Should a low-cardinality field like gender (only 2 values) be included in a MongoDB compound index?

Working with Data
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I’m designing indexes for a social media / dating app running on MongoDB.

Most queries include a gender filter (e.g., "gender": "male" or "gender": "female"), but gender only has two possible values.

From what I understand:

  • Low-cardinality fields (few distinct values) don’t provide much selectivity.
  • Compound indexes work best when the leading fields reduce the search space significantly.
db.users.find({
  gender: "female",
  city: { $in: ["Chicago", "LA", "NY"] },
  intention: "travel",
  age: { $gte: 25, $lte: 35 }
})

Candidate index examples:

db.users.createIndex({ gender: 1, city: 1, intention: 1, age: 1 })

// Option B
db.users.createIndex({ city: 1, intention: 1, age: 1, gender: 1 })

My questions are:

  1. Is it worth including gender in a compound index at all, given it only cuts the search space in half?
  2. If so, should gender be first in the index, or last (after more selective fields like city or age)?
  3. Are there cases where MongoDB can still efficiently use the index if gender is always in the query but not indexed?

I’d appreciate an explanation of best practices for low-cardinality fields in compound indexes, especially in the context of queries that always include the field.