How about a button we can click when everyone else has quit the strike? To re-matchmake the strike.
Sometimes I play the whole strike alone and not get another player until the boss is nearly dead. Guess who is likely to get the better rewards? Yep, the person who just joined with few to no kills!
Or improve the matchmaking to actually find more people. It can always find 2 when I start the strike so I know there are others looking. Id even choose to join another on my same map if they are also waiting.
My 2¢
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I also want this so that if one of my Fire Team members gets bumped because of a network error, etc. , by the time they can re-join some else has already been added by matchmaking.