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• Step 4: Weighted Damage (if applicable): If your character deals damage, then it needs to be weighted by its probability of success to determine just how good it is. One can say, "assuming all hits" and come up with a huge damage figure, but it means nothing if you have only a 1% chance of landing all hits. Calculating weighted damage is as simple as multiplying the probability of each attack by the damage that it deals.
  

Just for clarity.. Calculating weighted damage is as simple as multiplying the propability of each attack by the average damage that it deals and adding the results together.

• The probability that N - m, where m < N, will hit you is equal to the product your probability of success for the m that miss you, multiplied by the product of your AC's probability of failure for the N- m monsters that hit you. Your probability of failure = 100% - Probability of Success.
  

This is a little unclear. First part of the first sentence states the calculating of propability of m out of N unmarked hits, while second part of the first sentence calculates the propability of m marked hits; these propabilities differ.
*sure nobody wants the formula for the propability of m unmarked hits - it's just too impractical. Just note if anyone wants, I'll post it*

SRD]If the result equals or exceeds the target number, your character succeeds. If the result is lower than the target number, you fail.

But, apparently, I've been playing the game wrong all this time. :embarrass

Sooo, ah, yeah, all I need to do is separate out the tie probability, subtract it from my "win" probability and then state that a modifier check is needed here -- with the tie probability being the chance that one would need to perform a modifier check.

@maurezen: Thanks for the corrections. I'll make 'em as soon as possible, along with fixing this other wrote:

Tleilaxu_Ghola wrote:

Oh

See, for some reason I got it in my head that no opposed check required a modifier check to break the tie. In my experience we alway did it so that the offender won ties (bluffer wins versus sense motive, tripper wins trip check ties, etc, etc). That all make sense to me since the core mechanic is:


But, apparently, I've been playing the game wrong all this time. :embarrass

No, you've just been playing it your way.

Ideally, if the system was completely logical, it would work your way. My guess is that it works the way it does so that instead of favoring the offender, it favors the more skilled of the two participants (or the better grappler, or the stronger one, or what have you).


EDIT: Since the opposed modifier isn't so much a "check" as a direct comparison (i.e. my Strength mod is +3, his is +6, he wins), and we have average values for nearly every relevant modifier... it shouldn't be hard to adjust the rubric ever so slightly to account for the probability of success on a tie. However, without standard deviations, I don't see an easy way to completely account for your odds of success on a tie.