General Seeding Packs - An Exercise in Randomness

[Jason Waddell]

I've been thinking about how to arrange packs, since I can now do it electronically. During our 8p draft, I opened a pack with like 8 red cards and 7 lands. This is non-ideal for a number of reasons. The worst is when you see say, 6 black zombie cards in one pack, and you know that the random shuffle just neutered an entire archetype.

How should we fix the problem?

Any seeding method has pros and cons. Say your rule is "at least one card of each color should be in every pack". Then, if you open a P1P2 with no white cards, then you know with absolute certainty that the player beside you picked a white card P1P1.

Conversely, if there is, say, a max of 4 cards per color in a pack, then if you get a pack with 4 red cards, you know for a fact the player next to you did NOT pick a red card.

Is this good, bad? Who knows. Some control over signaling is surely valuable.

How do we weigh our desire to not have lopsided packs against the threat of 100% signals?


Something like "make sure there are at least 2 cards of each color" won't work, because this uses up 28 cards per color, and super clear signalling.

Anybody have ideas for how to do this?

Initial thoughts

Setting clear guidelines like "there will be between 1 and 4 cards of each (mono) color per pack" seems like an easy rule that you can communicate quickly, and in some corner cases leads to perfect signalling.

Concretely, I would start by putting one of each color (with lands as the '6th' color) in each pack. Then assign the rest randomly. If this causes there to be more than 4 of a color in a pack, replace as needed.

 

[whydirt]

Honestly anything more than just making sure there's at least one of each monocolor card per pack seems like too much work and micromanagement for my tastes.

Past that I'd rather just double up on Cogwork Librarians or even start everyone out with a free one in their draft pile.

 

[Jason Waddell]

Honestly anything more than just making sure there's at least one of each monocolor card per pack seems like too much work and micromanagement for my tastes.

Past that I'd rather just double up on Cogwork Librarians or even start everyone out with a free one in their draft pile.

To be clear, in my context it would all be done electronically, so there's no real "work" involved.

 

[Eric Chan]

This is a problem in paper as well as digital, with any cube randomization method: What you want is not true randomness, which produces odd spikes that are really bad for signalling, but the appearance of randomness, when in fact you're doing something more akin to a uniform distribution.

Two options:

1) The sweet pseudo-random shuffling method that I use for my actual cube, which has worked great for us over the last year. People have stopped complaining "did you even shuffle these packs?!" because they don't get the odd pack with five green cards and nine lands anymore.

2) Something more akin to print runs, which is close to impossible in paper, but seems like it would be doable for digital. Your algorithm would:
- Randomize the entire cube according to pre-set "slots" that you've made, e.g. W-U-B-R-G-Gold-Land, or whatever. (If you have fewer artifacts than the other categories, just sprinkle them in anywhere.) After this step, you should have your 360 list in a pseudo-random "print run" format.
- Divide the print run into five-card "chunks". So your first chunk is W-U-B-R-G, next is Gold-Land-W-U-B, followed by R-G-Gold-Land-W, etc. For a 360 cube, you should have 72 chunks.
- Randomly take three chunks to make a pack.

 

[shamizy]

I don't know how you could implement this electronically, but I've been using this method in paper for the last few months and it's worked out great:

1) Divide everything by color (WUBRG), with lands, colorless, and gold in a sixth pile.
2) Take 20% of each color and shuffle it into the gold/colorless/land pile.
3) Distribute the mixed pile evenly into each colored pile, and shuffle those.
4) Take three cards from each pile to make your packs.

I'd imagine that on MODO it would probably be more like a print run sort of thing if anything, slots for a given color and whatnot.

 

[Eric Chan]

Yeah, from what I understand, MODO actually does use print runs in its digital-only products, so with the Holiday Cube (or whatever they call it now) all the Power was clumped together. It sounds weird - and I think sealed deck was busted?! - but it made sense for draft, because it ensured that if one person opened power, everyone got to eat a piece of that pie.

 

[whydirt]

To be clear, in my context it would all be done electronically, so there's no real "work" involved.

Fair enough! I should have read your OP more thoroughly!

I stand by running double Cogwork Librarian though!

 

[psly4mne]

I guarantee one card from each of 8 sections (incl. fixing land, multicolor, colorless) and at most one conspiracy/draft-affecting card in each pack, with the rest being uniformly random. I have slightly more multicolor cards, but they are downweighted so that multicolor is as frequent as a color. This does mean that 100% signals occur occasionally, and 5+ of a color in a pack can occur but is rare. This has worked out pretty well so far.

 

[Jason Waddell]

2) Something more akin to print runs, which is close to impossible in paper, but seems like it would be doable for digital. Your algorithm would:
- Randomize the entire cube according to pre-set "slots" that you've made, e.g. W-U-B-R-G-Gold-Land, or whatever. (If you have fewer artifacts than the other categories, just sprinkle them in anywhere.) After this step, you should have your 360 list in a pseudo-random "print run" format.
- Divide the print run into five-card "chunks". So your first chunk is W-U-B-R-G, next is Gold-Land-W-U-B, followed by R-G-Gold-Land-W, etc. For a 360 cube, you should have 72 chunks.
- Randomly take three chunks to make a pack.

This method has a 3-card per color group cap. Still trying to decide if these hard caps are desirable, and if so, what it should be.

 

[Suicufnoc]

I like something close to what Eric's doing, but probably a little more random.

 

[James Stevenson]

Why not distribute cards according to some curve? So like, you get max 4 cards of a color most of the time, but occassionally 5, 6 at a stretch. Much harder to infer something about the drafter passing to you. I guess? I mean, if you see 6 or 7 of a color, you can pretty safely know they didn't take one of those... but that will also be a rare occurrence.

 

[Jason Waddell]

I implemented an algorithm. First it puts one of each color in a pack (just the 5 primary colors), then it does the remaining 10 using a slightly modified version of the method Eric linked.

Here are the 24 packs. I haven't looked at it yet, so maybe the method is garbage.

Spoiler

Pack A:


Pack B:


Pack C:


Pack D:


Pack E:


Pack F:


Pack G:


Pack H:


Pack I:


Pack J:


Pack K:


Pack L:


Pack M:


Pack N:


Pack O:


Pack P:


Pack Q:


Pack R:


Pack S:


Pack T:


Pack U:


Pack V:


Pack W:


Pack X:

 

[Jason Waddell]

So.... that's basically perfect, right?

 

[Jason Waddell]

The method, precisely is:

1) Put 1 card from each color in each pack.
2) Set aside 20 remaining cards from each color, and put the rest into a pile of all the remaining cards (gold, lands, colorless). This "remainder" pile is 140 cards.
3) Add 28 cards of the remainder pile to each color pile. So each color pile now has 48 cards.
4) Add two cards from each new color pile to each pack.

Done!

 

[Alfonzo Bonzo]

This might be interesting / relevant

https://www.reddit.com/r/mtgcube/comments/34fet8/novel_method_for_shuffling_a_cube/

 

[Jason Waddell]

This might be interesting / relevant

https://www.reddit.com/r/mtgcube/comments/34fet8/novel_method_for_shuffling_a_cube/

This is what Eric linked. I basically use this after first putting 1 card of each color in each pack.

 

[James Stevenson]

This is what Eric linked. I basically use this after first putting 1 card of each color in each pack.

This seems really good.

 

[Eric Chan]

I might even do that the next time I shuffle my paper cube. It seems like less work overall than the original method that I'm currently using!

 

[safra]

It's the only way I shuffle my cube now, full concurrence.

 

[japahn]

My method is:

• The cube is divided into 6 sections: one for each color, one with artifacts+lands+multicolor (ALM).
• For each player, take 6 cards of each colored section and 15 from ALM, for a total of 45 cards.
• Each player shuffles their pile and divide into 3 boosters of 15.
• Each player passes one booster to someone else.
• Draft.

Pros:

• Better color distribution. See math below.
• The largest pile to be shuffled is ALM. This decreases the chance of bad shuffles and is more comfortable.
• Very parallelizable.

Cons:

• Need to keep cards organized by color.
• The proportion needs to stay the same (6 cards of each color for each 15 in ALM) in the cube to keep equal odds of seeing each card.
• If somebody pays very close attention to how boosters are exchanged and has a very good memory, they can count the colors and figure from what section the cards are missing. This can be worked around by exchanging boosters more.

For a normal pack distribution, the odds of having exactly N cards from a section of 48 in a 360 card cube is:
F(N) = HYPGEOMDIST(N;15;48;360)
F(0) = 11.16%
F(1) = 26.97%
F(2) = 29.67%
F(3) = 19.72%
F(4) = 8.84%
F(5) = 2.83%
F(6) = 0.67%
F(7) = 0.12%
Rest is negligible.

With my method, it becomes: F(N) = HYPGEOMDIST(N;15;6;45)
F(0) = 7.29%
F(1) = 26.24%
F(2) = 35.33%
F(3) = 22.68%
F(4) = 7.29%
F(5) = 1.10%
F(6) = 0.06%
F(7) = 0.00%
Rest is impossible.
I've done this since I started cubing in 2009 (couldn't find any topics about it at the time, so I made something up that looked practical), and have also tried multiple times other ways of shuffling. I found the "novel" way interesting and yields a nice distribution, but it's much more shuffling and the biggest pile is really big (half the cube). The simple "mash it all together" is extremely awkward physically and easy to screw up by not shuffling well one part, and creates bad color distribution.

 

[Meltyman]

Second pick knowing SOMETIMES what color you picked isn't a problem really. The third player will never know for sure what was picked. Signaling in cube doesn't start from first picks anyway does it?
If you see one pack with no white cards, would you already pull the trigger on picking anything else than white if you still see some great white cards ?

 

[VincePendrell]

What I've been doing since ever is the following:

1. Keep the cube separated in sections (1 per color, multicolor, and colorless). Keep your test pool* separated, if you have one.
2. Shuffle each section separately and seed one card of each section to each pack (2 for multicolor). Each booster has 8 cards now.
3. Shuffle some amount of cards from each section together. Distribute 7 cards to each booster. If you have a test pool, make sure they are shuffle between the first cards you are distributing to guarantee they will be in the draft pool.
4. Draft!

* The test pool was my way to test cards in a big cube. Basically, I just seeded them into the boosters to guarantee availability and see how they played out. I used it to both insert and remove cards to the cube, as well as occasionally testing some weird stuff.
Besides having to keep the cards of each section separated, there isn't a lot of prep work for this method. It won't guarantee anything besides the fact that no booster will be without a single color, and with half of my multicolor cards being mana-fixing, it also guaranteed that there would be plenty of lands going around (and that the test pool would be available for testing, ofc). It's quite simple to do physically, which I don't think is a plus if you are making your packs digitally.
I've been toying with the idea of having a "first pick slot", which would pretty much take the strongest cards (or the ones that would be most likely first picked) and seed one per pack, as a way to emulate rarity. Another idea is, if you are making packs digitally, you could have your cube set in a way that each booster will have slots for specific functions, instead of colors. For instance, a booster would be rigged to have 1 removal, 1 two-drop, 1 combo-friendly card, 1 finisher card, 1 mana fixing land, etc. Since you are doing digitally, you can also try distributing it in a way that all colors are represented. I've never pushed this idea forward, and since I'm only cubing with physical cards, it would be impossible for me to maintain this, but I'll throw it out here to see if it sparks some ideas.