Short answer: there is no single official city pass that covers Moscow's museums the way the Paris Museum Pass covers Paris. Several products carry names that sound like one, and travellers arrive expecting a card that does not exist. Here is what is actually available, and how to budget without one.
What Moscow does have
A transport card. The Troika card is real, official and worth getting on arrival. It covers the metro, buses, trams, trolleybuses and the Moscow Central Circle, costs a 150-rouble deposit with 50 refundable, and brings a single ride to roughly 38 roubles against about 55 for a paper ticket. This is the one card that genuinely saves money for every visitor.
Combined tickets at individual sites. The Kremlin sells combined tickets covering the Armoury Chamber and the cathedral square as separate or bundled admissions. Several large museums do the same across their own buildings — the Tretyakov Gallery and the Pushkin Museum both operate on more than one site. These are per-institution, not city-wide.
Free admission days. Many state museums run free or reduced days on a published schedule, usually tied to particular dates in the month. Schedules change, so check the museum's own site rather than a list in a guide.
What this means for your budget
Without a pass, a museum day in Moscow is simply the sum of its tickets. The practical planning question is not "which pass" but "which three or four places matter most", because most visitors overestimate how many museums fit into a day. Two substantial museums with a walk between them is a full day; three is a rush.
Book the popular sites in advance where the option exists. The Kremlin Armoury runs on timed entry with limited slots, and turning up hoping for a ticket is the most common way to lose an afternoon.
Why the confusion exists
Tourist city cards are common in European capitals, and travellers reasonably assume Moscow has one. Various commercial products have appeared over the years under similar names, with varying and changing coverage. If you are offered one, the questions worth asking are which specific venues it admits you to, whether admission is free or discounted, whether transport is included, and how long it is valid — the answers differ sharply between products and change from season to season.
The practical approach
Get a Troika card for transport. Pick your museums deliberately and book the timed-entry ones ahead. Check each site's own page for current prices and free days. That is the whole method, and it costs less than most bundled products would.
