Judicial Opinion: Shuffling your Deck

Randomizing your Deck – shuffling it – serves to make the order of your cards in it unpredictable to both players. It is a core element of card games. Still, I see a surprising number of misconceptions about it floating around, even among veteran players. So, let’s talk about that.

In section 1, I will go over what proper randomization is; what results it produces, and how you’ll sometimes brick. In section 2, I talk about ways you can brick less. In section 3, I wrap up and re-state the most important points.

What is Randomization?

After you randomize your Deck, the order of the cards in it should be unknown to both players. To do this, randomization has to achieve two goals. First, it must make sure neither player can predict the position of any card in your Deck. Second, it has to position any given card independently of where the other cards end up.

What does this mean? First, after shuffling, you won’t know what the top card of your Deck is. Second, once you draw the top card and look at it, you still won’t know what the next card will – or won’t – be. This may seem obvious when spelled out. Yet, it pays to dwell on the implications. Assume you are playing three copies of Ash Blossom & Joyous Spring in your 40-card Deck. You randomize this Deck, and draw the top card from it. It’s Ash Blossom! Now, what about the next card in our well-randomized Deck? Could it be another Ash Blossom, when we shuffled properly?

Yes, it could be! There are 39 cards left, so two copies of Ash Blossom are about 5% of the cards. You definitely shouldn’t be always drawing a second Ash Blossom – but you definitely also shouldn’t be never drawing it. That’s the nature of randomization.

How do I brick less?

Show up to the tournament with a different Deck. There is no other way.

As outlined above, a properly randomized Deck will be random. It won’t be perfectly distributed. Having your Deck always alternate between giving you engine cards and generics is the opposite of randomness. Sometimes, you’re going to draw unplayable hands. That’s the nature of a card game.

A five-card opening hand. It consists of two copies of Ash Blossom, and one copy each of PSY-Frame Driver, Solemn Strike, and Infinite Impermanence.
Sometimes, it simply do be like that.

Now, some players will confidently tell you that that’s not quite true. If you pre-arrange your Deck in just the right arcane pattern, they’ll tell you, you’ll brick less. They’ll call it “de-clumping,” or “mana-weaving,” or “pile sorting,” or even “making it more random.” But aren’t I cheating?, you may ask them. “Don’t worry,” they’ll exclaim, “as long as you shuffle properly afterwards, it’s fine.”

If I’m a Judge staffing your (hypothetical) event, and you do this, there’s exactly two possible results.

Possibility one, you are shuffling properly. In this case, your pre-arranging did absolutely nothing. After you randomize your Deck, no trace of the original pattern remains – remember, that’s what randomization is. Your trick didn’t work. All you did is waste everyone’s time. This is the more benign of the two results.

Possibility two, you aren’t shuffling properly. Some traces of your arrangement remain afterwards, and you end up drawing fewer duplicates. Your trick worked. You’re more likely to draw a good hand than you’re supposed to be. Re-read that sentence – we’ve got a name for that. It’s called “stacking your Deck.” If it works, you’re cheating, plain and simple. The penalty for UC – Cheating is Disqualification from the event.

The phrases "Then why are you doing it?", "I think it benefits me", "It's Cheating", and "But I perfectly randomize my deck afterwards" are arranged in a circle. A red arrow points from each phrase to the next.
It’s a fun conversation to have with your event’s Head Judge.

Conclusion

A properly randomized Deck will not always be evenly distributed. If your Deck is always evenly distributed, you’re not shuffling it properly. If you’re doing this intentionally, it’s UC – Cheating, and the penalty is Disqualification. When a Judge notices you re-arranging your Deck before shuffling, you will be asked questions. There are no good answers.

Starting with a randomized Deck is an integral part of Yu-Gi-Oh!, just as with most card games. Sometimes, you will draw brick hands. Sometimes, your opponent will. The way to address this is to build your Deck differently, or to deal with it. The way to address this is not to “shuffle” your Deck in a way that makes you brick less – that’s Cheating, and will get you disqualified sooner or later.

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9 thoughts on “Judicial Opinion: Shuffling your Deck


  • Avatar
    September 9, 2021 at 10:29 am

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    Reading ignorant shit like this legitimately makes me angry, especially from a person aping a position of authority. The author is demonstrating a gross ignorance of how both gameplay and shuffling affect the probability distribution of deck orders.

    This article is approaching seriously dangerous levels of misinformation.

    If you want a truly randomized deck order, where P(card_2 = y | card_1 = x) = P(card_2 = y) = 1/39, then you would have to shuffle forever. There is literally no other option. The issues are:

    1. Is the probability any one card happens to be any specific card reasonably independent of the previous card (aside from non-replacement)?

    2. Is the probability your deck order happens to be any specific deck order reasonably close to independent of its starting state?

    3. Can you accomplish this in a reasonable amount of time?

    When you play, your routes of play will usually be funneled into certain sequences (Handtraps at/near the bottom; Activate A to search B, Normal Summon B, Special Summon C, Link Summon D…). When the game is over, and you pick up your field and GY, you are starting with a fairly high amount of knowledge of your deck order. The probability distribution over all possible deck orders is: 1. not uniform, and 2. highly interdependent.

    One mash shuffle introduces a fairly small amount of randomness – the number of cards from one stack that end up between each card in the other stack. But the cards that were in your field + GY are almost certainly still in the order in which you picked them up!

    The purpose of de-clumping is that it brings your deck to a state from which shuffling will more quickly bring you toward any arbitrary deck order independent of the card stack that you picked up at the end of the previous game.

    Imagine a deck that was already perfectly randomized. In this state, a “de-clumped” deck order is much more common than a “clumped” deck order. Yes, some “clumping” is common. But severe clumping is very uncommon. If we observe a severely clumped deck, which is more likely: that it is in fact the result of true randomization, or that the deck was not sufficiently randomized?

    This effect is much more common in MTG and Pokemon, since you have fairly large pools of cards (Lands; Energy & Trainers) that are obviously of the same type and which it’s easy to understand how gameplay biases them toward each other. This is also why “de-clumping” is more commonly understood as being a part of an efficient shuffling process in those games.

    If you don’t believe me, then please try it out for yourself. Sleeve up 2 decks with the same sleeve, but different colors (say, red & blue), but swap 5 red cards into the blue deck. Do each of the following 1,000 times:

    1. Start with the 5 red cards on top, mash shuffle 5 times, then record if any red cards are touching.

    2. Insert the 5 red cards into non-adjacent spots, mash shuffle 5 times, then record if any red cards are touching.

    3. Start with the 5 red cards on top, mash shuffle 25 times, then record if any red cards are touching. (This simulates something reasonably close to “true randomness” – even from a “clumped” initial state.)

    Do you expect the frequency of positives (adjacent red cards) from Case 1 or Case 2 to be closer to that of Case 3 (true randomness)?

  • Avatar
    September 9, 2021 at 12:46 pm

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    So Fashionablehat just because there’s no way to be truly random, you’re going to cheat? :/

  • Avatar
    September 9, 2021 at 3:02 pm

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    >A properly randomized Deck will not always be evenly distributed

    when i had my lunalight deck this statement was false

    >If your Deck is always evenly distributed, you’re not shuffling it properly.

    but is this backed up by science and not by op’s opinion? if anything the opposite is true.

    >If you’re doing this intentionally, it’s UC – Cheating, and the penalty is Disqualification.
    from how the text is written, are you saying that, if ”

    properly randomized Deck will not always be evenly distributed.” is that a uc or is “If your Deck is always evenly distributed, you’re not shuffling it properly. ”

    >When a Judge notices you re-arranging your Deck before shuffling, you will be asked questions.

    will i ? why would a judge ask ?

    >There are no good answers.
    you sure about that ? i know you said if i Think then it benefits me then its cheating, but this just dose not make sense, just because if i think i am a elephant dose not mean i am nor dose me putting my lucky coin in me left pocket will effect the outcome, i mean of curse i hope it would.

    >The way to address this is not to “shuffle” your Deck in a way that makes you brick less – that’s Cheating, and will get you disqualified sooner or later.

    so what you are saying here is…..to not shuffle my deck. but i think, what you are saying is just over lap the cards how yugi dose in the anime ? but if that is true then i can stack my deck, it’s one of the worst shuffles you can do. my other point is why even shuffle, if i can’t help my self brick less ? when i brick i think “wow i nor my opponent shuffle good”

    TL:DR If i shuffling then i am cheating

    a lot of this post was nothing but backwards logic.

  • Avatar
    September 9, 2021 at 7:49 pm

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    >

    Did you even read his comment?
    Declumping produces more random results.
    Nothing is ever truly random, but you can certainly achieve “randomer” shuffles by declumping.

  • Avatar
    September 10, 2021 at 10:11 pm

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    I’mma have to agree. KDE Judges have a group (which I am in), and literally Julia Hedberg says (multiple times) that declumping isn’t cheating as long as you randomize properly afterwards. I feel bad for people who got/will get dq’ed by judges who think declumping is cheating :oops:

  • Avatar
    September 12, 2021 at 11:10 am

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    I like to point out that what konami considers a “randomised” state does not need, in theory, be actually random. As long as two actions are performed the deck state is considered to be “randomised”. I shuffle and my opponent cuts.

    lets say i shuffle once moving 20 cards from the bottom of the deck to the top of the deck.
    Then my opponents cuts by moving 20 cards from the top of the deck to the bottom.
    Even though the deck is exactly the same konami will consider the deck as to be “randomised”.

  • Avatar
    September 13, 2021 at 4:40 am

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    That would be false. Here’s something from the policy document.
    “Your Deck must be randomized using an accepted shuffling method (riffle, pile, Hindu, etc.) and then cut. This must be done at the start of every Duel, and whenever a game mechanic requires you to shuffle your Deck.”

    Placing 20 cards from the bottom to the top does not count as an accepted shuffling method, and thus will not make the deck be considered “randomized”.

  • Avatar
    September 15, 2021 at 8:02 am

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    > So Fashionablehat just because there’s no way to be truly random, you’re going to cheat? :/

    No. This is the correct way to think of it: By NOT de-clumping after a game (and siding), you are (inadvertently) “anti-cheating” yourself – you are biasing the probability distribution across deck orders in favor of deck orders that are worse for you.

    There is indeed no way to be “truly random” (what you mean is uniform and independent). However, imagine a “black box” that you could put any deck in, in any order, and the black box gave you a 1 in 40! probability of every possible deck order, regardless of how it was when you put it in. (The typical Yugioh player’s shuffling process is nowhere remotely near this good – even between matches, let alone games or during a game. This is because most players mash shuffle very closely to a Faro “Shuffle,” perfectly weaving cards from the 2 stacks in a “zipper” pattern.)

    Imagine you are playing a Magic deck with 30 lands out of 60 cards, and you observe that you draw no lands. Which of the following is more likely: that you hit the 0.5% probability of drawing no lands, or that your deck was not actually properly randomized in the first place? (This is a Bayesian question.)

    This is to say: Severely clumped deck states are more likely to be the result of insufficient randomization than of random chance.

    And as a corollary: It will take more (many more) shuffles to take you from a severely clumped deck order (which happens as a natural consequence of play) to a 0.5% probability of 0 lands, than it will to take you from a de-clumped deck order to a 0.5% probability of 0 lands.

  • Avatar
    September 15, 2021 at 6:11 pm

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    So I ran this sim (albeit replacing step 3 with random.shuffle()) 100000 times; once you break like 8 shuffles, they’re pretty much as close to 3 as each other (on different ends). For best accuracy, mash 10-12 times. Piling has no significant change at that point.

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