Mindfire
Istar
Reasonably equipped? Not for me. Average Joe cutting down a tree with a chainsaw is nothing…..a toothpick, however, that would be something!!
That’s an extreme, but my point is this – if it is reasonable for the protagonist to overcome the situation, then no heroic feat has occurred. Even in realist fantasy you will have situations where you could use the term ‘Against All Odds’. This is because either – the situation is unreasonable or the characters are ill-equipped, or both.
Nowadays the question is less ‘Will they survive?’ and more ‘HOW will they survive this time?’
WyrdMystic has a point. In general, the more implausible the feat, the more glorious the victory. The trick is not crossing that invisible line where SoD is strained to breaking point. WyrdMystic is also right that you can't please everybody. Write for yourself first, worry about the reader during revision. (Maybe.)