General Optimal Draft Variants for Less than 8 Players

[Rowan_CB]

This is my first post on the forum, so I figure I’ll start with a little introduction before diving in.

I have very recently completed my first 360 card cube. I discovered this forum about a month ago and let me tell you, this place has been enormously helpful and influential in how I designed my cube. I intend to start a thread in the Cube Blog forum shortly, and I am excited (and maybe a little nervous!) to get feedback from this community.

With that said, the first draft of my cube is taking place this weekend. We will have a group of either 4 or 5 (one person is unsure if they will be able to make it).

This being my cube’s maiden voyage, I am very keen on this draft going as well as possible, and I have been somewhat obsessively trying to figure out the best way to draft with 4 or 5 people. As with everything else, the most useful insights I have found have been right here on riptide. I have enjoyed reading about Tenchester and Grid drafting, as well as other variants people have tried (e.g. 5 packs of 9, 4 packs of 11, etc.). The concerns I have are as follow:

• How well will the archetypes and synergies I’ve built into my cube function if only a percentage of the cards in my cube actually turn up in the card pool?
• Conversely, if I give a small pool of players access to the entire 360 card universe, will the decks be too “on rails”, i.e., will every player basically get every payoff card for the color combination they’re in, eliminating some of the tension from the draft?

Facing some analysis paralysis, I decided to turn to my buddy Excel and see if I could let the numbers choose for me.

For the purposes of my exploration, I started with the assumption that a “normal” booster draft of 8 people drafting 3 packs of 15 each was the ideal by which other variants should be measured against. What I ended up with was a system for analyzing draft variants that scored each potential variant based on how closely its results matched up with this “ideal” based on three factors:

1. What percentage of the total 360 card cube does each player see over the course of the draft? (ideal is 77%)*
2. How many cards does each player end up with (ideal is 45)
3. 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%).

**the idea behind this category is to simulate a similar type of wheeling experience as in an 8-person draft.

I then set up an Excel Solver to generate the variants with the maximum possible score for 3-7 players by running iterations adjusting (1) how many cards in each pack, (2) how many packs each player opens, and (3) how many cards are discarded from each pack without being picked. For example, if I understand correctly, 4-person Tenchester calls for 10 card packs, each player opening 9 packs, and 6 cards discarded at the end of each pack.


The solver results are as follows:



So, based on this my plan is to make 13 card packs.

If we end up doing a 4-player draft, each player will start with 6 packs, 8 picks will be made out of each pack, and the remaining 5 will be discarded.

If we end up with 5-player draft, each player will start with 5 packs, 9 picks will be made out of each pack, and the remaining 4 will be discarded.

In each iteration, each player will see between 76-77% of the cube, get between 1.8-2 picks per pack, and end up with 45-48 cards, closely mirroring the 8-player draft experience.

What do people think? Do you agree that the three factors I identified are the correct ones by which to compare draft variants to a normal 8-person draft?

Will the fact that players will see a similar % of the cube compared to an 8-person draft, but will end up with a smaller percentage of those cards in their picks mean decks will be much more powerful?


Very curious for your feedback!

 

[Grillo_Parlante]

I think I am going to experiment with this, and let you know how it goes. Really interesting topic, and something that I think could help a lot of people. I've seen this for years where players design cubes around the assumption of 8 players every draft, but the reality is that attendence fluctuates tremendously for most play groups.

It also opens up the ground for analysing the 77% baseline. Tweaking the pack numbers, might impact the draft texture in interesting and novel ways.

 

[Aston]

I've got a four player draft planned for this weekend and I will probably try this out. I usually do 5 packs of 9 for 4 players, which I do like, but having the overall card pool be greatly reduced can be an issue.

 

[Suicufnoc]

This doesn't really fix the wheeling experience, as its much easier to wheel a card when there's only three other players than if there's 7 other players. And with more packs, there's more chances to wheel. It does at least keep you from wheeling 3-4 cards per pack, but makes it much more likely to wheel this first one.

Good stuff, though

 

[Onderzeeboot]

This is an excellent first post! Welcome to the forums!

 

[James Stevenson]

Welcome! Nice to see a good excel table. As we used to say before cubetutor, "Cube: come for the drafting, stay for the spreadsheets."

Only one thought about the above: With 6 or 7 players, I don't think I would bother discarding any cards from the packs. My only reasons are:
A. I quite enjoy the last few picks of a pack, and seeing your final card, gifted to you by your benevolent neighbour.
B. Double-wheeling cards is fun.

So you would end up with 48 and 53-card pools, but I don't mind this. When we did 4 packs of 11 everyone always really enjoyed it.

It sounds good with fewer players, when you're binning the 4+ last cards of each pack.

 

[Onderzeeboot]

I actually did a 4*11 draft with 6 players last year, and that worked out really well!

 

[wahoopride]

I do my drafts with almost exclusively four players and I have tried a few different ideas to address the concerns.

The most simple:

-4 packs of 14
-Draft and pass like normal
-When there are 3 cards left in the pack, discard the whole remaining pack in the middle

Notes: The idea of this method is to fix the problem of card pool. If you did 3 packs of 15 and drafted them all like normal with four people, you would get the same number of total cards (45) but you would see far fewer distinct cards than if you were drafting with 8. Using this method allows you to see 200 different cards instead of 162 while still getting approximately the same number of cards to build your deck with (44). We tried it with 4 packs of 15 and found that decks were just slightly too powerful with 48 so we tuned it down to 4 packs of 14 so you only get 44.

Slightly more complex:

-4 packs of 14
-Draft and pass like normal
-Each time a given pack makes an orbit, randomly burn one card in the pack (so every 4 picks, all packs have 1 random card burned)

Notes: This produces something similar as before. You see the same total amount of cards (200), except that instead of all the cards being burnt at the end, they are burnt throughout the draft. This fixes the "wheel problem" where it becomes too easy to pass a good card and have it wheel since it only needs to make it through 3 other players. By randomly burning a card after each orbit, it is almost as if there is a fifth drafter so wheeling is slightly harder. Decks will be slightly less strong than before since the cards are burned throughout instead of at the end of each pack.

Most complex:

-6 packs of 15
-A card is burned at random between EACH drafter from EACH pack
-Think of it basically like there being a ghost drafter between each player that takes a card at random
-During each round, there should be 8 total packs in play, not 4. So for instance, you start one of your first six packs and take a card (15 to 14). Instead of then taking the pack from the person to your right, you take another one of your full packs of 15, randomly burn a card (15 to 14) then pick from that. Then you take the pack that the person to your right started with, burn one from it (14 to 13) and draft from that. So each the 8 packs are now either with a drafter, or between the drafters with a "ghost drafter"

Notes: This should effectively mimic the numbers of a real, 8 person draft, except half the drafters take cards at random instead of strategically drafting so its not perfect. However, you will get card flow/wheel/etc numbers that perfectly mimic a standard 8 person draft. One modification to address the fact that the "ghost drafters" are random instead of strategic is to do a pick-and-burn. Do everything the same except instead of burning a card at random, the drafter who just picked gets to burn a card of his/her choosing. This will likely make "wheeling" feel more true to form as players will burn powerful cards that they don't want their opponents to draft which roughly simulate how a real drafter would pick.

Hopefully those all make sense.

 

[inscho]

It's largely a question of what you determine to be the ideal style of drafting. To oversimplify my experience:

360 seen amongst 8 players
produces greater draft tension than:
360 seen amongst 4 players

360 seen amongst 4 players
produces greater deck quality than:
360 seen amongst 8 players

I feel that for small pods of people, deck quality (to a point) is more important as any attempts to recreate the tension of the 8 man draft is either undesirably complicated or anemic by comparison.

(For better or worse) Burning between picks results in more chaotic tension than a standard 8 man, because randomness is replacing the fact that your neighbors in a standard pod are drafting specific color combinations. While signaling from your neighbors is less emphasized in cube than retail limited (due to power disparities), it's still present.

For 4 man pods, I've been defaulting to 4 packs of 15 burning the last 4. You see 240 cards and end up with 44 card pool. We tried it once, and liked the resulting strength in decks. The tension was present, but fairly low.

I want to spend a little more time reading everyone's posts when I'm not at work. I just wanted to chime in with my .02


EDIT: I'm not sure this post was very helpful after reading a little more into the posts....

 

[Rowan_CB]

Thanks for all the great responses!

So much to think about. I think inscho sums it up nicely in that it really boils down to a subjective idea of what the most important aspects of a draft are. It's useful to hear from people that they run 4*11 or 5*9 drafts and have fun (I think the safest conclusion to draw is that a cube draft is going to be fun pretty much regardless of how you set it up). My compulsion to see more of the cube stems at least in part from insecurity regarding the design of my cube. It has never been played, by I know at least I designed it with a larger card pool in mind.

One idea for people like me who will likely almost exclusively draft with 4-6 people, would be to establish a 180 card "core" cube and have 4 "expansion" sets of 45 cards each to add for each additional drafter beyond the 4th, although I suspect even as a type this that this is getting far too cute. For instance, I've read elsewhere on this forum that Jason has purposefully built card variance into some card slots, which suggests that, if the cube is well-designed, the randomness that comes with seeing only part of your cube can be a feature, not a bug.

I will probably go ahead with the method I outlined in my OP, but will experiment with some of the others mentioned in this thread. I'm of course very curious to hear if anyone else tries out one of the "optimal" methods my spreadsheet generated, because, unlike me, you all will have other draft variants to compare them too!

 

[inscho]

Another thing to consider (forgive me if this is mentioned already) is that depending on the design of your cube, some archetypes might not be draftable without seeing the full/near-full cube pool.

Storm is perhaps the easiest example to articulate this....it's a deck that traditionally requires a maximum amount of support and key pieces to be successful. You can be fed piece after piece, but maybe that Crow Storm and Brain Freeze is setting aside in the undrafted portion. I have some ways to mitigate this in my cube, but it can be a concern. I've briefed my drafters on this to help them avoid potential draft traps, and so far have managed to avoid any feel-bads. I think in general my drafters know that going for Storm is always a bit of a risk.

 

[James Stevenson]

Oh by the way, when we've done 4 packs of 11, it actually feels even better than 3x15.

 

[Laz]

Oh by the way, when we've done 4 packs of 11, it actually feels even better than 3x15.

I actually build 264 card cubes for my playgroup... Since we normally target 6 drafters for 4x11. It actually works out to 77% of the cards seen too, which is kind of neat (and I never realised before now...).

 

[marwatt]

I tried the suggested 3 player variant this weekend, and I liked the result.
Enough of the card pool was available to actually be able to draft an archetype in 2 colors.
Opening a bad pack wasnt that bad either, since it doenst keep tabling forever.

 

[James Stevenson]

I tried the suggested 3 player variant this weekend, and I liked the result.
Enough of the card pool was available to actually be able to draft an archetype in 2 colors.
Opening a bad pack wasnt that bad either, since it doenst keep tabling forever.

You don't get to wheel anything though, right?

 

[marwatt]

yes you do out of 2 of the 3 packs that get opened. 11 cards in each pack, discarding 6

 

[James Stevenson]

yes you do out of 2 of the 3 packs that get opened. 11 cards in each pack, discarding 6

Oh thanks, I misread the table. Thought it was packs of 9.

 

[Mad Prophet]

​

Welcome to the forum Rowan.​

My playgroup of 3 has been happily drafting 4 packs with sizes 15-8-8-15 for ages now. With only three people, we like to nullify any effects of seating arrangement; particularly relevant for me since I never sit facing west.​

We could have equalized the pack sizes, but BookendinG the draft with two 15 card packs is so satisfying. The 8-card packs are skill testing in an interesting way, but I find 15 card packs lend themselves better to peak experiences.​

​

That said, I'm eager to test your algorithm's suggestion, as I find your methodology compelling.​

 

[Chris Taylor]

​

Welcome to the forum Rowan.​

My playgroup of 3 has been happily drafting 4 packs with sizes 15-8-8-15 for ages now. With only three people, we like to nullify any effects of seating arrangement; particularly relevant for me since I never sit facing west.​

We could have equalized the pack sizes, but BookendinG the draft with two 15 card packs is so satisfying. The 8-card packs are skill testing in an interesting way, but I find 15 card packs lend themselves better to peak experiences.​

​

That said, I'm eager to test your algorithm's suggestion, as I find your methodology compelling.​

Why did you...There's a card called nullify...

 

[Mad Prophet]

Why did you...There's a card called nullify...

Why indeed...​

 

[ravnic]

We do it quite simple:

With 2 players
- 10 packs of 10 for both players
- pick and pass regularly
- discard the packs when 6 cards are left
- 190 cards seen/40 cards drafted per player

With 3 players
- 7 packs of 10 for everyone
- pick and pass regularly
- discard the packs when 4 cards are left
- 189 cards seen/42 cards drafted per player

With 4 players
- 6 packs of 15 for everyone
- pick 2 cards for two seperate pools, then pass regularly
- 288 cards seen/90 cards drafted per player in two draft pools
- choose one pool and build a deck from it (if there is time after playing, you can play again with the other draft pool)

With 5 (or 6) players
- 4 packs of 12 for everyone
- pick and pass regularly
- 200 (228) cards seen/48 drafted per player

With 7 to 10 players we just do the regular 3x15 draft

 

[Rowan_CB]

I tried the suggested 3 player variant this weekend, and I liked the result.
Enough of the card pool was available to actually be able to draft an archetype in 2 colors.
Opening a bad pack wasnt that bad either, since it doenst keep tabling forever.

Very happy to hear that this worked for you--especially the 3-player variant, which is a trick number of players to work with. For my part, I can say that the 5-player variant played out exactly like I was hoping it would. We saw enough cards that the archetypes were there, but wheeling was limited to the point where there were definitely packs where tough decisions had to be made--it didn't feel on rails.

The "ideal" wheeling situation that these variants aim for emulates a regular 8-player draft in that each player should see 2 cards from every pack but 1, from which they will only see 1 card.

 

[MoshiMaro]

Necro'ing up my account and this thread

My playgroup usually drafts with 4 and sometimes 5 or 6 players.
We derived a method from the tenchester method on which Jason wrote an article titled "Cube design - grid drafting and more".

The most important argument is that in a normal draft the table gets to see 180 cards : 4 (players) x 3 (boosters) x 15 (cards) = 180 out of 540 cards.
With Tenchester you get to see 4 (players) x 9 (boosters) x 10 (cards) = 360 out of 540 cards which is the same when you draft with a full pod of 8 persons.
Every player only picks 1 card out of each booster -> the booster wheels to the original player "opening" the booster but he doesn't get to pick again (see below). With 4 players, 6 cards get burned.

If you change the numbers of players, the number of boosters changes.
36 boosters are always divided by the number of players:
E.g. 5 players 7 boosters each (35)
6 players 6 boosters each.
3 players 12 boosters.
This leads to every player always getting 35/36 picks and the method of shuffling up the boosters never changes.

The thing we changed compared to the tenchester method is dat we don't draft open but closed.
Besides the fact that drafting is much faster due to players taking picks simultaneously- you don't get to see who picks what.
To mitigate the lack of information/signaling you get your own booster returned to you.
This merely to look at what's missing, no additional card drafting from that booster except every player gets 1 "joker" per draft which can be used to make a second pick in one of your own boosters once it wheels (one time only)

We have been playing like this for a couple of years and it works well for us.

I'm now looking to change things up and increase the available card pool.
I want to make 40 boosters in total so that player's get 40 picks and the available card pool increases to 400/504.
The only worries I have is that the card pools available to each player will become too strong.
Do you guys share that opinion?

Edit: the answers might lie in the numbers: