Hussar
Legend
You guys played 2e way differently than we did. No way a 1st-level fighter in 2e could kill a troll in one round. And a 1st-level party taking on a giant is suicide.
We never really used weapon speeds in 1e or 2e, but initiative was never a problem area. Roll the dice. Modify. Done. We rather liked rolling each round. Made combat more chaotic and well...combat-like.
Umm, yes, yes he could.
1st level fighter with specs in longsword and proficiency in short sword, using 2wf from the Complete Fighter (so no attack penalties). No strength bonus.
2e troll has 6d8+6 HP so, 33 on average.
The fighter on the second round attacks three times, doing a total (before strength bonus) of 14+14+8 or 36 points of damage.
Note, I said CAPABLE not that he'd do it every time. Add in an 18 percentile strength (which was pretty much standard for any 2e or 1e fighter I ever saw) and you're whacking that troll like a pinata. That's 45 damage in a single round to a troll with any percentile strength.
But, again, these conversations get so difficult to have because I can't argue against the game you were playing at your table with your set of house rules. I can only talk about what the game actually said.