BirdsOfParadise's Cube

I joined this site to be able to make pretty pictures of the decks that my friends and I draft.

My cube contains one copy of every card that I own. To each card is associated a strength rating, a knowledge rating (how well the strength is known), and a color alignment. Before a draft session, I generate that session's draft pool by filling 95% of the slots with cards with the highest strength rating (the cards that have won the most times) and 5% of the slots with cards with the lowest knowledge rating (the cards that have been played the fewest times). Of course, the draft pool is balanced from a color alignment perspective.

In other words, even though the cube is many hundreds of cards in size (my collection is small), my friends and I only play with the "strongest" and "most unknown" 180 or 240 cards. The theory is that eventually the draft pool will self-organize around the most successful cards, while having constant variation. I have no idea how this will turn out but I think it's a cool idea. (In the meantime --- while the algorithm is still learning what cards are good --- it's not too different from normal limited, because using all the cards in my collection means there's a lot of chaff.)

I should mention that the strength rating is not assigned by me; it's algorithmic. I update the strength ratings after each draft based on which deck was the overall winner. It's a very crude and simplistic method.

The group is small. No 360-card drafts yet. So far we've done booster draft, grid draft, and sealed.

I want to be able to share links to the deck lists, so I'll be putting the deck lists in the next few posts.
 
Thanks!

(I'm trying to get used to the card display tools. The post below the OP contains other text in addition to the deck image --- any idea why that's not displaying? Thank you Laz!)
 

Laz

Developer
It isn't displaying because you didn't close the 'cubedeck' tag with a '/'. Here you go:


Also, I love the idea! I mean, sounds like a pain to assemble in paper, but an awesome self selecting cube? That is awesome. I am not sure your measure of success 'cards that have been in the most winning decks' will create the most interesting draft environments from a game-design perspective, but it excites me from a conceptual point of view.
 
Also, I love the idea! I mean, sounds like a pain to assemble in paper, but an awesome self selecting cube? That is awesome. I am not sure your measure of success 'cards that have been in the most winning decks' will create the most interesting draft environments from a game-design perspective, but it excites me from a conceptual point of view.
Agreed on not being sure whether the draft environments will be interesting. Right away, we had the problem that the first deck (by virtue of containing good cards) set the blueprint for what the second deck would look like; the results from the first draft seeded the second draft with good red and green cards, while the blue, black, and white cards remained essentially random. Once some blue, black, and white cards have been in winning decks, the process will start to understand that they are good and recycle them, but until then, green/red decks enjoy the best tools. (The third decklist will show evidence of other colors creeping in.)

Anyway, here's January 2014.









January 2014

Creatures (16)
Frostling
Gold Myr
Goblin Piker
Thornweald Archer
Nessian Courser
Goblin Replica
Goblin Spelunkers
Treespring Lorian
Viashino Fangtail
Sakura-Tribe Springcaller
Bladetusk Boar
Shock Troops
Dragon Whelp
Clockwork Vorrac
Ghor-Clan Savage
Tangle Golem

Other spells (7)
Guerrilla Tactics
Earthbrawn
Echoing Courage
Gruul Cluestone
Sword of Fire and Ice
Chandra's Fury
Thrive

Lands (17)
Mountain
Forest
 
Here is a deck list from February 2014. Green/red is still the best, but at least this sealed deck splashes for Silkbind Faerie and cards with Sunburst. In this deck it doesn't matter whether white or blue mana is being produced for the splash, so Island, Rampant Growth, Izzet Signet, and Gold Myr are all suitable splash mana sources.










February 2014

Creatures (15)
Frostling
Timberpack Wolf
Goblin Piker
Canopy Spider
Deadly Recluse
Thornweald Archer
Gold Myr
Goblin Replica
Silkbind Faerie
Akki Drillmaster
Wood Elves
Giant Spider
Bladetusk Boar
Tangle Golem
Siege Wurm

Other spells (9)
Pyrite Spellbomb
Izzet Signet
Rampant Growth
Guerrilla Tactics
Flowstone Embrace
Earthbrawn
Sword of Fire and Ice
Opaline Bracers
Heliophial

Lands (16)
Island
Mountain
Forest
 

Laz

Developer
Agreed on not being sure whether the draft environments will be interesting. Right away, we had the problem that the first deck (by virtue of containing good cards) set the blueprint for what the second deck would look like; the results from the first draft seeded the second draft with good red and green cards, while the blue, black, and white cards remained essentially random. Once some blue, black, and white cards have been in winning decks, the process will start to understand that they are good and recycle them, but until then, green/red decks enjoy the best tools. (The third decklist will show evidence of other colors creeping in.)


I suspect this comes from having 95% of the pool come from the pool of the strongest cards. That number is really high, and will prevent the other cards from bubbling up because colours are a real thing in Magic. You need a critical mass of them...

I wonder if you need a scale that refines as you get more and more 'knowledge' about cards. So, start with completely random, then have 25% of the cube be from the top power, then 35%, then 45% etc. Probably a clumsy approach. We need Jason in here with his statistical wizardry...
 
I never though of doing it that way! I have already generated the next card pool (which is tedious) so I'll go ahead with what I have, but your idea seems worth a try if we continue having low deck variety.

My hope, however, is that people will fight over red and green enough that they'll be forced into a non-red, non-green secondary color. Another source of "hope" (really just another problem) is that any deck with Sword of Fire and Ice can win even if the rest of the deck is 24 Fugitive Wizards and 15 Islands. So far I've been the lucky person with the broken equipment each time.
 

Jason Waddell

Administrator
Staff member
This is a cool thread, thanks for bringing it to my attention Laz. I'll chime in with thoughts later when I have some time.
 

Jason Waddell

Administrator
Staff member
Okay, so there are some things to consider here:

The current mechanism for changing cards looks like it will lend itself to a rather static cardpool. Well, kind of. Let's explore.

For the sake of simplicity let's say we have 360 card cube. ~340 of those cards will be there because they cross some power threshold. I know there is a different threshold per game, but let's say (again for simplicity) that we have a flat power threshold of 0.5 (50% win rate).

We see ~20 test cards each draft. Whichever cards pass the power threshold are added to the cube's "core", and a corresponding number are dropped out. Let's look at one of the dropped cards. Let's call him Iron Myr.

Iron Myr was in the cube for a couple drafts, so it has some knowledge tied to it. It's not going to qualify for the "low knowledge" part of the draft, perhaps ever, depending on the size of your pool. He also has a power score of say, 0.45. Iron Myr is never coming back unless the power threshold drops low enough to include him. I would imagine that the power threshold is relatively stable, or, if anything increasing because the marginal cards work their way out while while stronger cards continue to beat the weak cards.

Now, everything I said about Iron Myr also applies to a new card like Courser of Kruphix. If it has a bad first showing for whatever reason, it's not going to be tested again until it qualifies for the "low knowledge" pool again. Even then, it has to really perform well to cross the "power threshold", because it's already being weighed down by its first draft.


If we take a large card pool and a large sample size of drafts, "power score" of known cards stabilizes. I expect that each draft the pool slowly churns as some of the ~20 test cards pass the power threshold each draft and bump off a few others.

I'm not saying this is good or bad, but the question I'd pose is "what do you want to accomplish?" There are of course other issues (sample size, whether a card is actually drawn, etc.), but many of these would theoretically work themselves out in the long run. But a large focus in such algorithmic approaches is to try and optimize the speed at which our algorithm "converges".

A tried and true approach in Statistics is something along the lines of "simulated annealing" (google away). Basically, you set up your algorithm to allow it to explore the parameter space a lot in the beginning and to slowly stabilize over time. In practice here the recommendation would be to start by including a MUCH higher percentage of "low knowledge" cards and as you gather more and more drafts worth of data you can start to narrow that down. This allows you to learn more about a wide variety of cards early. With 5% your card pool will change too slowly and we get lots of Iron Myr style cards that get stuck in a sort of no-man's land.
 

FlowerSunRain

Contributor
As a practitioner of the fine art of bashing shit together until it works, I can say that I am simultaneously completely uninterested and morbidly curious as to how this will work. I do agree with both Jason and Laz that your system needs to be more lenient to new cards. Perhaps set aside some percent of your cube specifically for "new cards" and don't remove them until you have enough games played that you are confident in your data. You can adjust or even remove this percentage of your cube if you don't currently have new cards. Particularly as your cube expands, 5% of 180 is only 9 cards, which is literally less then the contents of one booster pack from the newest set, a lot of cards are going to be lost in the metaphorical shuffle unless you both a) rarely ever add new cards to the pool and b) play an obscene amount.
 
Here I am, after a hiatus. Several folks have pointed out that it makes sense to have a higher number of cards come from the "unknown" camp than the "strong" camp, in order to ensure turnover. So far, the turnover rate has actually been really high, so I'm not worried about that, but I'll have the option in my back pocket. Also, the green-red hegemony has shifted, so I'm looking forward to an emergence of new decks with guarded optimism. My next question is whether a winning deck can be non-red, but I don't know if the world is ready for that yet.

As for Jason's question about what I'm trying to accomplish: I want to see what happens when I remove design oversight from the cube, while still allowing more synergy and streamlining than pure randomness would give. Things might emerge from this chaos, and if they do, the journey will have been the best part. I was really happy with a friend's weird mono-green creature spam deck (20+ saprolings from Sprout Swarm in one game) that somehow achieved metalcraft for Razorverge Rhino. It won games even though it didn't win the overall draft.

A winning list:









May 2014

Creatures (19)
Gustcloak Runner
Firefright Mage
Deftblade Elite
Gust-Skimmer
Myr Sire
Keldon Marauders
Fresh Volunteers
Silkbind Faerie
Blazing Blade Askari
Moonlight Geist
Brutal Deceiver
Kitsune Blademaster
Bloodscale Prowler
Akki Drillmaster
Dross Ripper
Dragon Whelp
Sootwalkers
Flickering Spirit
Clockwork Vorrac

Other spells (4)
Leonin Bola
Adventuring Gear
Flowstone Embrace
Sword of Fire and Ice

Lands (17)
Evolving Wilds
Mountain
Plains
 
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