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A group of contestants are living in a poor condition because they haven't built a shelter on the remote island they haven't been sent to while the other group is doing just fine. A member of the struggling group says "They [the other group] are better off than us".

I do feel the preposition off is needed but at the same time, the version without it is not that bad. What meaning does "off" add to the sentence?

Thanks in advance!
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There is a HUGE difference between saying "Mary is better than Sue" and "Mary is better off then Sue."

Do you know the phrasal verb "to be better off"? It meas to have an improved condition.

The original says that the other group has better living conditions than they do, not that they are simply better.

(Did you mean to say "on the island they haven't been sent to"?)
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Thanks, GG. Sorry for the typo. It should be "have been sent to". I think I should have said "on the island they were sent to"
Were is fine, and "have been sent to" is okay if it was pretty recent. I just couldn't figure out why they were expected to have a shelter on a place they have not been!