Check multi-day transit passes.
A multi-day pass spreads a fixed price over a fixed window, so the useful break-even is expressed per day rather than in total trips: pass price divided by validity days and single fare. A 22 dollar three-day pass against a 2.90 fare breaks even at 2.5 trips a day, which almost any visitor exceeds. Two details change the answer. Passes are usually validity-day based rather than 24-hour based, so a pass first used on Friday evening may expire Sunday night rather than Monday evening — buying it on the morning of your first full day extracts more value. And check whether airport transfers and express services are included, since exclusions are common and can be a large share of your fares.
Multi Day Transit Pass
Pay-as-you-go = days x trips per day x single fare; saving = pay-as-you-go - pass price; break-even trips per day = pass price / (days x single fare)
Usually two to three. Most city passes are priced at roughly two and a half single fares per day of validity, which any sightseeing itinerary comfortably exceeds.
It varies, and it is worth checking. Activation-on-first-use passes are more flexible; purchase-dated passes lose a day if you buy them the evening before you start.