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Mathematicians help with dice probabilities!
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<blockquote data-quote="steenan" data-source="post: 6740495" data-attributes="member: 23240"><p>You must remember that the probability distribution is two-dimensional here - probability of success depends on the difficulty level and on skill level. It is very hard to keep it reasonably intact when translating to a different resolution mechanics. </p><p>In other words, you will have to decide what exactly you want to keep and what can change with the change of dice.</p><p></p><p></p><p>A pool of d6 with success on 4+ definitely has less granularity than a pool of summed d6, but for a reasonable number of dice rolled (let's say, 4 and up) it is possible to keep the difficulties and skill levels equivalent.</p><p></p><p></p><p>With success on 5+ or on 6 you not only change the expected number of successes, but also the shape of the distribution. The bell curve you get is no longer symmetrical; the mean is moved to lower values, but you have a long "tail" towards high number of successes. </p><p>In other words, the rare lucky rolls are much better compared to the average than they are in a symmetric distribution. Maybe that's something you want, maybe not.</p><p>If you want to use this kind of roll in your system, you should probably re-scale the skills.</p><p></p><p></p><p>The d20+bonus makes it much harder to get any kind of equivalency. You may easily set the difficulty levels to get the same probabilities for a fixed value of skill bonus, but you won't be able to get correct probabilities for different difficulties and skill levels. If all characters are at a similar skill value, that may not be a problem. But if you want a wide range of skills to matter (and that's what I suspect, judging from the wide range of difficulties), it's going to be hard.</p><p>Probably the best you can aim for is keeping the difficulty-skill equivalency as it was (with the target numbers you gave, 2 dice have around 50% at easy, 3 at routine etc.).</p><p></p><p></p><p>With percentile roll-under you have to think how you'd like to represent the skill values and difficulty levels. Unless you use some fancy math to calculate the success threshold from skill and difficulty, you won't get anything resembling the dice pool results. </p><p></p><p></p><p>It is easier to switch resolution systems if you aim for a specific behavior. If you want general equivalency, it's very hard to do.</p></blockquote><p></p>
[QUOTE="steenan, post: 6740495, member: 23240"] You must remember that the probability distribution is two-dimensional here - probability of success depends on the difficulty level and on skill level. It is very hard to keep it reasonably intact when translating to a different resolution mechanics. In other words, you will have to decide what exactly you want to keep and what can change with the change of dice. A pool of d6 with success on 4+ definitely has less granularity than a pool of summed d6, but for a reasonable number of dice rolled (let's say, 4 and up) it is possible to keep the difficulties and skill levels equivalent. With success on 5+ or on 6 you not only change the expected number of successes, but also the shape of the distribution. The bell curve you get is no longer symmetrical; the mean is moved to lower values, but you have a long "tail" towards high number of successes. In other words, the rare lucky rolls are much better compared to the average than they are in a symmetric distribution. Maybe that's something you want, maybe not. If you want to use this kind of roll in your system, you should probably re-scale the skills. The d20+bonus makes it much harder to get any kind of equivalency. You may easily set the difficulty levels to get the same probabilities for a fixed value of skill bonus, but you won't be able to get correct probabilities for different difficulties and skill levels. If all characters are at a similar skill value, that may not be a problem. But if you want a wide range of skills to matter (and that's what I suspect, judging from the wide range of difficulties), it's going to be hard. Probably the best you can aim for is keeping the difficulty-skill equivalency as it was (with the target numbers you gave, 2 dice have around 50% at easy, 3 at routine etc.). With percentile roll-under you have to think how you'd like to represent the skill values and difficulty levels. Unless you use some fancy math to calculate the success threshold from skill and difficulty, you won't get anything resembling the dice pool results. It is easier to switch resolution systems if you aim for a specific behavior. If you want general equivalency, it's very hard to do. [/QUOTE]
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