us. We don't get that luxury. If you allow what you want your deck to do to bias your attempts to randomize it, you're cheating.
I just throw my opponent's deck on the floor and make him pick it up. Is that sufficiently random?
A comic about the world's most addictive game, Magic: The Gathering.
I've never sat down and figured out the exact number I should do but it seems to work alright.
Older Magic as a Board Game: Panglacial Wurm , Mill
A properly done riffle would also be very useful to show in a video. It seems most people don't know how to riffle magic cards. To be fair, it is a little more complex than riffling a standard deck of cards.
Hoping for a cure, or at least an outbreak.
Level 1 Judge (yay)
Someone who knows how please do this.
That said, many people (myself included) have offered explanations of various proper riffling/mashing techniques throughout this thread--there is more than one right answer.
If you really need a visual aid, there are plenty of videos on youtube that can be found with a quick and simple search showing:
It might help to riffle a deck you're comfortable riffling for practice, like a 52-card deck, or personally I'd recommend gathering up the magic cards you would feel comfortable riffling, like your cheap two-cent commons, and riffle those to get the feel of riffling magic cards, since the cards themselves are slightly thicker than regular 52-card playing cards and you have to get the hang of how they feel. When you perform your riffle (casino riffle or otherwise), before you slide the cards together, observe how they're distributed from each split half of the deck: if you did it right, the "clumps" from each half will be mostly 1 and 2 cards, rarely 3. That distribution right there is what you're trying to emulate during a mash, such that your mashes essentially function as riffles.
Even though your mashing method isn't perfectly ideal, if you're doing it "nearly right" 12-14 times instead of the regular 7-8 times, you're probably fine. The additional shuffles compensate. Again, though, I'd recommend riffling a deck of Magic cards you don't care about (like 60 crap commons) or at least a deck of 52-cards, paying close attention to how a riffle actually distributes the cards from each pile, and then shoot for that same distribution as your "gold standard" every time you mash in the future.
Between casino riffling (for people who have faith in the fact that, with proper protection, riffling doesn't damage cards) and mashing done in emulation of riffling (for sticklers who insist their cards remain straight at all times), and considering that both of these techniques can easily be performed at least 9 or 10 times in a minute, there's really no excuse to use any method of shuffling other than mashing or riffling, with the sole exception of maybe one pile shuffle at the beginning of the game to quality-control your deck (ensure you're using the right number of cards, make sure your sleeves are all good, etc.).
Legacy: GWR Enchantress <--That's my banner! (lol tinypic removed it)
Casual: WB [[Primer]]Clerics Tribal; BU Affinity
EDH: ...U [[Primer]]Arcum Dagsson; BG Legal Stax; B Illegal Stax
Proxy: .WX TriniStax
Other stuff: [[Official]]Shuffling, Truth + Maths
All shuffling introduces wear on sleeves. There's no avoiding it.
Riffle shuffling will not bend cards, bridging a riffle shuffle does.
Legacy: GWR Enchantress <--That's my banner! (lol tinypic removed it)
Casual: WB [[Primer]]Clerics Tribal; BU Affinity
EDH: ...U [[Primer]]Arcum Dagsson; BG Legal Stax; B Illegal Stax
Proxy: .WX TriniStax
Other stuff: [[Official]]Shuffling, Truth + Maths
I practice shuffling on a stack in my spare time. I'm pretty bad at it though so I get fairly large clumps. I'm always looking to improve it, but the way I do it now seems to work fairly well. I can end a game and pile up all my cards (including a big pile of lands if I'm playing control) and shuffle and not have that clump remain. There's still streaks of land/no land, but that's what there's supposed to be. I don't get a giant block of 10 lands though.