Silver Palace — Privilege Cards Guide
Complete reference matrix for all 39 Privilege Cards in Hilbert's Hotel. Understand the 1.5x tier scaling multiplier, draft top-priority Universal Multipliers, and unlock the 6 restricted Gold Tier III cards.
- Team-Wide Permanent Buffs: Unlike Hotel Catalysts, every Privilege Card drafted applies to all 4 squad members at once for the remainder of the hotel run.
- 39 Cards Across 13 Math Families: Each family features Tier I (Blue), Tier II (Purple), and Tier III (Gold) variants scaling by a consistent 1.5x multiplier per tier.
- Six Cards Locked Behind Ledger Expansions: The best Tier III Gold cards (including Zero Convergence III and Differential Strategy III) require Ledger Expansion I & II in Membership Privileges.
- Drafting Priority Hierarchy: Always prioritize Universal Multipliers (Zero Convergence for Final DMG, Differential Strategy for DEF Ignore) over specific attack-type buffs.
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What are Privilege Cards?
Privilege Cards represent team-wide passive stat bonuses offered as a rare third draft card upon clearing select combat chambers in Hilbert's Hotel. They're themed after advanced mathematics (calculus, linear algebra, and topology).
Unlike single-character Catalysts, every Privilege Card in your ledger applies to all four operatives on your team at once. Stacking multiple offensive cards turns off-field Tactical Assaults into devastating burst strikes.
Card Structure & The 1.5x Scaling Multiplier
The 39 cards follow a structured 3-tier evolutionary hierarchy:
- Tier I (Blue Cards): Common baseline drafts available from floor 1.
- Tier II (Purple Cards): Enhanced drafts offering 1.5x the base value.
- Tier III (Gold Cards): Elite pinnacle drafts offering 2.25x the Tier I value (1.5x the Tier II value).
- Linear Regression Exception: Linear Regression (Healing Received) scales non-linearly from +15% (Tier I) → +30% (Tier II) → +50% (Tier III).
You can also get 1–2 bonus Privilege Cards mid-run from the Secret Shaker Memento, and refresh card options via the VIP Guestlist and Bonus Ledger nodes in Membership Privileges.
All 39 Privilege Cards (Complete Reference Matrix)
Below is the complete 13-family matrix of all 39 Privilege Cards:
| Card Family | Team Stat Buffed | Tier I (Blue) | Tier II (Purple) | Tier III (Gold) | Pool Unlock Requirement |
|---|---|---|---|---|---|
| Matrix Multiplication | ATK | +20% | +30% | +45% | Base Pool (Always Active) |
| Infinite Series | DMG Bonus | +18% | +27% | +40% | Tier III requires Ledger Expansion I |
| Random Variable | CRIT Rate | +20% | +30% | +45% | Tier III requires Ledger Expansion II |
| Singularity Near | CRIT DMG | +40% | +60% | +90% | Tier III requires Ledger Expansion II |
| Zero Convergence | Final DMG | +10% | +15% | +22% | Tier III requires Ledger Expansion I |
| Differential Strategy | DEF Ignore | +20% | +30% | +45% | Tier III requires Ledger Expansion I |
| Series Expansion | Skill DMG Bonus | +40% | +60% | +90% | Base Pool (Always Active) |
| Imaginary Value | Ultimate DMG Bonus | +40% | +60% | +90% | Base Pool (Always Active) |
| Hypercomplex Series | Basic Attack DMG Bonus | +40% | +60% | +90% | Base Pool (Always Active) |
| Exponential Growth | All-Attribute DMG Bonus | +20% | +30% | +45% | Tier III requires Ledger Expansion II |
| Line Integral | Max HP | +20% | +30% | +45% | Base Pool (Always Active) |
| Topological Invariant | DEF | +20% | +30% | +45% | Base Pool (Always Active) |
| Linear Regression | Healing Received Bonus | +15% | +30% | +50% | Base Pool (Always Active) |
Best Privilege Cards to Draft First
Follow this 3-tier drafting hierarchy when presented with Privilege Card choices:
- 1. Top Priority (Universal Multipliers): Always draft Zero Convergence (Final DMG) and Differential Strategy (DEF Ignore) first. Because enemy DEF escalates dramatically on Difficulty V and VI, DEF Ignore acts as the strongest damage multiplier in the game.
- 2. Second Priority (CRIT Scaling): Draft Singularity Near (+90% CRIT DMG at Tier III) and Random Variable (+45% CRIT Rate at Tier III) to guarantee devastating critical hits across your entire squad.
- 3. Third Priority (Attack-Type Alignment): Choose Series Expansion (Skill DMG), Imaginary Value (Ultimate DMG), or Hypercomplex Series (Basic DMG) to align with your main carry's primary damage engine.
Frequently Asked Questions
Do multiple tiers of the same Privilege Card family stack? +
Yes. Drafting both Tier I and Tier II of the same card family combines their stat percentages additively for the entire team.
How do I unlock Privilege Card rerolls? +
Unlock VIP Guestlist (Tier 5 Survival Lane) in Membership Privileges to refresh card offerings, and Bonus Ledger for an extra reroll charge.
Why are Zero Convergence and Differential Strategy considered top priority? +
Final DMG and DEF Ignore scale multiplicatively against high-level enemy armor, significantly outperforming additive ATK buffs on higher difficulties.
Does Exponential Growth buff all six Reactor Attributes at once? +
Yes. Exponential Growth grants an All-Attribute DMG Bonus (+45% at Tier III) that applies to Ignis, Glacies, Fulmen, Gravitas, Radiatio, and Alba all at once.
