Hilbert's Hotel Privilege Cards

Privilege Cards are the third kind of pick in a Hilbert's Hotel run. Most rooms offer you one or two Catalysts when you clear them. The rare rooms that offer a third pick offer a Privilege Card, and every one of them buffs the whole team, so none is wasted on a character you rarely tag in.

A three-card offer from the Dichotomy beta: Matrix Multiplication I, Series Expansion I and Linear Regression I.

The names follow the mode's mathematics theme, and the Roman numeral is the tier, not a stack count. The tier also sets the card's colour: I is blue, II purple and III gold. In twelve of the 13 families each step up adds half again, so a gold card is about 2.25 times its blue one. Linear Regression climbs faster, from +15% to +50%.

Which card to draft

The rule is to pick the card that touches the most of your damage. The 13 families sort into four groups by what their stat reaches, and the cards below are grouped the same way.

Every hit. ATK, DMG Bonus, Final DMG, DEF Ignore and All-Attribute DMG Bonus raise every attack your team makes. These are the default pick. Zero Convergence III's +22% looks small next to the 45s around it, but Final DMG is the same stat as Golden Reputation, one of the two best combat nodes on the Membership Privileges tree.

Critical hits. Singularity Near III is the biggest number in the pool at +90% CRIT DMG, and it does nothing on a hit that does not crit. Take it when your team already crits often, or alongside Random Variable, which adds up to +45% CRIT Rate. The two together are the strongest pair here.

One attack type. Skill, Ultimate and Basic Attack DMG Bonus run to +90% at gold, more than double the every-hit cards. Series Expansion III's +90% Skill DMG beats Infinite Series III's +40% DMG Bonus only if most of your damage comes from skills. Know where your team's damage comes from before you take one.

Survival. Max HP, DEF and Healing Received keep a team alive and add no damage. Linear Regression needs a healer on the team to do anything at all. Take these when a run is losing fights, not when it is clearing them.

Refreshes, Mementos and the gold cards on the tree

Three things outside the offer screen change which cards you see:

• Refreshes. On the Membership Privileges tree, VIP Guestlist unlocks refreshing a Privilege Card offer and Bonus Ledger adds one more refresh. Both sit at the end of the survival lane.
• Ledger Expansion I and Ledger Expansion II. These two Tier 7 nodes each list three gold cards they add to the pool you draft from, 6 in all. Those cards are marked in the list above.
• Secret Shaker. This Memento grants one or two random Privilege Cards.

Frequently asked questions

What are Privilege Cards in Silver Palace?

Privilege Cards are the team-wide buffs you draft during a Hilbert's Hotel run. There are 39: 13 families, each in three tiers (I blue, II purple, III gold). Every one reads "All characters on the team gain" a stat, so unlike Catalysts none of them is bound to a character or an attribute. They last until the run ends.

How do you get Privilege Cards in Hilbert's Hotel?

Most rooms offer one or two Catalysts when you clear them. The rare rooms that offer a third pick offer a Privilege Card instead. The Secret Shaker Memento grants one or two random ones. On the Membership Privileges tree, VIP Guestlist unlocks refreshing the card offer and Bonus Ledger adds one more refresh.

What is the best Privilege Card?

Singularity Near III has the biggest number, +90% CRIT DMG to the whole team, but it pays only on hits that crit. For a team without much CRIT Rate, a card that raises every hit is the safer pick: Zero Convergence III for +22% Final DMG or Infinite Series III for +40% DMG Bonus.

Which Privilege Cards does Ledger Expansion unlock?

Ledger Expansion I adds Infinite Series III, Zero Convergence III, Differential Strategy III. Ledger Expansion II adds Random Variable III, Singularity Near III, Exponential Growth III. All 6 are gold, tier III cards.