Building an MTGA Cube Draft Assistant

I’ve built a draft assistant for MTGA Powered Cube draft. This is difficult because we have to balance several aspects: 1. The power and win rate of each card individually. 2. How does each card work with other cards I have previously taken. 3. Based on the distribution of cards that we are seeing and what we’ve seen taken (after a pack goes all the way around) what are the open colors, strategies, and lanes.

This post summarizes the current state of the project: the models, the offline results, the first Monte Carlo tree search experiments, a walk-through of a pack experiment, as well as a live example.

A more paper-style writeup is also available here: Policy–Value Learning for Magic: The Gathering Arena Cube Draft.

The setup

A draft pick is represented with only information available to the drafter:

• the current pack
• my previously drafted pool
• cards I have seen but did not pick
• pack number and pick number
• the known cube list

The base model is a contextual pick policy trained from public 17lands Powered Cube draft logs. Each card is represented by combining a card-specific learned vector with features extracted from Scryfall metadata and rules text: mana value, color and color-identity bits, card-type bits, rarity, power/toughness fields, keyword indicators, and oracle-text features. In model terms, the representation is

card_repr = learned_card_embedding + alpha * MLP(scryfall_features)

where alpha starts high and is annealed to a nonzero floor. This lets common cube cards specialize through their learned embeddings while still giving reasonable representations to changed or unseen cube cards from their rules text and metadata. The policy scores every card in the current pack and is trained to imitate human picks.

There is one extra practical problem for live Arena Cube: the cube list changes, and some cards in a new live list were not present in the 17lands training/scoring vocabulary. To account for this and prevent a failure mode of an unknown card breaking the tool, I added a function-aware k-NN fallback for those cards. Instead of mapping every missing card to one generic UNK vector, the assistant builds a pseudo-embedding from similar known cube cards. Similarity combines structured Scryfall features, face-balanced rules text with card names removed, and curated role tags like removal, protection, tutors, rituals, fixing, artifact synergies, and graveyard synergies. This lets a new protection creature borrow from cards like Mother of Runes or Giver of Runes, while a new burn spell borrows from cards like Lightning Bolt or Abrade.

Models trained:

1. Human imitation / human continued is the pick policy trained only to match logged 17lands human picks. This is the most human-like baseline.
2. Deck-quality model is a separate value model trained from 17lands game results. It takes a completed 40-card deck plus sideboard and metadata, then predicts game win probability. I use it to ask: “if this draft pool became this deck, how good would the deck be?”
3. Value reranking means taking the human pick policy’s score for each card in the pack, then adding a small bonus from the deck-quality model after hypothetically adding that card to the pool.
4. Card-bonus model is a simpler outcome model trained from game results. Instead of evaluating full deck structure, it learns a per-card win-rate bonus: cards that often appear in winning maindecks get positive bonuses, cards that underperform get lower bonuses. This is useful, but less contextual than the deck-quality model.
5. Safe game-data is a DPO fine-tune that nudges the pick policy toward card-bonus-preferred picks while staying close to the human-imitation model.
6. Aggressive game-data is a stronger DPO fine-tune that optimizes the card-bonus preferences harder. It improves game-data preference accuracy, but loses a lot of human-pick agreement and sometimes makes weird-looking picks.
7. MCTS value-conservative is not a separately trained model. It is inference-time search using the value-conservative policy as a prior and the deck-quality/value model to score simulated draft continuations.

Model and training details

The pick model is a cube-context contextual preference ranker. For a cube with C cards, every training example has a C-dimensional current-pack mask, pool count vector, seen-but-unpicked count vector, and cube mask. The model first computes card_repr for every card in the cube. It then uses separate DeepSets encoders for three unordered sets:

pool_repr = DeepSet(cards in my pool)
seen_repr = DeepSet(cards I saw but passed)
cube_repr = DeepSet(cards in the cube list)

The draft context is the concatenation of those three set embeddings, an explicit WUBRG color-commitment vector from the pool, and learned embeddings for pack number and pick number. A small MLP maps that context to the same dimension as a card representation. Each card is scored by a dot product plus a card bias:

context = MLP(pool_repr, seen_repr, cube_repr, color_commit, pack_idx, pick_idx)
score(card | context) = dot(context, card_repr(card)) + bias(card)

The policy is trained over the in-pack support only. The main loss is a contextual preference / triplet ranking loss: the logged human pick should score at least a margin above every other card in the pack.

loss = mean_over_unpicked_cards max(0, margin - score(picked) + score(unpicked))

In the current implementation the representation dimension is 128, the hidden dimension is 256, and the default margin is 0.2. The Scryfall feature contribution alpha anneals from 1.0 to a floor of 0.3 over early training. I also use random cube-list masking during training so the model is robust to partial or changing Arena Cube lists.

For missing live-cube cards, the k-NN fallback precomputes top neighbors against the trained scoring vocabulary and caches the weighted average. On the Arena Powered Cube 5.0 list, 117 of 540 cards were missing from the current scoring vocabulary, and all were resolved through Arena/Scryfall lookup. In synthetic leave-20-cards-out tests over 20k held-out pick states and 200 trials, overall degradation was small because only a minority of states are affected: top-1 -0.0068, top-3 -0.0036, and MRR -0.0049. On the directly affected states where the picked card was held out, the drops were larger: top-1 -0.1253, top-3 -0.0714, and MRR -0.0902. So k-NN is a useful live fallback, not a substitute for training on those cards once data exists.

The outcome model is separate. It takes a built deck and sideboard, encodes maindeck and sideboard cards with DeepSets over the same card representation, concatenates rank/event/color covariates, and predicts game win probability. I train this on 17lands game data, both per-game and aggregated by (draft_id, build_index). For deployment, a simple heuristic deckbuilder maps a draft pool to a 40-card deck before scoring.

The game-card bonus model is an even simpler outcome model:

logit(win_probability) = intercept + sum(card_in_maindeck * card_bonus) + covariates

I tested pair-interaction variants, but they overfit relative to the card-only model. The learned top bonuses were plausible Powered Cube cards: Ancestral Recall, Time Walk, Black Lotus, Sol Ring, Mana Crypt, and the Moxen.

Finally, I generated static preference pairs for DPO. For a logged pick state, if one in-pack candidate has a sufficiently higher learned game-card bonus than another, that pair becomes (preferred, rejected). DPO fine-tunes the pick policy toward those game-data preferences while anchoring it to the human-pick reference policy with a KL penalty. This gives the safe/aggressive trade-off in the table below.

Current offline results

On a held-out Powered Cube split, the strongest human-imitation model gets roughly:

Model / setting	Human top-1	Human top-3	Game-data pref. acc.
Human continued, no value rerank	0.6240	0.9093	0.5494
Human continued + value rerank	0.6234	0.9077	0.6062
Safer game-data DPO + value rerank	0.6161	0.9048	0.6406
Aggressive game-data + value rerank	0.5092	0.8411	0.7262

It seems that the safer game-data model keeps most of the human-pick accuracy while improving game-data preference agreement. The aggressive model optimizes game-data preferences much harder, but it no longer behaves like a human drafter and often makes suspicious picks.

How much does previous-pick context matter?

A lot. I tested the human-continued model by removing or corrupting the previous-pick context on a 20k held-out sample:

Context	Top-1	Top-3	Same top pick as full context
full pool + seen	0.6168	0.9070	1.0000
no pool, keep seen	0.4268	0.7545	0.5116
keep pool, no seen	0.6160	0.9065	0.9409
no pool, no seen	0.4070	0.7384	0.4856
shuffled pool	0.3507	0.6533	0.4088

The pool matters enormously. The seen-but-unpicked channel matters much less in the current model.

Adding inference-time search

The next experiment was to add Monte Carlo tree search at inference time. This is not training. The model is already trained; MCTS is a search procedure that evaluates each legal pick by simulating possible continuations of the draft and scoring the resulting pools.

For each candidate pick, the search:

1. forces that pick,
2. samples plausible future packs from the cube,
3. completes the draft with the policy,
4. builds/scores the final pool with the value model,
5. combines rollout value with the policy prior.

Because MTGA logs do not reveal hidden packs or opponent picks, this is an information-set approximation. It knows my pack and my pool, but future packs are sampled rather than perfectly reconstructed.

Latency with the model loaded once, on CPU, using real 17lands pick states:

Simulations	p50	p95	Mean
10	418 ms	574 ms	378 ms
25	942 ms	1370 ms	850 ms
50	1825 ms	2697 ms	1642 ms

So 25 simulations is a reasonable default for live search-based reranking.

The current MCTS default is:

--simulations 25
--rank-by final
--root-policy-weight 0.15
--root-value-weight 1.0
--root-value-mode prob
--rollout-temperature 0.0
--cpuct 1.5

A real depleted-pack example

The following trace uses real packs from the held-out 17lands eval data. These are not independently sampled fake packs. They are the packs as seen by a real drafter, already depleted by previous picks. Pack sizes go from 14 down to 7.

Caveat: the later packs are real for the human’s actual draft path. If a model makes a different earlier pick, the later packs are not a perfect counterfactual. Still, this is much closer to reality than testing on random packs.

The real packs

Pick 1, pack size 14

Arena of Glory; Blood Crypt; Containment Priest; Endurance; Godless Shrine; Grief; Omnath, Locus of Creation; Ouroboroid; Skyclave Apparition; Snapcaster Mage; Sundering Titan; The Wandering Emperor; Wishclaw Talisman; Yavimaya, Cradle of Growth

Pick 2, pack size 13

Birds of Paradise; Chain Lightning; Cosmogrand Zenith; Gitaxian Probe; Hymn to Tourach; Life // Death; Multiversal Passage; Soul-Guide Lantern; Talisman of Indulgence; Talisman of Unity; Torsten, Founder of Benalia; Wasteland; Witch Enchanter // Witch-Blessed Meadow

Pick 3, pack size 12

Dark Confidant; Deathrite Shaman; Demonic Tutor; Expressive Iteration; Get Lost; Liliana of the Veil; Questing Druid // Seek the Beast; Razorverge Thicket; Sylvan Caryatid; Underground Mortuary; Virtue of Loyalty // Ardenvale Fealty; Windswept Heath

Pick 4, pack size 11

Copperline Gorge; Elvish Reclaimer; Flickerwisp; Mine Collapse; Savai Triome; Scrubland; Talisman of Progress; Trumpeting Carnosaur; Unexpectedly Absent; Valki, God of Lies // Tibalt, Cosmic Impostor; Zuran Orb

Pick 5, pack size 10

Archon of Cruelty; Bleachbone Verge; Mana Confluence; Questing Beast; Sacred Foundry; Blazing Firesinger // Seething Song; Stomping Ground; Taiga; Tersa Lightshatter; Titania, Protector of Argoth

Pick 6, pack size 9

Crucible of Worlds; Emperor of Bones; Grim Lavamancer; Jetmir’s Garden; Restless Cottage; Restless Fortress; Rofellos, Llanowar Emissary; Sanguine Evangelist; Vampire Hexmage

Pick 7, pack size 8

Bone Shards; Collective Brutality; Exploration; Keen-Eyed Curator; Overgrown Tomb; Restless Vents; Utopia Sprawl; Winds of Abandon

Pick 8, pack size 7

Celestial Colonnade; Deep-Cavern Bat; Gloomlake Verge; Jadar, Ghoulcaller of Nephalia; Prismatic Ending; Sink into Stupor // Soporific Springs; Talisman of Conviction

Model choices

Pick	Human log	Human imitation	Safe game-data	Aggressive game-data	MCTS
1	Skyclave Apparition	Snapcaster Mage	Skyclave Apparition	Ouroboroid	Blood Crypt
2	Gitaxian Probe	Gitaxian Probe	Cosmogrand Zenith	Birds of Paradise	Hymn to Tourach
3	Windswept Heath	Demonic Tutor	Windswept Heath	Demonic Tutor	Demonic Tutor
4	Scrubland	Scrubland	Unexpectedly Absent	Zuran Orb	Valki, God of Lies // Tibalt, Cosmic Impostor
5	Sacred Foundry	Archon of Cruelty	Sacred Foundry	Titania, Protector of Argoth	Archon of Cruelty
6	Sanguine Evangelist	Emperor of Bones	Sanguine Evangelist	Emperor of Bones	Emperor of Bones
7	Winds of Abandon	Collective Brutality	Winds of Abandon	Keen-Eyed Curator	Bone Shards
8	Deep-Cavern Bat	Deep-Cavern Bat	Prismatic Ending	Deep-Cavern Bat	Deep-Cavern Bat

Final pools

Human log

Skyclave Apparition; Gitaxian Probe; Windswept Heath; Scrubland; Sacred Foundry; Sanguine Evangelist; Winds of Abandon; Deep-Cavern Bat

Human imitation

Snapcaster Mage; Gitaxian Probe; Demonic Tutor; Scrubland; Archon of Cruelty; Emperor of Bones; Collective Brutality; Deep-Cavern Bat

Safe game-data

Skyclave Apparition; Cosmogrand Zenith; Windswept Heath; Unexpectedly Absent; Sacred Foundry; Sanguine Evangelist; Winds of Abandon; Prismatic Ending

Aggressive game-data

Ouroboroid; Birds of Paradise; Demonic Tutor; Zuran Orb; Titania, Protector of Argoth; Emperor of Bones; Keen-Eyed Curator; Deep-Cavern Bat

MCTS value-conservative

Blood Crypt; Hymn to Tourach; Demonic Tutor; Valki, God of Lies // Tibalt, Cosmic Impostor; Archon of Cruelty; Emperor of Bones; Bone Shards; Deep-Cavern Bat

What happened in this example?

The safe game-data model most closely follows the human’s white/fixing lane. It takes Skyclave Apparition, Windswept Heath, Sacred Foundry, Sanguine Evangelist, and Winds of Abandon.

The human-imitation model actually chases more raw power here: Snapcaster Mage, Demonic Tutor, Archon of Cruelty. That is interesting because it is the model optimized for human agreement overall, but on this trace it is less committed to the logged human’s fixing-heavy path.

The aggressive game-data model still looks unsafe. Picks like Ouroboroid, Zuran Orb, Titania, and Keen-Eyed Curator are plausible outputs of a model chasing static game-outcome bonuses, but they look contextually dubious.

The most interesting part of the real-pack example is that MCTS appears to choose a lane and strategy early. After taking Blood Crypt, it moves into a black/red, maybe Rakdos-reanimator-ish, power lane: Hymn to Tourach, Demonic Tutor, Valki/Tibalt, Archon of Cruelty, Emperor of Bones, Bone Shards. Whether or not Blood Crypt is the best first pick, the later MCTS picks are at least coherent with that early commitment.

The other models look less strategically consistent in this trace. Human imitation takes individually strong cards, but jumps between Snapcaster, Demonic Tutor, Scrubland, Archon, black interaction, and Deep-Cavern Bat without as clear a deck plan. Safe game-data follows the logged human’s white/fixing lane more closely, but sometimes takes value/removal cards over synergy. Aggressive game-data mixes value and combo cards and produces the least coherent path. This suggest that search can amplify a questionable early lane choice, but it can also make the subsequent picks more internally consistent.

Current takeaways

1. The base policy is already strong at human-pick imitation.
2. Prior picks matter a lot; removing the pool cuts top-1 accuracy by about 20 points.
3. Safe game-data tuning improves game-data preference agreement while mostly preserving human agreement.
4. Aggressive game-data tuning is useful for analysis, but not safe as a default recommendation policy.
5. MCTS is promising as an inference-time search/reranking method because it often commits to a lane and then chooses strong cards for that lane. Its disagreements still need auditing, especially when the initial lane choice is questionable.
6. Real depleted-pack traces are much more informative than random pack examples.
7. Function-aware k-NN makes live cube updates usable when cards are missing from the training data, but those cards should still be folded into future training data when possible.

Example from a live draft

P1P1

Pack 1, pick 1 shows all strategies rank Sol Ring the highest, because well it is the stringest card by far. Next is Animate Dead, which is a strong card for the reanimate archetype.

P3P1

At pack 3, pick 1 we’ve taken a bit of a controlling artifacts deck. In which Staff of the Storyteller or Tezzeret would fit nicely into. But Ugin is very strong, providing removal, ramp, and card draw in a single car, and we have a good amount of acceleration and colorless artifacts that he might work well.

The deck ultimately ended up fine, not fantastic. Went 2-2. 2nd loss was due to my misplay (forgot to crew bankbuster and kill Kaito when I had the chance). Both wins were with playing Ugin (once the opponent scooped immediately and the other time I exiled their remaining board the next turn. But was the deck capable of 7 wins? Doubtful. Was it interesting? Very. I hope to get more runs and data from the next round of cube draft.