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Message: <blockquote data-quote="Esker" data-source="post: 7893945" data-attributes="member: 6966824">No. The set of DCs is the same. I am looking at trying to meet DCs in the range -5 to 27, and comparing apples to apples.If I'm a rogue with a +12 to stealth and I need to beat a passive perception of 11, then my target on a d20 is 0. That's the minimum value I could roll and succeed. I can't actually roll 0, but that's still my target number. And I can still find the probability of getting 0 or better. It just happens to be the same as the probability of getting 1 or better.It's the same exactly when the probability of "equal to" is zero. I'm starting to think that you don't think it's valid to talk about events with probability zero; that the event doesn't exist or something? Is that what's happening?No, I've subtracted 10 from the rolls so that I can compare same DC to same DC. You roll 3d6, multiply it by 2, and subtract 10. If the result after all of that is above your DC, you succeed. So when I consider a DC of -4, that's a DC of -4 for either method: a rogue with a +15 in thieves tools trying to pick a DC 10 lock. I need to roll a -4 or better to succeed. If I'm rolling 1d20 this is a guarantee, and it's the same difficulty as a target of 1. If I'm rolling 2*3d6-10 and have to confirm on ties, it's almost a guarantee, but not quite, since I could roll -4 exactly and then fail to confirm. But this is extremely unlikely.Nope, not what this shows. Actually none of the points are either of those things. If you read the paragraph above the plot, or even looked at the Y axis label, you'd see that all the points are the change in the probability of success if I'm trying to hit a DC X and I get an extra +1 to my roll (effectively making the DC X-1). This works out to be the probability of hitting X-1 exactly. You can relabel the Y axis P(roll = X-1). (That's why the d20 probabilities are 0.05 from 2 to 21 and not 1 to 20, since if I start at DC 2, I gain 5% success if I get +1, but if I start at DC 1, I gain nothing if I get an extra +1)I'm graphing the same thing for both evens and odds. The reason there are points at odds on the 2*3d6-10 curve is that I'm really rolling 2*3d6-(d2-1), and so I really can hit both odd and even numbers.I mean, it depends on how your measure the discrepancy. I'm actually measuring the discrepancy at those values (as simple difference in probability) and including it in the plot. Not sure why you think I haven't taken it into account. If you want to measure discrepancy as a ratio, well then yeah, it's big, since one of the terms is zero. But you've never in this whole massive thread suggested that your problem was in the way I was comparing probabilities.</blockquote>

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