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.
As I've beaten to death in Chaos vs. Randomness, simply having a deck that seems random doesn't necessarily mean it's random. That said, though, the way you described it earlier, I think you're pretty OK as it is now. If you really want to get it down pat, though, as with any other skill, anyone can master the shuffling technique (ideally first master riffling, then master mashing in the form of a riffle) with a bit of practice.
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.
I sincerely hope so, too. I see this thread's beginning to quiet down; after so many days of floating, I suspected it would eventually. That said, I hope, as the thread falls off the front page such that people will no longer readily browse through it, that it remains a valuable reference for people to recommend to others when the topic of shuffling comes up around MTGS. Just doing a quick google search on "magic the gathering shuffling," there's several good resources and several bad resources as the top hits, and with how widespread shuffling misconceptions are already, the last thing we need are unsure people referring to bad resources instead of good ones.
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.
The reason I postsed about random not being neccesarily optimal is that I've tried this before (shuffling is a big discussion point on sleight of hand forums and amoung stage magicians) and I noticed my decks did decidedly worse when I was doing 8 riffle shuffles. I had way more mana flood and mana screw then just doing a few mash shuffles and a quick casino riffle.
I added new links to another outstanding article of a real-life example of how a knowledgeable MTG player can actually employ pile shuffling to stack their deck during competitive play. The article is by Tim Pillards and can be found here.
This article was written back in 2003, even earlier than the Flores article. Today, ten years later, the notion of pile shuffling as an effective substitute for riffles is STILL all too pervasive!
I added new links to another outstanding article of a real-life example of how a knowledgeable MTG player can actually employ pile shuffling to stack their deck during competitive play. The article is by Tim Pillards and can be found here.
Reading that, I noticed something that I am not gonna call an error, but something to at least take note of.
After dividing this deck into four piles, we get:
A first pile with cards 0, 4, 8, 12... 32, 36 = 0+4*k.
A second pile with cards 1, 5, 9, 13... 33, 37 = 1+4*k.
A third pile with cards 2, 6, 10, 14... 34, 38 = 2+4*k.
A fourth pile with cards 3, 7, 11, 15... 35, 39 = 3+4*k.
Two things I would at least note here:
- it **SEEMS** he assumes you, in piling, go from last to first or first to last, and do that each time... For me anyways, I've noticed most people I play with casually at least, who pile, don't go from first to last, or last to first, for each pass but alternate.
What I mean: If you use the author's example of 4 piles, instead of going
P1, P2, P3, P4
they do:
P1, P2, P3, P4
P4, P1, P2, P3
P3, P1, P2, P4
...
...
etc.
- He seems to assume the piles will always be just stacked - not mashed together per-se, and also seems to assume the stacks will be re-stacked first over 2nd over 3rd over 4th pile over ... over Nth pile, or some other manner that is somewhat consistent like that... I've seen people stack 3rd over 1st over Nth over... and change it up with each pass, or even instead of doing any stacking, just mash the piles together.
Am I crazy in feeling like this is a lot to assume in drawing a conclusion all together, without taking in alternate methods [changing up the order of the piles you put a card in each pass, mashing the piles together instead of stacking, etc] into consideration - and if a player does all those things, for example, as opposed to if a player does not?
Do the author's examples using his modulus math hold true still if you did those things? [mashed instead of stacked, instead of going stack1 stack2 stack3 ... stackN each time alternating the order with each pass until all the cards were sorted into piles, etc]?
Reading that, I noticed something that I am not gonna call an error, but something to at least take note of.
Thank you for commenting on the thread. Sorry I didn't get to your post until just now. As always, your criticism is much appreciated.
- it **SEEMS** he assumes you, in piling, go from last to first or first to last, and do that each time... For me anyways, I've noticed most people I play with casually at least, who pile, don't go from first to last, or last to first, for each pass but alternate.
Whenever I see my friends pile shuffle, they all pile shuffle in the way he described:
P1, P2, ... , PN
P1, P2, ... , PN
P1, P2, ... , PN
over and over again, as if they were dealing out hands of poker. But we're both speaking from anecdotal evidence--without a doubt, people plaing Magic all over the world pile shuffle in different ways: different numbers of piles, mixing up the order of piles, and so forth.
But as I'll get to in a moment, none of that really matters.
Am I crazy in feeling like this is a lot to assume in drawing a conclusion all together, without taking in alternate methods [changing up the order of the piles you put a card in each pass, mashing the piles together instead of stacking, etc] into consideration - and if a player does all those things, for example, as opposed to if a player does not?
No, you're not crazy at all. He stipulates or assumes many things in his mathematical model (as is necessary for just about any mathematical model), and any savvy mathematician or statistician knows that those assumptions may not always be met in real life.
Nowhere in the article does Pillards say he was actually there at the tournament watching with his own eyes Mike Long shuffle his deck. He makes a reference to another article by Bob Dougherty in the first sentence, but if you follow that link you'll see it's dead (not surprising figuring Pillards' article itself is already ten years old).
Can we say that Pillards has proven beyond a reasonable doubt that Mike Long was cheating? Just from reading Pillards' article, no, we can't. But that's missing Pillards' broader point.
Do the author's examples using his modulus math hold true still if you did those things? [mashed instead of stacked, instead of going stack1 stack2 stack3 ... stackN each time alternating the order with each pass until all the cards were sorted into piles, etc]?
Piling in a different order, such as
P1, P2, P3, P4
P4, P3, P2, P1
as you described, would undoubtedly require a different formula, because the piles would look like
The math wouldn't be as simple, and at first glance I don't think the modulo would work as straightforwardly as it does in Pillards' article, but even here you can see a clear, predictable pattern: P1 increases by 7, then by 1, then by 7, then by 1. P4 is the opposite. P2 increases by 5, then 3, then 5, then 3. P3 is the opposite.
If you were to stack them up with P1 on top and P4 on bottom and pile them out one more time, you'd notice the same pattern going between the piles instead of within them (look at the columns instead of the rows):
I have no idea whether or not piling out in this method a certain number of times returns to the original deck configuration as it does in the scenario Pillards described. I'd have to do it by hand a bunch of times to find out. But like any pile shuffling method, it does create a pattern in the deck--it does NOT randomize it.
Again, the point is that pile shuffling creates patterns, not randomness, and Pillards' message (also Flores' message) still rings true that pile shuffling CAN be used by knowledgeable players to cheat...and if it CAN be used to cheat, in the interest of keeping the game fair for everyone, you must assume that it WILL be used to cheat--intentionally or otherwise. Pile shuffling is NOT a valid shuffling strategy. That's the bottom line.
Now, you brought up mashing the piles together instead of stacking them.
As I described in the OP and in several other posts, "mashing" can be the equivalent of a riffle (and therefore an effective contributor to deck randomness) if it's done in a certain way. But if you're going to mash anyway, you mind as well just skip the whole piling process that comes before it, because it's the mashing that's really "mixing up" your deck--the piling is just making your deck more patterned and therefore less random.
As I've said before, the mashing needs to be done in a manner that emulates a riffle, which in practice is a lot harder to accomplish and a lot less consistent than just double-sleeving your cards and riffling the edges like the way it's supposed to be done in the first place.
I hope this helps. Please don't hesitate to ask any questions or provide any further comments or criticism.
Riffle shuffling (or any form of shuffling), no matter how many times you do it, ultimately takes a deck from one arrangement to another arrangement. The more times you do it, the more random the arrangements become, but the net result is still a specific arrangement.
So what if somebody wrote a program that virtually executed X number of riffle shuffles on a list of integers equivalent to the number of cards in the physical deck of a player, then told the player how to rearrange their deck to match the arrangement of the shuffled integers?
It'd probably be slower unless the computer was executing the equivalent of an excessive number of riffle shuffles, but at least it wouldn't put excessive wear on the cards or require such ridiculousness as double-sleeving them.
So what if somebody wrote a program that virtually executed X number of riffle shuffles on a list of integers equivalent to the number of cards in the physical deck of a player, then told the player how to rearrange their deck to match the arrangement of the shuffled integers?.
If someone performs this technique before the deck is randomized, then they can still end up knowing the positions of various cards.
So what if somebody wrote a program that virtually executed X number of riffle shuffles on a list of integers equivalent to the number of cards in the physical deck of a player, then told the player how to rearrange their deck to match the arrangement of the shuffled integers?
That's an interesting thought.
There are already many algorithms that can do just that (the one in that link is a module for SAS, one of the leading computer programs for statistical analysis. Unfortunately SAS isn't really widely available--it's quite expensive and has a learning curve made for professional statisticians, not your average MTG players--but I'm sure someone out there could make a free applet or something that anybody could run on his or her laptop (unfortunately I'm only a budding novice at programming or I'd be doing it myself).
There are a few main problems with the concept, however, even if a riffle shuffling program were readily accessible and could spit out a sufficiently-randomized list of #'s from 1 to 60 in the blink of an eye:
Blind designation of cards. Those #'s 1 to 60 have to correspond to actual cards in your deck. If the player is the one assigning to which cards those 1, 2, 3, etc. correspond to (i.e. if the designation is not player-blind), then that defeats the whole point. Consider the scenario: you've just finished a game and you scoop your cards into a stack and slap it on top of your library. You know the order of cards in that stack because you just scooped it. You deal your library out individually (i.e. into 60 piles of 1 card each) and number those piles 1 to 60. You know which card is in which pile. Now you have your randomization algorithm tell you how to stack them up in a randomized manner. You STILL know what order they're in. This is in contrast to shuffling by hand, where there is no designation of cards required, and so the whole process is player-blind. I think this is what TeckGecko is saying--for this to work, you'd have to have the cards in an unknown order (i.e. shuffled) to begin with. There are mechanical shufflers into which you could feed a deck and it'll shuffle it for you (many casinos use these machines), but if people are paranoid about damaging their cards when handling them by hand, undoubtedly they won't let them be touched by a shuffling machine.
Time. Even if you had your deck in an unknown order, spreading them out into 60 different piles and ordering them back up one-by-one is a time-consuming process. Riffle-shuffling 7 or 8 times by hand would be a lot quicker, I'd assume. This problem becomes even more evident when you're shuffling 100-card EDH decks or 250-card Battle of Wits decks or what have you.
Human error/honesty. You're banking on the fact that the human player will indeed follow the computer's instructions to the letter, which he might not--whether because he's a cheater or just because he's human (and humans make mistakes). Again, this problem only gets worse for bigger decks.
It'd probably be slower unless the computer was executing the equivalent of an excessive number of riffle shuffles
If we were looking to shuffle 20 times, then yes, most certainly getting a computer program to do it would be more efficient. But "excessive" is a critical word--you only need to shuffle a 60-card deck 7 or 8 times to achieve a sufficiently random configuration.
but at least it wouldn't put excessive wear on the cards or require such ridiculousness as double-sleeving them.
I understand why double-sleeving your cards might seem ridiculous or redundant, but compared to the complexity and inconvenience of other options, double-sleeving your cards and riffling the old-fashioned way really does emerge as the LEAST ridiculous option available.
All the problems with my idea (except for time) are easily fixed by simply having players shuffle each others decks.
The problem I have with the idea of double-sleeving your cards to protect them from getting bent during riffle shuffling is that it seems to me that the very act of trying to double-sleeve cards would create moderate risk of bending the cards, which kind of defeats the purpose of it.
Anyway, as a kind of proof-of-concept, I created an Excel spreadsheet which generates a random number between 1 thru X, where X is the # of cards in your deck, then 1 thru X-1, 1 thru X-2, all the way until there are no more cards left in your deck. I sorted a deck of 60 GateCrash cards by card number then proceeded to shuffle following the randomly generated numbers in the spreadsheet. First number was 45, so I counted from the bottom of the deck up to 45, removed the 45th card and placed it as the 60th card in the shuffled deck. Next was 34, then 54, then 36, etc.... all the way to the end. It took me approximately 6 minutes to shuffle using this method for the first time, and that's with me occasionally loosing my place in the Excel spreadsheet and having to take a few seconds to determine which step I was on.
Looking through the newly shuffled deck, I'm very pleased with the results. It might be a relatively slow method compared to riffle shuffling, but it's an alternative that can achieve effectively random arrangements. With practice, and with a program specifically designed for this kind of shuffling instead of resorting to an Excel spreadsheet, this method could become reasonably fast. Still slower than riffle shuffling, but it would become a less drastic victory for riffle shuffling in this area, perhaps allowing this method's other benefits to make it a more appealing choice than riffle shuffling to some.
The problem I have with the idea of double-sleeving your cards to protect them from getting bent during riffle shuffling is that it seems to me that the very act of trying to double-sleeve cards would create moderate risk of bending the cards, which kind of defeats the purpose of it.
Double-sleeving is a great way to protect your cards. I've heard of people having problems bending the cards when using the Ultra-Pro perfect fits, but I've heard of no such problems with the KMC ones.
Double-sleeving will not appreciably protect against damage from riffle shuffling.
Double-sleeving is a great way to protect your cards. I've heard of people having problems bending the cards when using the Ultra-Pro perfect fits, but I've heard of no such problems with the KMC ones.
Double-sleeving will not appreciably protect against damage from riffle shuffling.
As much anecdotal evidence (just flip through this thread) seems to suggest that double-sleeving DOES appreciably protect against damage from riffling, particularly if you're riffling only the very edge as opposed to the whole card (and especially if you're not bridging--that's just a showmanship thing).
That said, I won't make any sweeping statement that double-sleeving does or does not offer complete protection, because all that's out there is anecdotal evidence, which is insufficient to merit a conclusion one way or the other.
What I can say with certainty is that double-sleeving certainly helps (or at least never hurts, unless you buy bad products), and that compromising the integrity of MTG as a game by permitting or turning a blind eye to unfair conduct in the interest of preserving card value is definitely the wrong choice.
Quote from Lain »
Anyway, as a kind of proof-of-concept, I created an Excel spreadsheet which generates a random number between 1 thru X, where X is the # of cards in your deck, then 1 thru X-1, 1 thru X-2, all the way until there are no more cards left in your deck. I sorted a deck of 60 GateCrash cards by card number then proceeded to shuffle following the randomly generated numbers in the spreadsheet. First number was 45, so I counted from the bottom of the deck up to 45, removed the 45th card and placed it as the 60th card in the shuffled deck. Next was 34, then 54, then 36, etc.... all the way to the end. It took me approximately 6 minutes to shuffle using this method for the first time, and that's with me occasionally loosing my place in the Excel spreadsheet and having to take a few seconds to determine which step I was on.
Well if you're using Excel a faster way to randomize be to simply put numbers 1-60 in a single column, let's say Column A, generate 60 random numbers in the next column over (Column B) with the =rand() input, and then sort Column A in order according to the random numbers in Column B (ascending or descending, your choice). Excel comes with a pretty solid pseudorandom number generator built-in.
A faster way to re-organize your deck (assuming you have enough table space to do it) would be to lay out each of your cards into 60 separate piles of one card each, ideally in a neat grid (e.g. 6 rows of 10 cards each), such that when you see #54 you can just say look for the 4th card in the 5th row instead of having to count through each card in your library until you reach #54.
Even with these improvements, sorting via excel will no doubt be slower than just riffling seven or eight times. And yes, it would need to be executed by an opponent, not you, to ensure it was done blindly
But y'know what, if you're willing to put up with it, and your friends are willing to put up with it, then more power to you. At the end of the day, your method results in a fair and appropriately randomized deck, and that's the whole agenda of this thread--to encourage people to prepare their decks in a fair and randomized manner instead of the ubiquitous pile shuffle or mana weave.
Maybe one day Wizards will come out with a machine that shuffles MTG decks for you and is guaranteed not to bend. Or maybe someone will develop an iPhone app to make this sort of technology you're desciribg more readily available. Who knows?
So what if somebody wrote a program that virtually executed X number of riffle shuffles on a list of integers equivalent to the number of cards in the physical deck of a player, then told the player how to rearrange their deck to match the arrangement of the shuffled integers?
It'd probably be slower unless the computer was executing the equivalent of an excessive number of riffle shuffles, but at least it wouldn't put excessive wear on the cards or require such ridiculousness as double-sleeving them.
Well, remember, a computer can do many, many, many, many times more computations in a second that we can, so the actual execution of multiple shuffles [or sorts, rather] of these integers would be very fast.
The other problem is, that would probably be stacking the deck - others want to chime in if I'd be right or wrong on this one?.
The other problem is, that would probably be stacking the deck - others want to chime in if I'd be right or wrong on this one?.
The problem isn't that Excel (or whatever other computer program) is stacking the deck, it's that you (the human) have to put together your deck in the exact way that the program tells you to while simultaneously being "blind" to which cards you're putting where.
Like if the computer were to tell you "to randomize your deck, put Forest first, then Troll Ascetic second, then Giant Growth third..." and so forth, and you followed those instructions, well then you now have a randomized deck, but you also know the order of all the cards.
tl;dr As I explained in my post above, it CAN be done fairly using a computer program, if you do take all the appropriate steps. But until someone (ideally Wizards, since then it could actually be approved for tournament/FNM use) comes up with a more efficient automated system, the easiest and fastest method is just to riffle seven times and call it a day.
And if that means double-sleeving your cards, and riffling only the edges, then so be it. "I'm worried about damaging my valuable cards" should NEVER be an excuse to do what effectively amounts to cheating.
The problem isn't that Excel (or whatever other computer program) is stacking the deck, it's that you (the human) have to put together your deck in the exact way that the program tells you to while simultaneously being "blind" to which cards you're putting where.
Which is exactly what I was talking about - though maybe I WAS admittedly a bit unclear.
Loved the article, and no longer just cut the opposing deck after they pile shuffle. I actually have started shuffling all of them, regardless of the level of the event.
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Personally I would never riffle my cards, and I would never let an opponent riffle my cards either. I would drop out of a tournament before I let that happen (though the more realistic thing is I would call a judge and ask him to shuffle in a non-bendy way). Cards are too expensive nowadays. I don't tolerate "minimal" bending. Only "zero" bending is acceptable.
The way I do things is I double-sleeve my deck beforehand. Afterwards I pile shuffle with seven piles once to remove all traces of stacking from the previous game and count the cards at the same time. After that I do a couple of side-shuffles (are they called "mash" shuffles now?). I don't care if the cards clump at that point. I will also let my opponent side-shuffle if he wants, or do a couple of overhands, or just cut the deck. But riffling is a no-no for me. You can riffle my deck when I'm six feet under, and not a second before.
Personally I would never riffle my cards, and I would never let an opponent riffle my cards either. I would drop out of a tournament before I let that happen (though the more realistic thing is I would call a judge and ask him to shuffle in a non-bendy way). Cards are too expensive nowadays. I don't tolerate "minimal" bending. Only "zero" bending is acceptable.
The way I do things is I double-sleeve my deck beforehand. Afterwards I pile shuffle with seven piles once to remove all traces of stacking from the previous game and count the cards at the same time. After that I do a couple of side-shuffles (are they called "mash" shuffles now?). I don't care if the cards clump at that point. I will also let my opponent side-shuffle if he wants, or do a couple of overhands, or just cut the deck. But riffling is a no-no for me. You can riffle my deck when I'm six feet under, and not a second before.
You realize that if they do not damage the card and/or sleeves, you cannot tell your opponent how to shuffle when it is their turn to shuffle, correct? And thanks to the Bend Test, most judges I know will say that riffle shuffling does not do any damage to the card or sleeves, and is allowed to be used.
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You realize that if they do not damage the card and/or sleeves, you cannot tell your opponent how to shuffle when it is their turn to shuffle, correct? And thanks to the Bend Test, most judges I know will say that riffle shuffling does not do any damage to the card or sleeves, and is allowed to be used.
You can however ask them to not shuffle in a particular way, and if you don't like the way they shuffle, you can concede, which he specifically says he would do.
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You realize that if they do not damage the card and/or sleeves, you cannot tell your opponent how to shuffle when it is their turn to shuffle, correct?
If my opponent really wants to riffle at all costs, I will just concede or drop out of the event (and probably never play at that store again).
I might misunderstand or misread something, but how can 7 riffle shuffles can be enough for randomization, if the top card before shuffling will most definitely be among the first 5-10 cards after riffle shuffling?
Even if the top card moves only 1 position down the first time you shuffle, it then has the potential to move nearly 3 or 4 positions down every time thereafter. And as it approaches the middle, it has a higher probability of being dropped down to the bottom (since when you split the deck to riffle it, the bottom-most cards of the top half--i.e. the middle cards--are among the first you riffle and subsequently end up at the bottom of the deck).
You can, of course, intentionally endeavor to keep the top two cards on top by ensuring they don't slip out of your fingers and sink closer to the middle, but then you're moving more towards a Faro shuffle than a genuine riffle.
If you're still skeptical, that's OK, you can just cut the deck a few times after you're done shuffling. It certainly wouldn't hurt.
If my opponent really wants to riffle at all costs, I will just concede or drop out of the event (and probably never play at that store again).
I'm not going to advocate for mash shuffling because riffling is and always will be the gold standard that everyone should strive for (if I had it my way, riffling would be a required practice at sanctioned events to prevent cheating, intentional or otherwise).
That said, for those of you who are so vehemently opposed to riffling that you would rather not play Magic at all than riffle your cards, the very least you could do is try to mash in emulation of a riffle, and NEVER, ever pile.
As I've beaten to death in Chaos vs. Randomness, simply having a deck that seems random doesn't necessarily mean it's random. That said, though, the way you described it earlier, I think you're pretty OK as it is now. If you really want to get it down pat, though, as with any other skill, anyone can master the shuffling technique (ideally first master riffling, then master mashing in the form of a riffle) with a bit of practice.
I sincerely hope so, too. I see this thread's beginning to quiet down; after so many days of floating, I suspected it would eventually. That said, I hope, as the thread falls off the front page such that people will no longer readily browse through it, that it remains a valuable reference for people to recommend to others when the topic of shuffling comes up around MTGS. Just doing a quick google search on "magic the gathering shuffling," there's several good resources and several bad resources as the top hits, and with how widespread shuffling misconceptions are already, the last thing we need are unsure people referring to bad resources instead of good ones.
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The reason I postsed about random not being neccesarily optimal is that I've tried this before (shuffling is a big discussion point on sleight of hand forums and amoung stage magicians) and I noticed my decks did decidedly worse when I was doing 8 riffle shuffles. I had way more mana flood and mana screw then just doing a few mash shuffles and a quick casino riffle.
Thanks very much to everyone along the way who provided feedback on this thread and helped me tune it up to be what it is now.
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A small update--I changed the "mash shuffling" image link to a personal link to avoid image leeching.
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This article was written back in 2003, even earlier than the Flores article. Today, ten years later, the notion of pile shuffling as an effective substitute for riffles is STILL all too pervasive!
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Reading that, I noticed something that I am not gonna call an error, but something to at least take note of.
Two things I would at least note here:
- it **SEEMS** he assumes you, in piling, go from last to first or first to last, and do that each time... For me anyways, I've noticed most people I play with casually at least, who pile, don't go from first to last, or last to first, for each pass but alternate.
What I mean: If you use the author's example of 4 piles, instead of going
P1, P2, P3, P4
they do:
P1, P2, P3, P4
P4, P1, P2, P3
P3, P1, P2, P4
...
...
etc.
- He seems to assume the piles will always be just stacked - not mashed together per-se, and also seems to assume the stacks will be re-stacked first over 2nd over 3rd over 4th pile over ... over Nth pile, or some other manner that is somewhat consistent like that... I've seen people stack 3rd over 1st over Nth over... and change it up with each pass, or even instead of doing any stacking, just mash the piles together.
Am I crazy in feeling like this is a lot to assume in drawing a conclusion all together, without taking in alternate methods [changing up the order of the piles you put a card in each pass, mashing the piles together instead of stacking, etc] into consideration - and if a player does all those things, for example, as opposed to if a player does not?
Do the author's examples using his modulus math hold true still if you did those things? [mashed instead of stacked, instead of going stack1 stack2 stack3 ... stackN each time alternating the order with each pass until all the cards were sorted into piles, etc]?
Thank you for commenting on the thread. Sorry I didn't get to your post until just now. As always, your criticism is much appreciated.
Whenever I see my friends pile shuffle, they all pile shuffle in the way he described:
P1, P2, ... , PN
P1, P2, ... , PN
P1, P2, ... , PN
over and over again, as if they were dealing out hands of poker. But we're both speaking from anecdotal evidence--without a doubt, people plaing Magic all over the world pile shuffle in different ways: different numbers of piles, mixing up the order of piles, and so forth.
But as I'll get to in a moment, none of that really matters.
No, you're not crazy at all. He stipulates or assumes many things in his mathematical model (as is necessary for just about any mathematical model), and any savvy mathematician or statistician knows that those assumptions may not always be met in real life.
Nowhere in the article does Pillards say he was actually there at the tournament watching with his own eyes Mike Long shuffle his deck. He makes a reference to another article by Bob Dougherty in the first sentence, but if you follow that link you'll see it's dead (not surprising figuring Pillards' article itself is already ten years old).
Can we say that Pillards has proven beyond a reasonable doubt that Mike Long was cheating? Just from reading Pillards' article, no, we can't. But that's missing Pillards' broader point.
Piling in a different order, such as
P1, P2, P3, P4
P4, P3, P2, P1
as you described, would undoubtedly require a different formula, because the piles would look like
P1: 0, 7, 8, 15, 16
P2: 1, 6, 9, 14, 17
P3: 2, 5, 10, 13, 18
P4: 3, 4, 11, 12, 19
The math wouldn't be as simple, and at first glance I don't think the modulo would work as straightforwardly as it does in Pillards' article, but even here you can see a clear, predictable pattern: P1 increases by 7, then by 1, then by 7, then by 1. P4 is the opposite. P2 increases by 5, then 3, then 5, then 3. P3 is the opposite.
If you were to stack them up with P1 on top and P4 on bottom and pile them out one more time, you'd notice the same pattern going between the piles instead of within them (look at the columns instead of the rows):
P1: 0, 16, 14, 10, 4
P2: 7, 1, 17, 13, 11
P3: 8, 6, 2, 18, 12
P4: 15, 9, 5, 3, 19
I have no idea whether or not piling out in this method a certain number of times returns to the original deck configuration as it does in the scenario Pillards described. I'd have to do it by hand a bunch of times to find out. But like any pile shuffling method, it does create a pattern in the deck--it does NOT randomize it.
Again, the point is that pile shuffling creates patterns, not randomness, and Pillards' message (also Flores' message) still rings true that pile shuffling CAN be used by knowledgeable players to cheat...and if it CAN be used to cheat, in the interest of keeping the game fair for everyone, you must assume that it WILL be used to cheat--intentionally or otherwise. Pile shuffling is NOT a valid shuffling strategy. That's the bottom line.
Now, you brought up mashing the piles together instead of stacking them.
As I described in the OP and in several other posts, "mashing" can be the equivalent of a riffle (and therefore an effective contributor to deck randomness) if it's done in a certain way. But if you're going to mash anyway, you mind as well just skip the whole piling process that comes before it, because it's the mashing that's really "mixing up" your deck--the piling is just making your deck more patterned and therefore less random.
As I've said before, the mashing needs to be done in a manner that emulates a riffle, which in practice is a lot harder to accomplish and a lot less consistent than just double-sleeving your cards and riffling the edges like the way it's supposed to be done in the first place.
I hope this helps. Please don't hesitate to ask any questions or provide any further comments or criticism.
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So what if somebody wrote a program that virtually executed X number of riffle shuffles on a list of integers equivalent to the number of cards in the physical deck of a player, then told the player how to rearrange their deck to match the arrangement of the shuffled integers?
It'd probably be slower unless the computer was executing the equivalent of an excessive number of riffle shuffles, but at least it wouldn't put excessive wear on the cards or require such ridiculousness as double-sleeving them.
If someone performs this technique before the deck is randomized, then they can still end up knowing the positions of various cards.
That's an interesting thought.
There are already many algorithms that can do just that (the one in that link is a module for SAS, one of the leading computer programs for statistical analysis. Unfortunately SAS isn't really widely available--it's quite expensive and has a learning curve made for professional statisticians, not your average MTG players--but I'm sure someone out there could make a free applet or something that anybody could run on his or her laptop (unfortunately I'm only a budding novice at programming or I'd be doing it myself).
There are a few main problems with the concept, however, even if a riffle shuffling program were readily accessible and could spit out a sufficiently-randomized list of #'s from 1 to 60 in the blink of an eye:
If we were looking to shuffle 20 times, then yes, most certainly getting a computer program to do it would be more efficient. But "excessive" is a critical word--you only need to shuffle a 60-card deck 7 or 8 times to achieve a sufficiently random configuration.
I understand why double-sleeving your cards might seem ridiculous or redundant, but compared to the complexity and inconvenience of other options, double-sleeving your cards and riffling the old-fashioned way really does emerge as the LEAST ridiculous option available.
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The problem I have with the idea of double-sleeving your cards to protect them from getting bent during riffle shuffling is that it seems to me that the very act of trying to double-sleeve cards would create moderate risk of bending the cards, which kind of defeats the purpose of it.
Anyway, as a kind of proof-of-concept, I created an Excel spreadsheet which generates a random number between 1 thru X, where X is the # of cards in your deck, then 1 thru X-1, 1 thru X-2, all the way until there are no more cards left in your deck. I sorted a deck of 60 GateCrash cards by card number then proceeded to shuffle following the randomly generated numbers in the spreadsheet. First number was 45, so I counted from the bottom of the deck up to 45, removed the 45th card and placed it as the 60th card in the shuffled deck. Next was 34, then 54, then 36, etc.... all the way to the end. It took me approximately 6 minutes to shuffle using this method for the first time, and that's with me occasionally loosing my place in the Excel spreadsheet and having to take a few seconds to determine which step I was on.
Looking through the newly shuffled deck, I'm very pleased with the results. It might be a relatively slow method compared to riffle shuffling, but it's an alternative that can achieve effectively random arrangements. With practice, and with a program specifically designed for this kind of shuffling instead of resorting to an Excel spreadsheet, this method could become reasonably fast. Still slower than riffle shuffling, but it would become a less drastic victory for riffle shuffling in this area, perhaps allowing this method's other benefits to make it a more appealing choice than riffle shuffling to some.
Double-sleeving is a great way to protect your cards. I've heard of people having problems bending the cards when using the Ultra-Pro perfect fits, but I've heard of no such problems with the KMC ones.
Double-sleeving will not appreciably protect against damage from riffle shuffling.
As much anecdotal evidence (just flip through this thread) seems to suggest that double-sleeving DOES appreciably protect against damage from riffling, particularly if you're riffling only the very edge as opposed to the whole card (and especially if you're not bridging--that's just a showmanship thing).
That said, I won't make any sweeping statement that double-sleeving does or does not offer complete protection, because all that's out there is anecdotal evidence, which is insufficient to merit a conclusion one way or the other.
What I can say with certainty is that double-sleeving certainly helps (or at least never hurts, unless you buy bad products), and that compromising the integrity of MTG as a game by permitting or turning a blind eye to unfair conduct in the interest of preserving card value is definitely the wrong choice.
Well if you're using Excel a faster way to randomize be to simply put numbers 1-60 in a single column, let's say Column A, generate 60 random numbers in the next column over (Column B) with the =rand() input, and then sort Column A in order according to the random numbers in Column B (ascending or descending, your choice). Excel comes with a pretty solid pseudorandom number generator built-in.
A faster way to re-organize your deck (assuming you have enough table space to do it) would be to lay out each of your cards into 60 separate piles of one card each, ideally in a neat grid (e.g. 6 rows of 10 cards each), such that when you see #54 you can just say look for the 4th card in the 5th row instead of having to count through each card in your library until you reach #54.
Even with these improvements, sorting via excel will no doubt be slower than just riffling seven or eight times. And yes, it would need to be executed by an opponent, not you, to ensure it was done blindly
But y'know what, if you're willing to put up with it, and your friends are willing to put up with it, then more power to you. At the end of the day, your method results in a fair and appropriately randomized deck, and that's the whole agenda of this thread--to encourage people to prepare their decks in a fair and randomized manner instead of the ubiquitous pile shuffle or mana weave.
Maybe one day Wizards will come out with a machine that shuffles MTG decks for you and is guaranteed not to bend. Or maybe someone will develop an iPhone app to make this sort of technology you're desciribg more readily available. Who knows?
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Well, remember, a computer can do many, many, many, many times more computations in a second that we can, so the actual execution of multiple shuffles [or sorts, rather] of these integers would be very fast.
The other problem is, that would probably be stacking the deck - others want to chime in if I'd be right or wrong on this one?.
The problem isn't that Excel (or whatever other computer program) is stacking the deck, it's that you (the human) have to put together your deck in the exact way that the program tells you to while simultaneously being "blind" to which cards you're putting where.
Like if the computer were to tell you "to randomize your deck, put Forest first, then Troll Ascetic second, then Giant Growth third..." and so forth, and you followed those instructions, well then you now have a randomized deck, but you also know the order of all the cards.
tl;dr As I explained in my post above, it CAN be done fairly using a computer program, if you do take all the appropriate steps. But until someone (ideally Wizards, since then it could actually be approved for tournament/FNM use) comes up with a more efficient automated system, the easiest and fastest method is just to riffle seven times and call it a day.
And if that means double-sleeving your cards, and riffling only the edges, then so be it. "I'm worried about damaging my valuable cards" should NEVER be an excuse to do what effectively amounts to cheating.
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Which is exactly what I was talking about - though maybe I WAS admittedly a bit unclear.
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The way I do things is I double-sleeve my deck beforehand. Afterwards I pile shuffle with seven piles once to remove all traces of stacking from the previous game and count the cards at the same time. After that I do a couple of side-shuffles (are they called "mash" shuffles now?). I don't care if the cards clump at that point. I will also let my opponent side-shuffle if he wants, or do a couple of overhands, or just cut the deck. But riffling is a no-no for me. You can riffle my deck when I'm six feet under, and not a second before.
You realize that if they do not damage the card and/or sleeves, you cannot tell your opponent how to shuffle when it is their turn to shuffle, correct? And thanks to the Bend Test, most judges I know will say that riffle shuffling does not do any damage to the card or sleeves, and is allowed to be used.
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You can however ask them to not shuffle in a particular way, and if you don't like the way they shuffle, you can concede, which he specifically says he would do.
If my opponent really wants to riffle at all costs, I will just concede or drop out of the event (and probably never play at that store again).
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Even if the top card moves only 1 position down the first time you shuffle, it then has the potential to move nearly 3 or 4 positions down every time thereafter. And as it approaches the middle, it has a higher probability of being dropped down to the bottom (since when you split the deck to riffle it, the bottom-most cards of the top half--i.e. the middle cards--are among the first you riffle and subsequently end up at the bottom of the deck).
You can, of course, intentionally endeavor to keep the top two cards on top by ensuring they don't slip out of your fingers and sink closer to the middle, but then you're moving more towards a Faro shuffle than a genuine riffle.
If you're still skeptical, that's OK, you can just cut the deck a few times after you're done shuffling. It certainly wouldn't hurt.
I'm not going to advocate for mash shuffling because riffling is and always will be the gold standard that everyone should strive for (if I had it my way, riffling would be a required practice at sanctioned events to prevent cheating, intentional or otherwise).
That said, for those of you who are so vehemently opposed to riffling that you would rather not play Magic at all than riffle your cards, the very least you could do is try to mash in emulation of a riffle, and NEVER, ever pile.
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