You’re ignorant if you think Camp Halfblood stands even a TINY chance of beating the Romans in a war.
Like come on. This isnt about favorites, this is about the cold, hard fact that Camp Jupiter has a camp full of military trained demigods/legacies and an entire CITY of ADULT demigods/legacies to back them up.
Camp Half-Blood doesnt even make the campers play Capture the Flag if they don’t want to, I mean really now.
Very possibly, it all depends on the fighting style they were taught at their respective camps. We know at Camp Jupiter they are taught the same as the Roman armies of the past, however they don’t go into to much detail of the Camp Half-Blood training. While they are very relaxed and lenient on training they could be taught the same style as the Greeks.
The Greeks actually had a very solid fighting style, consisting of a front line of soldiers holding their shields covering half their own body and half of the soldier next to them. Behind this front line is the second line, holding spears as the offensive. EX:
Also, we’ve seen that Camp Jupiter isn’t prepared for the Greek fighting style, as shown in Son of Neptune. Percy wrecked their ranks with his constant slashing and rolling. With that mind however, Percy is the greatest swordsman at Camp Half-Blood to our knowledge.
Without any knowledge of the training regime of Camp Half Blood, I don’t think we can actually make a clear prediction on who would win. Both have the upper hand in different situations. We also have to add the fact Leo sent the two thieving trolls from Italy to go harass and steal from the Roman’s on their way to Camp Half-Blood, so they have less resources than at their highest potential. You make a good point with the adult legacies, however I don’t believe they were required to join the army as they (the army) advanced to Camp Half-Blood. After the adult legacies serve in the army they are released from service, but I’m not cognizant of the possibility of volunteering.
The war could go either way, with the Romans handicapped by lack of supplies and possibly the Greeks handicapped with lack of training and experience.