Silver Palace — Hilbert's Hotel Guide

Hilbert's Hotel (officially designated as Gilbert's Infinize: Hilbert's Hotel) works as Silver Palace's premier weekly roguelike endgame challenge. In this mode, you bring a tailored 4-character squad - consisting of 1 on-field primary carry and 3 off-field teammates - to navigate a labyrinth of supernatural doors within an ever-shifting Victorian manor.

Every combat encounter or event room you conquer grants temporary run buffs designed to craft game-breaking combat synergies. Mid-run buffs only exist within the active run and reset once you cash out through the Cognito Gate or defeat the final floor boss.

Squad Layout

1 Lead + 3 Teammates

Your on-field lead spends 80% of combat on screen; your 3 teammates trigger off-field Tactical Assaults and share team-wide Privilege Cards.

Run Persistence

Save & Resume Anytime

Need a break? Pause at any door threshold. Your exact draft state, HP totals, and currency inventory are safely preserved.

Hilbert's Hotel is split into distinct themed rooms featuring dedicated enemy rosters, distinct environmental modifiers, and tiered reward payouts:

• Room 1: A Most Irrational Number: Features clockwork automatons, rogue Silverium constructs, and dense mob packs favored by AoE burst specialists.
• Room 2: Algebraic Topology: Introduces high-mobility human syndicate bosses, heavy shields, and aggressive projectile barrages.
• Room 3: [Locked]: Designated classified sector slated for release following the Dichotomy Beta cycle.

Each room features six progressive difficulty settings (Difficulty I through Difficulty VI). Clearing any tier permanently unlocks the next tier up, awards high-value first-clear bounties, and permanently elevates the Merit and Membership Stamp drop rate per run.

During a 12-stage expedition, you'll encounter diverse door icons leading to specialized mid-run mechanics. The four interlocking buff systems form your build loop:

• 1. Combat Doors & Hotel Catalysts: Clearing a combat room rewards you with Hilbert's Hotel Vouchers (temporary run currency) and lets you draft from 166 alchemy-themed Hotel Catalysts that upgrade into Refined and Synthesis tiers. [→ See Hotel Catalysts Guide]
• 2. Bonus Drafts & Privilege Cards: Select combat rooms offer a third draft choice called a Privilege Card - a math-themed Blue, Purple, or Gold card that gives a flat stat boost to your entire team at once. [→ See Privilege Cards Guide]
• 3. Random Event Doors & Mementos: Non-combat doors trigger a short dialogue choice that rewards one of 26 Mementos. Some grant massive buffs, while others are hidden traps or trade-offs. [→ See Mementos Guide]
• 4. Supplies Shop Doors & Vitality Chests: Spend your Hilbert's Hotel Vouchers mid-run to buy extra Catalysts and upgrades. Alternatively, open Check-In Incentives (Vitality Chests) to spend 40 or 80 Vitality for Fate Clippings (from Diff II+), Reputation, Ounce, and a random Lv. 20–60 Epiphany.

Note: All Hotel Catalysts, Privilege Cards, Mementos, and Vouchers reset when your run ends.

Your performance awards Merit towards a 6-step weekly reward ladder that resets every Monday at 04:00 server time. Every single 500-Merit milestone dispenses premium gacha currency and essential character progression materials:

Unlike temporary run buffs, the following systems provide permanent, enduring power to your Silver Palace account:

• Membership Privileges (Permanent Tree): Runs reward Membership Stamps used to unlock 22 permanent account nodes across Economy, Combat, and Survival lanes. [→ View 22-Node Skill Tree Guide]
• Points Exchange Milestone Ladder: A seasonal cumulative milestone track awarding extra Reactor Crystals, high-grade Insight books, and a 4-Star Mystery Motive at max rank.
• Currencies & Exchange Store: High-tier runs drop Cognito Sand and Noble Crystal Ornaments, spent at the Hotel Concierge for character enhancement materials.
• Daily Quest Synergy: A single hotel run completely satisfies your daily exploration quota (+80 Steps).