General 15 cards, 3x, out of 360

[fozzy fosbourne]

The discussion around various traditions like singleton inspired me to think about other norms, like the 3 packs of 15, see every card in a 360 card cube feature. Is this mostly an artifact of the retail pack? Is it doing useful things for cubes?

Another inspiration is how we typically draft if we have less than 8 -- if we have 7 people for example, we'll look at 17 cards in each pack but only draft 15, discarding the last 2. If we have 6, we'll draft four packs of 15, but only draft the first 12 of each pack. Etc. This let's us see nearly the full cube, or in a limited draft, gives us something closer to the distribution that wizards balanced around. So the build arounds they seeded like burning vengeance and spider summoning are more likely to be present in reasonable numbers.

Why not do something similar even with 8 drafters? An example might be 8 drafters picking 4 packs of 14, but only drafting the first 11 or 12 in a pack. This would lead to players looking at ~450 cards but only making decks with ~360.

Some pros:
- More width to archetypes. A safety buffer. A drafter might be more likely to survive another drafter cutting into their archetype. This could be tuned; make players see twice as many cards and there might be twice as much room in an archetype? Or, with the previous example above, it might provide just a little bit more padding so you still can't be reckless. Sort of like the tension in the amount of fixing you put in your cube.

- More cards. Yep.

- Larger margin for error in cube design. Maybe you built a package around land recursion, but don't realize that some of the pieces get sniped by people outside of the archetype and it never really comes together because it's too sparse. This might help pad it out a little bit.

- More room for risk and experiment as a drafter

Cons:
- Unorthodox. Having to explain new things is one more barrier to cube design. However, since I generally do something like this whenever we have < 8, I don't see this as a big deal for me personally.

- More cards. Yep.

- Less tension in draft. This might be the biggest issue. While it can be a big source of bad feels to realize that several people downstream must be in the same archetype, it's also one of the most skill-testing elements of draft. Sort of like the tension in the amount of fixing in a cube.

- Less similarities to retail draft. I feel like this would be minor compared to the features of cubes that already diverge from retail draft. A marketing thing, I think.

Thoughts?

 

[Velrun]

Man I do love ideas like this!

Whenever I read an idea like this I am instantly deciding to test it during the next tournament. Most people are very positive to new draft settings in my environment.

Another con: More cards in each pack also means slower drafts because players will have to read a little more.

 

[sigh]

there has been on and off discussion on this over the years here. Somewhere, someone did an analysis of the "optimum" number of cards/packs depending on how many people are drafting. By and large I'd say that 15x3 is an artifact (not even properly carried over to cube because retail packs have basic lands and tokens).

One common method for me is Tenchester: 10 packs of 10 for 4 people, take only 1 card per pack. I think in 360 cubes, it's 10 packs of 9. End up with a 40 card pool.

 

[Onderzeeboot]

I actually like the math behind 3 packs of 15, because that means in an 8 people draft, a pack will exactly not wheel. I was a mildly annoyed when WotC decided to cut the 15th card in favor of a land ages ago. Applying this same principle, I did a 4 packs of 11 draft with 6 people last year, and it worked out perfectly!

 

[Tzenmoroth]

I've thought about changing it up for 15x3 works so well. Any less and I'm afraid there just won't be enough cards seen to build functional decks. More cards maybe. Breaking up into 4 packs maybe but I like the way packs do almost 2 wheels. I could do something more complicated like cards being burned or the pack stopping at a certain point but I don't have enough faith in people to not screw that up. I have to get cubeamajigs so we stop getting an extra pack mixed in during pack 1.

 

[sigh]

Cubemajigs are neat, but 30 bucks for 24 packs? I can get 40 snack sized ziplocs for less than $3.........

 

[fozzy fosbourne]

Personally, I suspect that having an odd number of packs does more to warp things than the number of times a pack wheels. I imagine that if the norm was an even number of packs, people would be extremely resistant to going to an odd number of packs because of the balance between people on your left and right cutting into your colors.

Also, wow, I must be lucky! The people I draft with don’t have too much trouble keeping track of something like not drafting the last 2 cards each pack. It helps that a few of us are shouting at everyone the whole time lol

 

[Rowan_CB]

I explored "optimal" draft variants in this thread: https://riptidelab.com/forum/threads/optimal-draft-variants-for-less-than-8-players.1881/

But I'm not sure this is entirely relevant to your line of questioning, because my baseline assumption was that 3 packs of 15 for 8 players was optimal, and that's what you are exploring pushing back against. FWIW, I've had a lot of success so far with these variants, which try to replicate (1) the percentage of the overall cube seen by each player, (2) the size of each player's card pool, and (3) the number if times a pack wheels (relevant to Onderzeeboot's point above).

 

[japahn]

I like the feeling of 3 packs of 15, it might be just because it's familiar to me, but it will be familiar to other drafters as well.

That said, with fewer players than 8 I think we can do things in cube draft that cannot be done in retail to adjust the experience. I've always found that drafting in less than 8 in retail is a much worse experience than drafting a full pod. 6 and 7 are suboptimal, 4 and 5 is terrible. In my cube I use the following system (text copied from my cube thread - https://riptidelab.com/forum/threads/the-elegant-cube.1939)

Booster sizes for fewer players
To mitigate archetype dilution and keep them roughly with the same power with fewer than 8 players, the booster setup depends on number of players:

• 8 players: 3 packs of 15 cards (360 used, 45 picks, 360 impressions, 276 readings)
• 7 players: 3 packs of 16 cards (336 used, 48 picks, 408 impressions, 273 readings)
• 6 players: 4 packs of 13 cards (312 used, 52 picks, 364 impressions, 252 readings)
• 5 players: 5 packs of 11 cards (275 used, 55 picks, 330 impressions, 225 readings)

Used is the number of cards from the cube included in the draft.
Picks is the number of cards picked by each player.
Impressions is the number of cards seen by each player, counting repetitions.
Readings is the number of cards seen by each player, excluding repetitions.

 

[fozzy fosbourne]

I do something similar, but try to let everyone still see 360 cards.

Only seeing 45 cards x person can kind of suck as you have less players. Things like burning vengeance and spider spawning no longer become a thing and it starts feeling like Sealed. So the way we approached this problem is to err in the direction of seeing *more* cards per player as the number of players decreases. So for example with 7, we do 17 * 3, only draft the first 15 of each pack. This means that players will see nearly all 360 cards in a cube, or in a retail simulation draft they will see AsFan * (3 * 8). So if something by design needs 5 supporting cards to be in the pool to support the archetype, it won’t be crippled by a smaller pool.

However, this has the “drawback” of having more cards seen per player and thus slightly better decks. There will be more removal, bombs, etc in the pool per player, etc. This made me start wondering if this type of tuning should be considered outside of just less-than-8 scenarios. Should we really be considering the amount of cards seen per drafter as something to be tuned like everything else? Since I suspect that many don’t play with the full 8 at all times, I think most are already doing it anyways whether they realize it or not.

 

[fozzy fosbourne]

To use some examples at the extremes like Richard Garfield would:

1 drafter drafting 45 cards from a pool of 3 * 15 cards:
The deck would be really bad. It would need to run a bunch of lands and a bunch of different color cards that don't have much to do with each other.

2 drafters drafting 45 cards each from a pool of 6 * 15 cards:
Slightly better, but still pretty bad.

As you add more drafters and more packs, more playable cards will be available for each drafter's ~23, and eventually something that feels good will be reached. Maybe that's 24 * 15/14, if that's how the format has been tuned.

Going the other direction,
1 drafter drafting 45 cards from a pool of 24 * 15 cards:
They would have all of the cards available to them and would assemble something close to the best deck of an archetype.

2 drafters drafting 45 cards each from a pool of 24 * 15 cards:
A little more tension. People will have way more than 23 playable cards, so maybe some serious hate drafting occurs.

And so on, where some number that feels good will be arrived at (maybe it's 8 drafters with 3 * 15. Maybe not).

I guess my whole line of thought here is that this is all very arbitrary? How often do people draft cubes with exactly 8 drafters? Is that the ideal baseline to tune from?

As many have pointed out, there is a cost to deviating from expectations on this stuff so you don't just do it without good reason. But maybe there are some good reasons.

Maybe you want to increase the support for the archetypes available in a pool. What if you took a 360 card cube drafted by 8 people, and added 48 cards that were slightly more narrow archetype enabler and payoffs that you couldn't include in the more crowded 360 card build. Then, let the 8 players look at 17 cards in each pack and draft the first 15 of each pack. How would that transform the decks and the feel of the draft and games?

Or maybe you want to add more new archetypes. Add a few more packages into 48 cards and add those to a 360 card pool, 17 cards per pack. How does that warp things?

 

[Rowan_CB]

I think it's important to consider that 3 * 15 for 8 drafters is not exactly arbitrary, in that it is mathematically connected to 360 cards, which is the most common cube size. Now, the 360 card cube size is itself based on the 3 * 15 retail draft experience, so there's a snake-eating-its-own-tail thing going on here, but what's important is that cube size and draft logistics are tied together.

When I set out to build a cube, I did so with 360 cards in mind. I also wanted to ensure my archetype enablers and payoffs were present at sufficient volume to support decks of those archetypes in a scenario where all cards in the cube were being drafted. Therefore, it made sense to frame my draft logistics around the 3 * 15 for 8 dynamic, which is the only correct draft solution for 8 players drafting a 360 card cube, provided you want all cards to be included in the draft if possible. It then followed that my proposed variants for other numbers of drafters should use the 3 * 15 for 8 dynamic as the "ideal" to compare against, because that ideal was sort of baked into the cake when I was designing the cube.

Does that make sense?

In other words, I think that while you're right that all these numbers decisions are arbitrary to a certain point, they become vital pieces of the cube's architecture during construction. If you wanted to create a draft experience that differed significantly from the 3 * 15 for 8 baseline, you would need to have whatever your preferred draft variant is in mind when designing the cube, to ensure that drafters are seeing a sufficient volume of cards to play out your vision for the cube. The total number of cards in your cube should be a mathematical extrapolation of your draft function.

 

[Onderzeeboot]

To a degree I'ld say I run a 450 card cube to ensure more variety in an 8 people draft, because when I draft, it's often with 8 people. I'ld say that variety would be just as well achieved with 440 or 460 cards, and those numbers are not a mathematical extrapolation of my draft function. Your statement does hold true for a format where you want to ensure exactly all cards are seen in every draft though. 3 * 15 still isn't the only solution for an 8 people draft in a 360 cube though, 5 * 9 (and 9 * 5) also works

 

[Velrun]

Or 1 * 45

 

[Rowan_CB]

I may have been overly declarative .

 

[fozzy fosbourne]

I think it's important to consider that 3 * 15 for 8 drafters is not exactly arbitrary, in that it is mathematically connected to 360 cards, which is the most common cube size. Now, the 360 card cube size is itself based on the 3 * 15 retail draft experience, so there's a snake-eating-its-own-tail thing going on here, but what's important is that cube size and draft logistics are tied together.

When I set out to build a cube, I did so with 360 cards in mind. I also wanted to ensure my archetype enablers and payoffs were present at sufficient volume to support decks of those archetypes in a scenario where all cards in the cube were being drafted. Therefore, it made sense to frame my draft logistics around the 3 * 15 for 8 dynamic, which is the only correct draft solution for 8 players drafting a 360 card cube, provided you want all cards to be included in the draft if possible. It then followed that my proposed variants for other numbers of drafters should use the 3 * 15 for 8 dynamic as the "ideal" to compare against, because that ideal was sort of baked into the cake when I was designing the cube.

Does that make sense?

In other words, I think that while you're right that all these numbers decisions are arbitrary to a certain point, they become vital pieces of the cube's architecture during construction. If you wanted to create a draft experience that differed significantly from the 3 * 15 for 8 baseline, you would need to have whatever your preferred draft variant is in mind when designing the cube, to ensure that drafters are seeing a sufficient volume of cards to play out your vision for the cube. The total number of cards in your cube should be a mathematical extrapolation of your draft function.

I think we are on the same wavelength here. If you have variable numbers of drafters, then an approach where the draft is a function of the number of drafters and numbers of cards seen will allow you to maintain the probabilities that the archetypes and factors like removal will be seen in the same quantities as you sought out in your design.

I think your functions make a lot of sense.

What I’m also thinking about is this bit from your original post here:

What percentage of the total 360 card cube does each player see over the course of the draft? (ideal is 77%)*
How many cards does each player end up with (ideal is 45)
How many cards does each player pick per pack (ideal is 1.9)**
*this was my “breakthrough” consideration. When I started, I was comparing the variants based on the total number of cards seen overall. In a normal 8-person draft, all 360 cards will be seen by someone, so I was rewarding other variants where this was the case. I realized, however, that in order to more closely represent the feel of an 8-person draft, what matters is that each individual playersees roughly the same percentage of the cube as he or she would in an 8-person draft (which is 77%).

What if you tweak the the 360 above but maintain the 77%? What if you want every drafter to see 77% of 400 card cube, 450, etc?

I tried experimenting with this by throwing Grillo, Bonzo, and Raveborn into one massive cube after uniq’ing their lists. Then I increased the draft numbers in cubetutor to something like 4*15 picks per drafter in cubetutor. It was too overwhelming to complete during my lunch break due to so many new cards to read. This may be foreshadowing of the conclusion of this experiment, heh.

 

[Rowan_CB]

What if you tweak the the 360 above but maintain the 77%? What if you want every drafter to see 77% of 400 card cube, 450, etc?

You can play around with this pretty easily using this formula to determine the number of cards that will be seen per player during a draft:

((n/2)*(n+x))*y

Where:

n= # of players drafting
x= # of cards in each pack, and
y = # of packs per player

So for instance, a 3 packs of 15 for 8 players draft works out to ((8/2)*(8+15))*3, which equals 276, which is 76.67% of 360.

You can use a solver if you know how, or otherwise just manually play around with x and y and divide by z (where z = the number of cards in the cube) to see what you can come up with.

I don't have time right now to get into this too deeply, but from playing around it seems like the best way to get close to 77% with 8 drafters for a 400 card cube is to use 4 packs of 11 (players will see 76% of the cube). It's worth noting that, especially as you get to lower number of players, you get really wacky results if you only focus on the % of the cube, which is why it's important to include other factors, like cards seen per pack and cards drafted per player.

Applying my original scoring system to a 400 card cube, it still suggests good old 3 packs of 15 as the ideal for 8 drafters (4 x 11, despite coming closest to that 76.67% standard, is awkward, because each player only wheels 3 packs per round).

 

[VincePendrell]

I have played with 4 x 12 cards for a while some years ago. You get 3 cards above the usual 45, and I used the additional space in the draft to force more slots for sideboard cards in my list.

Over time, I went back to 3 x 15 for a bunch of reasons:

• Easier to explain. Everyone knows the size of a booster.
• The 4th booster was just too tiresome. Everyone already had good cards for a deck. It felt too much. (This is also why I don't like the utility land draft.)
• The extra 3 cards weren't really necessary. People don't play with all cards they draft anyways, so it was just a matter of cutting under-performing cards and keeping the sideboard options around.

Even with less than 8 players (which is pretty much describes all drafts that I manage to run these days), I felt like 3 x 15 was a good number. The pool of cards is smaller, but you get more chances to read the picks and figure out what colors and/or strategies are open.

By and large I'd say that 15x3 is an artifact (not even properly carried over to cube because retail packs have basic lands and tokens).

Nitpicking moment: Well, we've seen lots of retail formats recently that had a multicolor land in the slot reserved for lands, so if you run at least 24 dual lands in a 360 cube, you are not that far off. Especially if you seed the boosters and guarantees at least one dual land per pack. (And the token is not one of the 15 cards, but that's a minor thing)

The discussion around various traditions like singleton inspired me to think about other norms, like the 3 packs of 15, see every card in a 360 card cube feature. Is this mostly an artifact of the retail pack? Is it doing useful things for cubes?

(...)

Thoughts?

Back to the topic at hand, I think it is an artifact, but personally, I don't see this as a design knob that is interesting to be turned. There doesn't seem to be any problem with cubes that can only be solved by doing this instead of just curating the list. I say this especially because I've tried it before and the results were very meh. Feels like the sort of rule that we break to do away with tradition, and not to solve a real problem with the game, and we do so by adding clutter.

To me, the important question is "what would break the 3x15 mold allow us to do that we can't otherwise?", and frankly, there aren't many reasons. For instance, with drafting less cards that there are in a pack: There is already a large amount of cards that we pick that will never be played in our decks. I'm not sure increasing the amount of game pieces that won't be used during gameplay is a winning strategy in game design. You could just cut your least picked cards that are not archetype-specific and you have the same result.

The only reason that I can think of right now is to maintain the exact same numbers of cards that wheel, to try and make the experience of reading the draft similar to the retail draft experience. Though, unlike Japahn, I don't think the drafting experience is ruined with less than 8 people. In my list, it just guarantees the presence of 3-color decks, and allows 4-color ones (I'd usually expect mostly 2-colors and a splash, and a few 3-color decks with 8 people). The trade-off is that splitting the card pool in more packs makes the draft take longer, since the picks that take the most time are usually the first ones, when a booster is going around for the first time.