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Message: <blockquote data-quote="ggroy" data-source="post: 4922440" data-attributes="member: 83805">If you're designing your own homebrew rpg, another equation which is useful is related to how many attack rounds it takes to hit an opponent.With a probability p of hitting an opponent, the average number of attacks it takes to hit an opponent is 1/p with variance (1-p)/(p^2).For example, a 50% probability of hitting an opponent takes on average around 2 attacks to hit it.  A 25% probability of hitting an opponent takes on average around 4 rounds to hit it.  A 20% probability of hitting an opponent takes on average around 5 rounds to hit it.  More generally:[html]p    average number of attacks to hit0.50  20.45  2.220.40  2.50.35  2.860.30  3.330.25  40.20  50.15  6.670.10  100.05  20[/html]Changing the probability of hitting an opponent can drastically affect the average number of attacks it takes to hit the opponent.  For example, if the opponent suddenly gets buffed where it's AC is so high that there's only a 10% probability of a player hitting it, on average it will take 10 rounds to hit it.  Or even worse, the opponent is so buffed that there's only a 5% probability to hit it (ie. rolling a 20 on a raw d20 roll), on average it will take 20 rounds to hit it.I generally try to avoid situations where it requires the players to roll a natural 19 or 20 on their d20 rolls to hit an opponent.  It typically drags the encounter into a slow grind.  I'll usually adjust it so that the hardest is rolling a natural 18 on a d20 for a hit, under normal circumstances.The number of hit points to allocate to particular monsters will depend on how many rounds one would want an encounter to last.  These days I usually just use generic minion-like monsters, and modified minions which take 2 or 3 hits (or more) to kill them.  Though for "mini-bosses" or "big-bosses", I'll usually allocate an appropriate number of hit points.With modified minion type monsters/badguys that take 2 or 3 hits to kill, I usually try to make it such that it takes the party around 7 or 8 rounds to kill most of them.  The "mini-bosses" will take slightly more rounds.In general, I use this framework to check things like whether an encounter is too overpowered on one side, or if a skill challenge or check is too hard or too easy.</blockquote>

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