Slay the Spire: Hypergraph Deck Synergies

I trained hypergraph neural networks over 12,500+ runs to discover higher-order card combos, expose the math behind why static tier lists fail, and identify contextual trap picks.

Intro

In roguelike deckbuilders (Slay the Spire, Balatro, Monster Train), card value is completely non-linear:

Corruption alone exhausts your few defenses and gets you killed. Dark Embrace alone is 2 wasted energy without exhaust outlets. Dead Branch alone generates chaotic hands. Together, they form an infinite card-draw and block engine that solves the game.

Corruption Skills cost 0; exhaust

Dark Embrace Draw on exhaust

Dead Branch Random on exhaust

Infinite Loop +11.6 flr surge

Standard graph neural networks assume pairwise edges (u ↔ v). But combinatorial synergy is fundamentally a hyperedge connecting arbitrary subsets of cards and relics simultaneously (k ≥ 3).

Encode decks as hypergraphs with k-body edges connecting cards across global, archetype, and cost sets.

Prove why static tier lists fail: linear models mathematically cancel out deck context (w_A - w_B is constant).

Decompose 1-way, 2-way, and 3-way Shapley interactions to isolate super-additive synergy and contextual trap picks.

The Leaky Metric Trap

Before training deep architectures, we benchmarked simple heuristics on 5,556 Ironclad runs. We immediately found a critical methodological flaw in how deck models are typically evaluated:

Parsed Runs 12,524

Ascension 0–20 across 4 public archives

Ironclad Subset 5,556

4,444 train / 1,112 test held-out split

Floor MAE 3.78 flr

Survival prediction R² = 0.891 across 56 floors

Model Suite 10 models

Heuristic, linear, tree, set, graph, and hypergraph baselines

A trivial 1-feature heuristic that simply counts len(relics) achieves 0.921 ROC-AUC. In roguelikes, survival leaks directly into inventory size: dying on Floor 8 leaves you with 2 relics; beating Floor 56 leaves you with 18.

Predicting overall victory is artificially easy. The genuine modeling challenge is conditional drafting: given your current deck, which offered card maximizes expected survival?

Diagram contrasting pairwise GNN graphs with hypergraph multi-card hyperedges — Figure 1. Pairwise graphs decompose interactions into additive 2-body links. Hyperedges capture joint combinatorial explosions (k ≥ 3).

Model Architecture

We formulate deck state S as an incidence matrix H ∈ {0, 1}^{|V| × |E|} across global, functional archetype, and energy-cost hyperedges.

Diagram of the Hypergraph Neural Network architecture for Slay the Spire — Figure 2. Two-stage message passing (Node → Hyperedge → Node) over combinatorial deck structures.

Incidence Matrix H

Connects items across global deck, functional archetypes (Exhaust, Strength, Block), and cost tiers.

Hypergraph Conv

Two-stage propagation computes multi-body message aggregation in a normalized dense matrix multiplication.

Multi-Task Readout

Jointly predicts continuous floor survival (MAE 3.78 flr) and counterfactual pick rank deltas.

Category	Architecture	Features / Formulation	ROC-AUC	Accuracy	F1 (Wins)	Note
Heuristic	Relic Count Only	`Single scalar: len(relics)`	0.921	85.9%	0.531	Leaky baseline: surviving longer collects more relics
Heuristic	Deck Length Only	`Single scalar: len(cards)`	0.714	81.7%	0.239	Weak signal without item identity
Tree	XGBoost (GBDT)	`150 trees, depth 5, multi-hot counts`	0.942	89.2%	0.691	Strong tabular baseline
Linear	Logistic Regression	`L2-regularized Bag-of-Cards`	0.947	89.1%	0.698	High ROC, but 0% context sensitivity in drafting
Deep Set	Set Transformer	`Multi-head Self-Attention + PMA`	0.951	89.4%	0.735	Permutation-invariant card pooling
Deep Graph	Pairwise GCN	`Cosine Adjacency + Multi-head Pool`	0.955	90.1%	0.770	Pairwise card-to-card graph convolutions
Deep Hypergraph	Hypergraph Neural Net	`Multi-edge message passing (Ours)`	0.953	89.8%	0.739	Captures k-body combinatorial interactions

Why Card Tier Lists Are Broken

Every community tier list assigns each card a static score w_i. In any linear formulation, the difference in value between card A and card B is:

Compare Δ(A, B | S) = logit(S ∪ {A}) − logit(S ∪ {B})

Expand = (w^Tx_S + w_A) − (w^Tx_S + w_B)

Result = w_A − w_B

S disappears. The ranking cannot react to the deck you already have.

The existing deck S completely cancels out. A linear model or tier list will recommend the exact same card on Floor 2 as on Floor 50, regardless of whether your deck needs immediate damage or boss scaling.

Act 1 Starter Core (Needs Tempo)

Strike

Defend

Bash

Optimal Pick: Armaments (+1.01 flr)

Act 3 Block Core (Needs Boss Scaling)

Barricade

Entrench

Body Slam

Optimal Pick: Demon Form (+0.26 flr)

Model	Act 1 Starter Deck (5 Strikes, 4 Defends, Bash)	Act 3 Turtle Block Deck (Barricade, Entrench)	Context Sensitivity
Logistic Regression (Linear / Tier List)	Demon Form (+0.0129 logit)	Demon Form (+0.0129 logit)	0% (Deck context completely cancels out)
Hypergraph Neural Network (Ours)	Armaments (+1.01 flr advantage)	Demon Form (+0.26 flr advantage)	Dynamic Reversal (Adapts to survival vs scaling needs)

In Act 1, Armaments upgrades basic cards to survive Gremlin Nob. In Act 3, Demon Form provides the necessary scaling to defeat the Awakened One. The Hypergraph model correctly reverses its recommendation; linear models cannot.

Results & Higher-Order Synergies

We computed combinatorial Shapley interaction indices across held-out runs to isolate 1-way, 2-way, and 3-way hyperedge values.

Bar chart of 1-way, 2-way, and 3-way combinatorial card synergy contributions — Figure 3. Higher-order synergy decomposition for Exhaust, Block, and Strength engines.

Result 1

Super-Additive Hyperedges

In the Exhaust engine, Corruption alone has a negative single value (-1.13 flr) due to exhausting starter skills.

When combined with Dark Embrace and Dead Branch, it yields a pure 3-way super-additive boost (+0.27 flr). Once the core is assembled, adding a payoff surges survival by +11.56 floors.

Scatter plot matrix contrasting early starter deck value against mature synergy value — Figure 4. The Trap Pick Matrix: Starter Deck Δ vs Mature Synergy Δ.

Result 2

The Trap Pick Landscape

Demon Form is the classic novice trap: spending 3 energy for 0 immediate output in early Act 1 yields a negligible +0.17 flr. In mature decks, it surges to +2.19 flr.

The model also discovered anti-synergies without human rules: pairing Clash with Ascender's Bane produces -0.18 flr because curses brick Clash.

Heatmap showing learned archetype clusters among Ironclad cards — Figure 5. Learned card affinity matrix extracted from hypergraph embeddings.

Result 3

Emergent Archetype Discovery

The intermediate representations cleanly partition cards into four functional game clusters: Exhaust, Strength, Block / Body Slam, and Strike / Aggro.

The network learns functional card roles entirely from survival correlations across 12,500 games.

Archetype Hyperedge Engines

The Exhaust Engine

Corruption 0-Cost Skills -1.13 flr single

Dark Embrace Draw on Exhaust +2.29 flr single

Dead Branch Random Gen +1.51 flr single

3-Way Attrib +0.27 flr

Engine Surge +11.56 flr

Adding the 3rd piece to Corruption + Dead Branch explodes survival straight into Act 3 contention.

The Block Infinite

Barricade Block Retained +0.33 flr single

Entrench Double Block +1.07 flr single

Body Slam Damage = Block +1.70 flr single

3-Way Attrib +0.03 flr

Engine Surge +3.33 flr

Barricade + Body Slam pairs defense into lethal burst damage.

The Strength Engine

Spot Weakness +3 Strength +2.02 flr single

Limit Break Double Strength +0.67 flr single

Heavy Blade 3x Str Scaling +1.25 flr single

3-Way Attrib +0.22 flr (pair)

Engine Surge +4.28 flr

Limit Break doubles base strength, scaling Heavy Blade into a one-hit finisher.

Card	Type	Win Rate	Act 1 Starter Δ	Mature Synergy Δ	Divergence	Diagnosis
Demon Form	Power	28.7%	`+0.17 flr`	`+2.19 flr`	+2.01	TRAP PICK (Act 1)
Limit Break	Skill	31.5%	`+0.37 flr`	`+1.52 flr`	+1.15	TRAP PICK (No Strength)
Searing Blow	Attack	17.5%	`+0.15 flr`	`+0.20 flr`	+0.05	POOR IN ALL DECKS
Body Slam	Attack	34.3%	`+0.63 flr`	`+3.77 flr`	+3.14	SYNERGY ENABLER
Perfected Strike	Attack	18.6%	`+0.80 flr`	`+4.70 flr`	+3.90	ACT 1 TEMPO
Armaments	Skill	22.7%	`+1.18 flr`	`+3.29 flr`	+2.11	UNIVERSALLY STABLE
Feed	Attack	32.5%	`+0.73 flr`	`+2.83 flr`	+2.10	SNOWBALL SCALING

Interactive Card Drafting

To evaluate card reward screens during live runs, we built an interactive pick evaluator (scripts/pick_evaluator.py). Below are two real decision points:

Scenario 1 • Act 1 Floor 5

Starter Deck looking for Elite survival

Current Deck: 5x Strike, 4x Defend, Bash, Carnage + Burning Blood (Base: 5.1 / 56)

🌟 TOP PICK

Floor Δ +0.55 flr

Boss scaling, but sluggish for Gremlin Nob

DECENT

Floor Δ +0.35 flr

Zero-cost draw 3 cards

⚠️ TRAP PICK

Floor Δ -0.92 flr

Exhausts starter shields early

Takeaway: Drafting Corruption without skills or exhaust payoffs drops survival by nearly a full floor.

Scenario 2 • Act 2 Floor 24

Mature Exhaust Core with Dead Branch

Current Deck: Strikes, Defends, Shrug It Off, Corruption, Flame Barrier + Dead Branch (Base: 27.1 / 56)

🌟 TOP PICK

Floor Δ +11.56 flr

Infinite block engine with Dead Branch

TOP TIER

Floor Δ +10.36 flr

Infinite draw engine

DECENT

Floor Δ +6.78 flr

Solid, but inferior to exhaust payoffs

Takeaway: With Dead Branch in inventory, Feel No Pain catapults expected survival straight to Act 3 Bosses.

Discussion

Modeling deckbuilding requires moving beyond flat vector features and static tier lists. By modeling runs as hypergraphs and framing evaluation around counterfactual draft choices rather than leaky end-of-run win rates, neural networks can uncover deep strategic structure.

The useful result is not a marginal benchmark lead. It is a representation that changes its recommendation when the deck changes, exposes higher-order interactions, and separates cards that are broadly strong from cards that only become strong inside the right engine.

References

slay-the-spire-hypergraph: GitHub repository containing code, datasets, model weights, and interactive drafting evaluator.
Zhou et al., Learning with Hypergraphs: Clustering, Classification, and Embedding, NeurIPS.
Lee et al., Set Transformer: A Framework for Attention-based Permutation-Invariant Neural Networks, ICML.
Mega Crit Games: creators of Slay the Spire and provider of public run dump data batches.