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Message: <blockquote data-quote="Agback" data-source="post: 2898620" data-attributes="member: 5328">Okay, here we go. Suppose that combatant is facing n similar foes in mêlée. Obviously, his best strategy is to concentrate on one foe until that goes down, then switch to another, then to the next, and then to the next, until they are all down. His chance of hitting with any attack is not affected by the number of foes, and the damage he does with any hit is not affected either, so his average damage output is not affected by the number of foes. That means that the average number of rounds he takes to put any single foe down is not affected by the number of foes facing him at the time he is concentrating on that foe.(Note: in the following algebra, capaital letters denote values pertaining to the combatant of interest, and lower-case letters denote values pertain to his foes. AB is attack bonus (including STR bonus). AC is armour class (including DEX bonus). HP is hit points, SB is strength bonus to damage, R is the average value of the character's damage die roll.Ignoring for the moment cases in which the combatant either always hits or never hits, his chance of hitting is (21+AB-ac)/20, and it doesn't depend on number of foes. The damage he does on a successful hit is R+SB, where R is the average value of hit damage die roll and SB is his STR bonus. So the average damage output is (R+SB)(21+AB-ac)/20. If his opponents have hp hit points he will put the first down after 20*hp/{(R+SB)(21+AB-ac)}, and then the next after as long again, and so on until all n of them are down, which will take n*20*hp/{(R+SB)(21+AB-ac)}. Define T = 20*hp/{(R+SB)(21+AB-ac)}. The combatant will face n opponents for T turns, then n-1 for another T turns, then n-2 for another T turns, and so on for nT turns. He will face n attackers for T turns, then (n-1) for  T turns, and so on.During this process, each foe still standing will have a chance of hitting of (21+ab-AC)/20, and will produce r+sb hp per successful hit. So each foe the combatant faces will produce on average (r+sb)(21+ab-AC)/20.So for T turns the combatant will face n foes and take n*(r+sb)(21+ab-AC)/20 hit points per turn. a total of T*n*(r+sb)(21+ab-AC)/20.Then for another T turns the combatant will face n-1 foes and take (n-1)*(r+sb)(21+ab-AC)/20 hit points per turn. a total of T*(n-1)*(r+sb)(21+ab-AC)/20.And so on for nT turns in total, taking a total of T*{n*(n+1)/2)*(r+sb)(21+ab-AC)/20. Substituting the value of T bck in to the equation we get[20*hp/{(R+SB)(21+AB-ac)}]*{n*(n+1)/2)*(r+sb)(21+ab-AC)/20={n*(n+1)/2} * (r+sb)(21+ab-AC)/{(R+SB)(21+AB-ac)}That is exactly n*(n+1)/2 times the amount of damage the combatant takes fighting one such foe until it drops. There is no interaction term between n and AC.The argument is not affected if the monk uses 'flurry of blows'. You get a more complicated expression for the monk's average damage output, but the number of foes does not enter into the expression for damage output. The number of hit points the monk suffers might be lower but it will still scale strictly with the nth triangular number. And in fact, the strong monk's advantage is increased when he uses flurry of blows, because his attacks are made at reduced AB, and the STR bonus to hit is proportinately more valuable when the chance to hit is low.Dextrous monk has the advantage when the foes have attacks with low attack bonus, ones where a -5% chance of hitting chews up a large proportion of their chance to hit. It tried to show that with the xorn, a monster I chose because it had a lot of innaccurate secondary attacks. The problem is that in D&D low-accuracy attacks are nearly always weak, so that avoiding them is not critical.</blockquote>

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