Here is every one of them, in plain English, with what it is worth and when it is not worth it. Stopover runs the lot on every trip you plan.
Same cities, different order, slightly different days. Usually the biggest saving of the lot.
Visiting the same cities in a different sequence, staying a different number of nights in each, changes what you pay in airfare, often by hundreds of dollars, for exactly the same trip.
Moving one flight by a couple of days, letting one city get longer while the next gets shorter, can drop that leg's fare without changing the trip you are taking.
Cities you were never going to pay for: hours you already spend in a connection, and places that are cheap only because of where you already are.
A one-stop ticket whose connection is long enough to go into town, for at most $60 or 15% more than the cheapest way to fly that leg, whichever is larger. One ticket, one bag policy, one airline responsible for you.
Somewhere that is absurdly cheap from the last city on your route, where three more days plus a flight home from there costs little or nothing more than the return you were already buying.
Identical seats on identical planes, bought a different way: split in two, started somewhere else, or quoted in another country's currency.
Instead of one ticket from A to B, two separate tickets: A to a hub, then the hub to B a day later. Often cheaper, sometimes not, and worth it mainly for the time in the hub, which is only a day there if the gap falls in daylight. Nobody is responsible for the connection but you.
A cheap domestic hop to a gateway city, then a separate long-haul ticket from there, because the transatlantic fare out of New York or Lisbon can sit far below the one out of your home airport.
Three ways the same flights get re-priced by asking the airline a different question: buy both ends as one ticket, buy a round trip you only half use, or stop asking for every seat at once.
The same seat on the same plane can carry a different price depending on which country's version of the site you buy it from, and in which currency.
On short hops the train often wins once you count getting to the airport. And a night spent moving is a hotel night you never book.
On the pairs where the ground beats the plane (city centre to city centre, no airport, no bag drop), the planner treats a train, bus or ferry as just another way to fly the leg.
A red-eye flight, a night train or an overnight ferry is a hotel night you never book. The planner prices that night and lets the leg spend it.
When a trip has several train legs, a Eurail or Interrail Global Pass can beat buying the tickets one at a time, or not, and the plan tells you which.
A $19 fare into an airport ninety minutes from town, with a $55 bag, is not a $19 fare. These are the costs we add back before calling anything cheap.
The cheapest fare on a low-cost carrier, and the cheapest “light” or “basic” fare on a legacy one, does not include a checked bag. Across six legs that is another ticket's worth of money.
A cheap fare into an airport ninety minutes outside the city is not a cheap fare. The planner adds the transfer at both ends of every flight before it decides which flight is cheapest.
If you are under about 26, a dozen airlines sell you a different, cheaper fare, and no comparison site will show it to you unless you ask for it by age.
One trick that works and that every major airline forbids. We show it, we say exactly what you are risking, and we never count it in your total.
Most trips will not hit all fifteen. When one of these does not beat the obvious route, your plan says so on that section rather than inventing a win to fill the space.
Give it your cities