My monk win some one on one duals. My monk was awesome but.....
1. It was early in D&D
2. Rolled good stats eg started with an 18 and 16 iirc.
3. We were a bit more generous with magic items. Had a decent magic spear or sword iirc.
4. Picked the best archetype (accidentally).
5. Knew how to pace the ki and was proactive in getting short rests.
Using point buy and feats, the Kensai Monk is a 50/50 with the BM/SS/CE Fighter from 5th level onwards, at a starting range of 40'.
Human(V) Monk, Feats Martial Adept [Ambush, Menacing attack], Alert, D: 16, W 16, Con 14, W 10 S/Ch 8
Winning initiative is key (as it often is). He has +8 to initiative (and an extra d6 from Ambush if needed) vs the SS/CE BM's +3 (and maybe +1d8 from Ambush if selected).
He should go first, move 40', attack with a sword, fist and flurry for 2 more fists all at +6 vs an AC of 16 for the BM.
Two (of the 4) should hit, he spams Stunning strike on each, and the Fighter should (on average) fail 1 of the 2 x DC 14 Con saves (even with Con Save of +6), taking 1d10 (sword) +1d6 (martial arts) + 6 damage (15 damage) and using 3 Ki points.
Next turn the Monk unloads on the Fighter (at advantage) again flurrying and should hit 3/4 times now thanks to advantage, dealing 1d10+2d6+1d6 from Menacing +9 (another 25 damage) and triggering a Wisdom save (DC14 so the Fighter usually fails).
The Monk now has 1 Ki point left and the Fighter has taken 40 damage, and is frightened of the Monk (whos AC is currently 18).
Fighter has 9 HP left (presuming Con 16)
With disadvantage vs AC 18, he Action surges, choosing not to use Sharpshooter (+3 vs AC 18 at disadvantage is unlikely). At +8 vs AC 18 he hits 2/4. He uses precise shot on both attacks that miss, turning them both into hits, and blows his other 2 Superiority dice on Pushing attack on the two that hit without Precise shot.
We'll even let one of the hits be with Sharpshooter 'on'.
He deals a whopping 4d6+2d8+22 or 45 points of damage of which the Kensai absorbs 13 of this damage with deflect arrows.
As a bonus action he Heals 10 hit points with Second wind (now on 19 HP). He has now used all his Sup dice, Action surge, and Second Wind.
The Monk has 7 HP, and 1 Ki point left, and its his turn.
He attacks 4 times (flurry) vs AC 16 at +6 - two hit, for 1d10+1d6+6 (15 damage).
Fighter (now with 4 HP) attacks 3 times vs AC 18 at +8. He gets 1 1/2 hits out of 3, of which the Monk can deflect 1.
If the Fighter hits with the third attack, and rolls 4 or better on his d6 he wins. Otherwise the Kensai kills him next turn.
Pretty even, and we're talking about a fight with 'THE' DPR king of the game in the SS/CE BM.