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<blockquote data-quote="baudot" data-source="post: 4310970" data-attributes="member: 70224"><p>I save to disbelieve!</p><p></p><p>But seriously:</p><p>Look at what happens to the math when you let the party undo (Complexity+1) failures and assume +9+levelMod as the standard skill level. You get a 50/50 success failure split. Plenty of room from there to juggle challenge design in how you give them them those failure undos, and where you let them pick up bonuses to tip them over 50% odds.</p><p></p><p>For me, the big breakthrough was realizing that the permutation distribution for the possible rolls fell on Pascal's Triangle.</p><p>(See: http://en.wikipedia.org/wiki/Pascal's_triangle )</p><p>Once you spot this, you see that you can get your players back to even odds (if their individual skill checks are even odds) by giving them the remaining half of the triangle, rather than just a 3rd off to one wing.</p><p></p><p>Indulge me. Pull up the wikipedia link above. Scroll down until you get to the 16 row triangle.</p><p></p><p>Now look at row 5 (row 6, if you count the 0 at the top), the one that goes:</p><p>1 5 10 10 5 1</p><p>This is our row that represents a complexity 1 challenge.</p><p>That is:</p><p>There's at most 5 rolls of the dice.</p><p>1 possible version is all successes.</p><p>5 possible versions are all but one success.</p><p>10 possible versions are all but two successes.</p><p>10 possible versions are all but two failures.</p><p>5 possible versions are all but one failure.</p><p>1 possible version is all failures.</p><p></p><p>Right now, only the first two possibilities are considered to pass the check. If we can push the third in, we can get back to balance. - 16 out of 32 ways to succeed, 16 out of 32 ways to fail. If we fail as often as we succeed on the individual die rolls, badda bing, badda boom. 50% chance.</p><p></p><p>And this is where the idea of designing failure forgiveness into challenges comes in. Make sense?</p></blockquote><p></p>
[QUOTE="baudot, post: 4310970, member: 70224"] I save to disbelieve! But seriously: Look at what happens to the math when you let the party undo (Complexity+1) failures and assume +9+levelMod as the standard skill level. You get a 50/50 success failure split. Plenty of room from there to juggle challenge design in how you give them them those failure undos, and where you let them pick up bonuses to tip them over 50% odds. For me, the big breakthrough was realizing that the permutation distribution for the possible rolls fell on Pascal's Triangle. (See: http://en.wikipedia.org/wiki/Pascal's_triangle ) Once you spot this, you see that you can get your players back to even odds (if their individual skill checks are even odds) by giving them the remaining half of the triangle, rather than just a 3rd off to one wing. Indulge me. Pull up the wikipedia link above. Scroll down until you get to the 16 row triangle. Now look at row 5 (row 6, if you count the 0 at the top), the one that goes: 1 5 10 10 5 1 This is our row that represents a complexity 1 challenge. That is: There's at most 5 rolls of the dice. 1 possible version is all successes. 5 possible versions are all but one success. 10 possible versions are all but two successes. 10 possible versions are all but two failures. 5 possible versions are all but one failure. 1 possible version is all failures. Right now, only the first two possibilities are considered to pass the check. If we can push the third in, we can get back to balance. - 16 out of 32 ways to succeed, 16 out of 32 ways to fail. If we fail as often as we succeed on the individual die rolls, badda bing, badda boom. 50% chance. And this is where the idea of designing failure forgiveness into challenges comes in. Make sense? [/QUOTE]
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