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Message: <blockquote data-quote="Ainamacar" data-source="post: 5866088" data-attributes="member: 70709">I haven't had a chance to read the original post thoroughly, but this strikes me as an odd premise.  If all else is equal, the actual probability of hitting on an individual attack (e.g. 20, 50, or 80) doesn't change the probability of winning the fight at all if it is the same for both fighters: it will be 50% in all cases.  In fact, if all else is equal, it is clear the only possible way to have equal chances of victory is for both to have the same chance to hit.  This math works (it is the trivial case for balance), but it isn't terribly interesting.As I see it, the basic factors between fighters in your scenario are hit points, AC, attack bonus, and damage. (Initiative too, but unless fights typically last only a round or two it has a diminished impact, so I'll set it aside.)  To define all possible pairs of fighters in this schema is an 8 dimensional space, but since to-hit chances are a function of (fighter A attack bonus - fighter B AC) and vice versa, we can shrink this down to a 6 dimensional space if we don't mind no knowing the actual attack bonuses and AC, only their difference.  Either way, it is in these spaces that we can calculate the probabilities of winning between any two fighters, and the regions near 50% could be used to define how all those variables are collectively allowed to vary by level to maintain the "fair fight."Perhaps the result of such an analysis suggests the range for which fights can be kept near 50% cannot deviate much from fighters being equal in essentially every respect, in which case that might be the right choice to maintain balance.  I suspect, however, that there lies a "ribbon" of fighters which manage the tradeoffs between the variables.  Why?  Because for perfectly identical fighters the probability of victory is always 50%, so there is a diagonal running through the high-dimensional space that is fixed to 50% (the trivial balance), and values near it will generally be near 50% as well.  Thus one can select a point on the diagonal  and declare the region near that point to define the acceptable range for fighters of a given level.  Analysis of these regions can then determine what acceptable tradeoffs, if any, may be made in all 4 qualities to maintain a rough balance.If such a ribbon exists, then fighters can develop more freely with their own style, and in fact we might observe some rock-paper-scissors effects, with different styles of fighters strong against some kinds of fighters, and weak against others.  To me that is far more interesting than finding the diagonal and sticking to it.</blockquote>

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