Yes... another stun attempt.
This is why we often see a 5th level plus monk move into position, do the first attack of their multiattack, then the FOB attacks, and then after that do the last attack - because they can move before that last attack.
Sure, but if you are using FOB on 3 targets there have to be 3 targets in reach (or you need to use a ranged Monk weapon against the first at disadvantage and then FOB the 2 others in reach). This is situational. That does not mean it does not happen but it does not happen often enough that you can say you can do it at will.
Then when that is the case you need to hit all 4 of them.
FOB actually can reduce the number of enemies you can attack. If you don't use FOB you can attack, extra attack, maertial arts attack as long as you have enough movement to move within range of all of them. With FOB you can't move between one of your attack and the bonus action that gives you two more.
Regardless, you also have to remember that stun attempts fail a lot. Con saves tend to be strong on monsters, and your DC tends to be a bit behind spellcasters as wisdom is not your primary stat.
But they have to fail every time if you want to use another ki on the same enemy and you need to hit them.
Lets say for example you need a 6 to hit this enemy, and lets say they need a 6 to make their save. Even in that extreme case the chance you hit them 4 times in a row and they make their save the first 3 times is 13%. That is an enemy extremely easy to hit and with an extremely good con save. That is what would need to happen to spam 5 ki in the manner stated above. Make their save more difficult or their AC higher and the chance of doing that is much lower.
Using the Green Dragon example above against an 11th level Monk with a 20Dex and 20Wis (10 to hit, 7 needed to save) - the chance of hitting him 4 times is 9% assuming he starts with all 3 of his legendaries and can automatically succeed on the first three saves. The chance of doing it if he starts with no legendaries and makes the first three saves is 3%. The chance of doing that 3 rounds in a row is about 3 in 100,000.
It is rare that I don't have good uses for stun on all 4 attacks on the first round of a challenging combat.
The math shows that is not true. You need to hit to use stuning strike.
CR11 average AC is 17. With a +9 to hit at 11th level your chance of landing 4 successful strikes in 1 round is 18%. That is just the chance of hitting 4 times and does not account for the other stars you need to align in terms of position to make this work.
Mathematically, less than one in 5 combats you should be able to land 4 hits on round 1. If your caster put the enemie(s) in Faerie Fire and you are rolling with advantage you still would only hit 4 times in 60% of rounds, so nearly half the time you would not be able to do that EVEN WITH ADVANTAGE and 40% is not rare.
Heck, I have seen a gnarly gloomstalker 4/battlemaster 4/open hand 12 build in a one shot that was designed to eradicate legendary resistance. It moved in and attempted what would have been 8 stunning attacks to the big bad in the first round just to draw off the legendary resistances. It could force up to 15 saving throws in that first round...
Assuming you were in darkness agaisnt an enemy without blindsight and a +15 to hit (includes precision) against 20AC (average for CR20)
Your chance of successfully hitting 8 times with advantage, using precision is 72%. Using precision means you do not have battlemaster dice for whatever saving throws you are trying to draw legendaries. Without precision that number is only about 25%.
As for the argument it is not a good use of resources to stun early and often: This is absolutely incorrect.
I never said it was not a good use. What I said you can't very often use 5 ki for FOB and stunning strike and you can almost never use it for 3 turns in a row.
I stand by that because the math shows that is true. You have to hit to use stunning strike and you need the opportunity to even use FOB and attempt to hit.
Stunning early is the absolute best time to stun as it can allow you to prevent the foe from setting up a defense or from ever inflicting offense.
I agree with that.
When fighting a legendary monster, it can allow you to deplete those leganadry resistances and give you access to taking it down with a saving throw spell or ability.
It can, if they have a low AC and low con save or if you have a long time and get lucky dice. But it is not very common.
The Green Dragon above shows some actual numbers for this for an example enemy - On average an 11th level Monk 20 Dex, 20 Wisdom, spamming FOB and stunning strike against an adult Green Dragon: to drain all three legendaries on average will require 5 rounds, 18 attacks, hitting 10 times with stunning strike, resulting in 3 failed saves and using 14 ki (4 on FOB. 10 on stunning strike). With only 11 ki available the Monk will usually not be successful at using all the legendaries if he spams FOB and SS. The chance of successfully draining all 3 legendaries before he runs out of ki is only 27%. On average the Monk will run out of ki in round 4. Your chance of draining all the legendaries in the first round is 1.6%.
Note in this example you are using 3 ki a turn on average (1 for FOB and two for stunning strike the two times you hit the Dragon); 2 points below the 5ki that you claim to routinely use on FOB and SS in round 1.
He actually has a better chance of draining all legendaries if he does not use FOB. If he makes 3 attacks a turn instead of 4 he will on average drain the Dragon's last legendary at the end of the 6th round after using his 10th ki and on average having 1 ki left. His chance of succeeding in this case is 53% (assuming he and the dragon are still fighting after 6 rounds).
Note, those numbers do not include actually stunning the dragon. Stunning the dragon will on average require 3 more hits (using stunning strike on each) and 5 more attacks.
Outside of bad luck on the saving throw dice, I can't recall a single time I regretted stunning early and often.
I agree, but unless you have win the the lottery type luck I gaurantee you do not routinely use 5 ki on FOB and stunning strike in a round unless you are fighting extremely weak enemies.