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<blockquote data-quote="Aristeas" data-source="post: 4281518" data-attributes="member: 41008">Just to supplement the pure mathematics upthread, I wrote a Java simulator of a complexity 1 skill challenge and ran it ten million times on all of the interesting DCs. This is only an approximation, obviously, but at n=10^7 it's more or less equivalent to the actual probabilities, and you can see it matches what the mathematicians found before.If the PCs need 3 or better, success chance is 91.85738%If the PCs need 4 or better, success chance is 83.5259%If the PCs need 5 or better, success chance is 73.73342%If the PCs need 6 or better, success chance is 63.29145%If the PCs need 7 or better, success chance is 52.82564%If the PCs need 8 or better, success chance is 42.84524%If the PCs need 9 or better, success chance is 33.70783%If the PCs need 10 or better, success chance is 25.62302%If the PCs need 11 or better, success chance is 18.73536%If the PCs need 12 or better, success chance is 13.12077%If the PCs need 13 or better, success chance is 8.71162%If the PCs need 15 or better, success chance is 3.06186%If the PCs need 16 or better, success chance is 1.56657%So, as written, if our 1st level PCs somehow manage to have an average +10 to their checks, they have a 26% chance on moderate tasks, a 74% chance on easy tasks, and a 3% chance on hard tasks. If we drop the +5 DC, moderate tasks are 74%, and easy tasks are better than 90%, while hard tasks are still only 26%.</blockquote>

[QUOTE="Aristeas, post: 4281518, member: 41008"] Just to supplement the pure mathematics upthread, I wrote a Java simulator of a complexity 1 skill challenge and ran it ten million times on all of the interesting DCs. This is only an approximation, obviously, but at n=10^7 it's more or less equivalent to the actual probabilities, and you can see it matches what the mathematicians found before. If the PCs need 3 or better, success chance is 91.85738% If the PCs need 4 or better, success chance is 83.5259% If the PCs need 5 or better, success chance is 73.73342% If the PCs need 6 or better, success chance is 63.29145% If the PCs need 7 or better, success chance is 52.82564% If the PCs need 8 or better, success chance is 42.84524% If the PCs need 9 or better, success chance is 33.70783% If the PCs need 10 or better, success chance is 25.62302% If the PCs need 11 or better, success chance is 18.73536% If the PCs need 12 or better, success chance is 13.12077% If the PCs need 13 or better, success chance is 8.71162% If the PCs need 15 or better, success chance is 3.06186% If the PCs need 16 or better, success chance is 1.56657% So, as written, if our 1st level PCs somehow manage to have an average +10 to their checks, they have a 26% chance on moderate tasks, a 74% chance on easy tasks, and a 3% chance on hard tasks. If we drop the +5 DC, moderate tasks are 74%, and easy tasks are better than 90%, while hard tasks are still only 26%. [/QUOTE]

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