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I want to book a flight from DTW to SFO and a return flight from SFO to DTW. They're the same price if I book them separately or if I book them together. I'm just wondering whether I should book them separately or together?

So there's 2 situations that I think I have to consider. If no emergency changes of plans occur (and I don't really think any will), then none of this matters. However, let's suppose one of the following two situations occur...

Situation 1: Something comes up and I have to change/cancel one of the flights but not the other one. Will it cost me more to change if I had booked it together as opposed to separately? I think, either way, the change fee will be the same, but what about the difference in fares for the case where I booked both flights together? For example, if I want to change my SFO to DTW flight and I want to keep my DTW to SFO flight the same, will I have to pay the difference in fares for both flights? (By the time I realize I have to make a change, the price of both flights will likely have increased significantly.) Or will I only have to pay the fee + the fare difference for the one flight I want to change?

Situation 2: Something comes up and I have to change both flights at the same time. In this case, I think it could possibly be better to book them together and hope that I only have to pay the change fee once? Is this true?

Any thoughts would be appreciated. Situation 2 is probably an order of magnitude less likely than situation 1, so situation 1 is really the one I need to think about. Thanks!

There is a complication that could potentially change your calculation. The fare rules may include a condition that may be favourable - typically that after departure changes are repriced using historical fares, or that may be unfavourable - changes not permitted after departure.

In the former case, it wouldn't make any difference for the outbound flight, but if you wished to change the inbound flight, you could wait until after your outbound to change it and you may only need to pay the change fee (depending on availability). In the latter case, after taking the outbound flight, you may need to cancel the remainder of the flight and buy a new ticket.

Looking at a sample DL DTW-SFO-DWT Y fare a few weeks out, and also a UA fare, the change fee on either airline is $200 for a $400-500 round trip fare, so providing you're only likely to make one change of either inbound/outbound or both at once, then booking a r/t fare sounds like a better idea. Additionally, if it is were a DL fare the fare rules on matrix say:

AFTER DEPARTURE OF JOURNEY - APPLIES WITHIN TKT VALIDITY

CHANGES NOT PERMITTED/REFUND TKT-ANY REMAINING AMT WILL

APPLY TO NEW TKT.

The UA fare rules however:

REPRICE USING CURRENLTY TICKETED / HISTORICAL
FARES.

Also on matrix you can see what the typical prices are for your outbound and inbound journey at different times, i.e. < 7 days or > 14 days, which may shape your calculation.

Getting back to your questions:

Situation 1: Something comes up and I have to change/cancel one of the
flights but not the other one. Will it cost me more to change if I had
booked it together as opposed to separately? I think, either way, the
change fee will be the same, but what about the difference in fares
for the case where I booked both flights together?

It could cost more to change if you buy a r/t fare because you'd have to pay for the increase in fare, if any, for the flight you're not changing.

Situation 2: Something comes up and I have to change both flights at
the same time. In this case, I think it could possibly be better to
book them together and hope that I only have to pay the change fee
once? Is this true?

Yes

If you change even one leg, you will have to pay the change fee + the difference in fare for the entire itinerary (of course, if you booked the flight there and the flight back separately as two 1-way flights, then your entire "itinerary" is just one flight).

So, in your "Situation 2", booking the flights together is clearly better (only pay one change fee).

In "Situation 1", it all comes down to which prices you think will be more stable, 1-way or roundtrip. Anecdotally / from my experience, it seems that roundtrip prices are more stable, especially if the 1-ways are cheap only because of a special and temporary discount/sale (so you'd be better off booking both flights together), but I have no data to back that up. Perhaps you can try an airfare prediction site and see how both 1-way and roundtrip fares are predicted to change, and decide based on that.