Going to chime in here: 24 orcs absolutely does = 24 melee attacks per round, because
opportunity attacks are Reactions, and you only get 1 per round. Capricia has already mentioned this, but it honestly can't be emphasised enough.
It makes putting your back up against a tree exactly the same as standing in an open field and thereby reduces the exercise to a pure numbers game. Once the Fighter has made his single swipe at a passing creature, any number of them can do a conga right line past him in complete safety. I
hate it.
Anyway, let's do this. With 6 Ability Score Increases under his belt our Fighter can have stats of 20/20/18/13/11/9, so +6 Initiative (4 Dex/2 Remarkable Athlete) with 20 Str and 20 Con, making him statistically likely to win initiative against 18 of the Orcs. We'll have them start in move + attack range of each other, because if you game out a scenario where the two sides begin out of range it becomes a weird cold war of shufflestep spacing and readied actions. If there's a simple way I'm missing for the Fighter to gain advantage with a spaced start, though, I'm happy to look at this again in light of it.
Round 1:
- The 6 orcs who won initiative rush in and surround the Fighter, dealing 3.65 damage each and bringing him down to 167 HP.
- The Fighter uses Action Surge and makes 6 attacks, felling 3 of the orcs. 21 orcs remain.
- The 18 orcs who lost initiative conga line past. The Fighter wounds one of them with an OA. After their attacks he's on 101 HP.
Round 2:
- 3 orcs, 11 damage, 90 HP.
- The Fighter makes 3 attacks, killing 1 of the 3 orcs in contact with him and injuring another. 20 orcs remain.
- 18 orcs conga past, dealing 58 damage and leaving the Fighter on 24 HP. The Fighter holds his OA to finish off the orc he hit last time, killing it. 19 orcs remain.
Round 3:
- 2 orcs, 7 damage, 17 HP.
- The Fighter kills the 2 who just hit him.
- 17 orcs conga past, dealing 62 damage and taking the Fighter to -45. He injures one before he goes down.
The Fighter killed 7 orcs, and 17 remain.
Bonus Round 4:
- A Wizard who's been watching the whole time (invisibly) casts Fire Storm, incinerating all 17 of the remaining orcs at a single stroke, whether they make their saves (20% chance) or not. He could have done this at the beginning of the encounter, of course, but he wanted to give the Fighter a chance to strut his stuff.
- He then uses his Transmuter's Stone to cast Raise Dead on the Fighter without expending a spell slot.
- He then pats the Fighter on the head and says "Maybe next time."
A high level Fighter without any magic might have chosen to be that way because their player read
the Fighter Design Goals article and thought it sounded awesome:
And most importantly..
...
that's the Fighter class I want to play.