DraftFM: A FoundationModel for Day-Zero Drafting in Magic: The Gathering

Brian Ward

cs.LGAug 20, 2026

DraftFM: A FoundationModel for Day-Zero Drafting in Magic: The Gathering

Authors: Brian Ward

Organizations: Independent Researcher

Abstract

Drafting a new Magic: The Gathering expansion begins before any pick from it has been observed: the complete card list is public, but the draft logs that supervised pick models train on do not yet exist. We study this day-zero regime directly. DraftFM is a discrete-choice policy that scores exactly the cards available in the current pack, conditioned on the drafted pool and the state of the draft. Every card enters as a frozen 775-dimensional function of its public card record, structured features and a fixed text embedding, with no card identities, set identities, or usage statistics anywhere in the model, so an unseen card is scored by the same machinery as a familiar one. A 1.6-million-parameter network fitted on 149 million human picks from 29 expansions predicts held-out picks in three expansions withheld in their entirety, reaching 50.8%, 60.4%, and 56.7% top-1 agreement, where uniform chance at the opening pick is about 7%. Refitted on all 32 observed expansions, the same architecture produced a card ranking for the then-unreleased set The Hobbit, sealed with its complete cryptographic provenance and published roughly 36 hours before the set became draftable on MTG Arena. The sealed ranking agrees with six independent expert reviewers roughly as much as those reviewers agree with one another. Evaluation against realized outcomes is committed to a follow-on note, whatever it shows.

Figures & tables

Source	Unit	Information used
17Lands	One observed draft pick	The cards offered in the pack, the cards already drafted, the selected card, the pick’s location in the draft, and available drafter and event information
Scryfall	One card printing	Card identity, mana cost and value, colors, rarity, type line, rules text, numerical characteristics, layout and card-face structure, and set metadata

Table 1: The two data sources used by DraftFM.

Record	Field group	Fields
Card printing	Identity resolution	Scryfall identifier, name, set code, digital status
Card printing	Card features	Mana cost, mana value, colors, color identity
Card printing	Card features	Rarity, type line, rules text, keywords, layout
Card printing	Card features	Power, toughness, loyalty
Card face	Card features	Face index, name, mana cost, type line, rules text, colors, power, toughness, loyalty
Set	Printing selection	Set code, release date

Table 2: Scryfall fields used for identity resolution and card features.

Feature block	Dimensions	Contents
Mana value	10	Scaled value and buckets from zero through eight or more
Mana cost	10	Colored and colorless pips, generic mana, and indicators for $X$ , hybrid, and Phyrexian costs
Color	8	Five colors, number of colors, colorless, and multicolored
Color identity	5	WUBRG color-identity indicators
Supertypes and types	12	Legendary, snow, basic, and nine card types
Creature subtypes	129	Up to 128 reserved vocabulary slots and an unmatched count

Table 3: The structured component of the DraftFM card representation.

Panel of Figure 1 — Figure 1: The geometry of DraftFM for one observed pick. Each of the $K$ real pack cards begins as the same 775-feature representation and becomes one $d$ -dimensional row. The pool is compressed to one $d$ -vector, the observed draft state becomes one 64-vector, and the scorer receives $3d+64$ values for each candidate. Its $K$ scalar outputs form a probability vector over exactly the real cards in the pack. Batch and storage padding are omitted because they do not enter the scorer.

Component	Setting	Role
Optimizer	AdamW with $\beta_{1}=0.9$ and $\beta_{2}=0.98$	Adaptive stochastic optimization with decoupled weight shrinkage
Learning rate	Peak $10^{-3}$ with 2,000-step linear warmup, then cosine decay to a floor of 1% of peak	Stable initial updates followed by progressively smaller steps
Batch construction	8,192 picks with shard probability proportional to $n_{s}^{0.5}$	Balance large-set coverage against domination by the largest files
Regularization	Weight decay 0.01, dropout 0.10 in the candidate scorer only, and label smoothing 0.05	Discourage brittle weights and overconfident probabilities
Gradient control	Global gradient norm capped at 1.0	Prevent an isolated large update from destabilizing fitting
Stopping rule	At most four corpus-equivalent passes, validation every 2,000 steps, and patience of three checks	Retain the strongest unseen-draft checkpoint instead of the final update

Table 4: Fixed fitting recipe used for every model width.

Set	Formats	Picks	Drafts
BRO	Premier, Traditional	4,616,619	104,676
FDN	Premier, Traditional	6,346,832	152,968
MSH	Premier only	1,607,786	38,580
Total		12,571,237	296,224

Table 5: Evaluation population for the whole-expansion development comparison. Every scored pick in each set is evaluated, with no sampling.

Grade	A+	A	A $-$	B+	B	B $-$	C+	C	C $-$	D+	D	D $-$	F
Share (%)	2	3	5	8	12	12	13	15	12	8	5	3	2

Table 6: The frozen 13-level letter ladder. Each band is a percentage of the scored card universe, assigned by rank. The percentages sum to 100.

All picks
			Card width $d$
Set	Picks	Drafts	128	256	512
BRO	4,616,619	104,676	50.63	50.83	49.89
FDN	6,346,832	152,968	60.15	60.37	60.56
MSH	1,607,786	38,580	56.71	56.67	56.79
Mean	12,571,237	296,224	55.83	55.96	55.75

Table 7: Top-1 agreement (%) on the three whole-expansion development sets, all drafters, formats pooled. The three-set mean is unweighted and is a summary, not a winner rule. Point estimates are shown; the 95% percentile cluster-bootstrap intervals resampling drafts (

B=1000

) have half-widths of at most

\pm 0.09

percentage points on these values, and complete intervals accompany the artifact data.

Width $d$	Parameters	Share of $d{=}512$	Train (h)	Eval (picks/s)	Internal val. top-1
128	979,823	26%	2.35	230,496	68.59%
256	1,637,999	44%	3.02	129,494	68.56%
512	3,740,783	100%	6.99	53,458	68.62%

Table 8: Size and cost of the three widths. Training time is wall clock on the same device; evaluation throughput is measured over the full 12,571,237-pick development population. Internal-validation top-1 is measured on reserved drafts from the 29 fitting sets and is not a development-set result.

Figure 2: Top-1 agreement against draft position on the three development sets, with the uniform-random baseline, the mean of

1/n

, at each position. DraftFM

d=256

, all drafters, all picks, formats pooled. Agreement is highest at the first pick of each pack, falls to a minimum, marked, within the first five picks, and rises to the end of the pack, where the final pick is forced and agreement is one by construction. The baseline rises with the same geometry, so pack size and agreement move together. Shaded bands are 95% percentile cluster-bootstrap intervals resampling drafts (

B=1000

); they are narrower than the plotted line at most positions, with a median width of 0.006.

Figure 3: Chance-normalized agreement,

(\mathrm{acc}-b)/(1-b)

with

b

the mean of

1/n

at that position, against pick within pack, by pack. Forced final picks are excluded because

b=1

makes the statistic undefined. Top: the curve declines over the opening picks, turns at pick 5 or 6, shaded, and rises to the end of the pack. Bottom: the sign of every pick-to-pick change, classified by whether its 95% interval excludes zero. Bands and step classifications are 95% percentile cluster bootstraps resampling drafts (

B=1000

), with the normalized statistic recomputed inside each resample and

b

re-derived there. DraftFM

d=256

, all drafters, formats pooled.

Event	Start	End
Official preview season	2026-07-18	2026-07-31
Gen Con pre-Prerelease events	2026-07-30	2026-08-02
Complete card image gallery	2026-07-31	2026-07-31
Local game store Prerelease events	2026-08-07	2026-08-13
MTG Arena release	2026-08-11	2026-08-11
Global tabletop release	2026-08-14	2026-08-14

Table 9: Release chronology for Magic: The Gathering | The Hobbit .

Source	Rater or raters	Medium	Publication interval	Coverage
Nizzahon Magic	Nizzahon	YouTube	2026-07-31–2026-08-03	Full set in six videos
Card Game Base	Anže Mlakar	Website	2026-08-01	Full draftable set (188 cards)
Draftsim	Andrew Quinn	Website	2026-08-03	Full draftable set (188 cards)
Limited Resources	Marshall Sutcliffe and Luis Scott-Vargas	Podcast	2026-08-03	Commons and uncommons
Limited Level-Ups	Marc Anderson	YouTube and website	2026-08-05	Full draftable set (188 cards)
NicolaiBolas	NicolaiBolas	17lands tier list (via patron link)	2026-08-09*	Full draftable set (188 cards)

Table 10: Pre-Arena expert HOB set-review sources available as of August 9, 2026. *Retrieved date; the source carries no publication date.

File	SHA-256	Contents
hob_p1p1_forecast.csv	a16c34767aa382e7703f480207f8480484e29ad22bbab2142aa2195e9b9a94a9	Rank, name, score, percentile, and grade for all 321 records
hob_p1p1_forecast.parquet	4c539b9cd78d669c8b9d9b79745d8009f0fc65dc592cc6007bbba91767e20e25	The same table in columnar form
seal_manifest.json	f7832e79f918bd5b0f04daf0c280a2644941a78f7a74a4a1b7496924b9d7b553	Conditioning, universe, ladder definition, and the full provenance chain
README.md	a6fa0399cb0be38f0a9ebdd3495a53fc2692e57f7e552b00bfdc00cb1d54e48c	Plain-language description of the artifact and its limits

Table 11: Files in the published seal and their SHA-256 digests. Each file was re-downloaded from the published tag and re-hashed; every digest matched the value recorded at generation time.

Pair	$n$	Exact	Within one	Spearman	Rank agr.	Top-10
Limited Resources vs. Nizzahon Magic	120	0.308	0.683	0.583	0.497	8
Card Game Base vs. NicolaiBolas	188	0.303	0.723	0.748	0.631	11
Card Game Base vs. Nizzahon Magic	188	0.303	0.569	0.684	0.577	12
Card Game Base vs. Limited Level-Ups	187	0.294	0.668	0.785	0.667	10
Draftsim vs. Limited Resources	120	0.283	0.617	0.610	0.501	14
Limited Resources vs. NicolaiBolas	120	0.275	0.675	0.570	0.472	14

Table 12: Pairwise agreement among the pre-Arena forecasts, human and model, on the common 13-level ladder. Statistics use only the cards a pair shares, and

n

is that count. Rows are ordered by exact match rate within each block; the lower block holds the sealed DraftFM forecast against each human source. Two notes on construction. The sealed letters were banded over all 193 HOB card names, basic lands included, and all five basics landed in D, so on the shared 188-card comparison set DraftFM’s D band holds 5 cards, 2.7% against the 5% the band targets; that is an artifact of banding a universe wider than the comparison set, not a defect in the forecast. And a source’s top ten is inclusive of every card tied with its tenth, so the intersected sets are not all the same size: DraftFM is the only tie-free source and contributes exactly ten cards, while the creators’ inclusive sets run as large as 27, for Limited Resources. The overlap column is not a measure of selectivity.

Panel of Figure 4 — Figure 4: The five highest-rated HOB cards in the sealed DraftFM forecast. Scores are the model’s raw P1P1 scores under the frozen conditioning of Section 3.1.3 , and grades come from the fixed percentile bands of Table 6 . Both are taken from the sealed artifact and were fixed before the set was playable on MTG Arena. Card images are copyright Wizards of the Coast and are reproduced here at reduced size for scholarly commentary; images are served by Scryfall.

Appendix figures & tables3 assets

Supplementary material from the paper’s appendix.

Appendix

Set	Picks	$d$	Top-1	Top-3	Log loss	ECE
BRO	All picks	128	50.63	83.66	1.3167	0.0515
		256	50.83	83.58	1.3135	0.0546
		512	49.89	83.35	1.3231	0.0459
	Non-forced	128	47.11	82.49	1.4104	0.0552
		256	47.33	82.41	1.4071	0.0585
		512	46.32	82.16	1.4173	0.0492

Appendix

Table 13: Complete development results, all drafters, Premier and Traditional Draft pooled. Top-1 and top-3 are percentages; the mean is the unweighted three-set summary. Point estimates are shown. The 95% percentile cluster-bootstrap intervals resampling drafts (

B=1000

) have half-widths of at most

\pm 0.09

percentage points on top-1,

\pm 0.07

on top-3,

\pm 0.002

nats on log loss, and

\pm 0.0008

on calibration error; complete intervals accompany the artifact data.

Figure 5: Expert minus all-drafters difference across the draft, in chance-normalized agreement (percentage points) and mean log loss (nats). Experts are a win-rate bucket of at least 0.55 and a games-played bucket of at least 100, per Section 3.1.2 . Negative values mean expert picks are harder to predict. The difference is largest at the first pick of the draft and is no longer distinguishable from zero across most of pack 3. Bands are 95% paired cluster-bootstrap intervals on the difference, resampling drafts (

B=1000

), with expert and all-drafter statistics recomputed within the same resample.

Figure 6: Mean top-label confidence against top-1 agreement by draft position, non-forced picks, DraftFM

d=256

, all drafters. The vertical gap is the model’s overconfidence. The annotated per-pack calibration error, 15 equal-mass bins, coincides with that gap to within 0.0004, so the model is overconfident in every bin rather than mixing over- and under-confidence. Overconfidence falls from pack 1 to pack 3 in all three sets. Bands are 95% percentile cluster-bootstrap intervals resampling drafts (

B=1000

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Open paper AskPDF arXiv

Many real-world games do not admit a fixed, compact rule set: instead, their dynamics are defined by interactions among a large and often evolving collection of game pieces, making general-purpose policy learning impractical. Magic: the Gathering (MTG) exemplifies this setting, where the cards themselves define and alter gameplay rules, strategic constraints, and long-term outcomes, while the pool of available cards is ever-changing. We study Draft, a constrained deck-building format of MTG in which eight players make 39-45 sequential selections from semi-random packs to construct a 40-card deck under partial information. By isolating the card selection process from gameplay, Draft provides a tractable yet non-trivial setting for studying decision-making driven by combinatorial card synergies. We propose an encoder-based model that produces set-contextualized card embeddings to encode the draft decision sequence, with a consistent improvement over linear baselines on large-scale real-world data, establishing a first learned benchmark for outcome prediction in MTG Draft. Our code is available at github.com/akulen/MtGDraftEncoder.

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