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Help me understand "average rolls"
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<blockquote data-quote="shurai" data-source="post: 513233"><p>Foist of all, the chances of rolling an 11 on 2d10 isn't 0.08 but 0.1, and the chances of rolling a 10 on 2d10 is 0.09. Also, I'm no sure what your definition of 'drastically' is, but the probability of rolling minimally falls from 0.05 to 0.01. For most people that would be a pretty drastic drop.</p><p></p><p>The curve isn't that slight either, at least not to me (though it's a subjective thing so maybe we just disagree about what 'slight' is).</p><p></p><p>Anyway, one thing I can be sure of is the math, so here it is:</p><p></p><p>Sure, for getting an 11 it goes up by 5 percentage points, but if you look at a <em>spread</em> of values, things get more pronounced. </p><p></p><p>Let's look at the chances of getting a range of values close to the expected value of both rolls, say 8 to 13. For the d20, there's 6 values that equal success, all equally likely, and 20 possible outcomes, so 6/20 or 0.3.</p><p></p><p>For 2d10 it's a bit more complicated. There are 100 possible rolls, all equally likely. Several combinations of rolls will result in any given target result, as follows:</p><p></p><p>8: 17, 26, 35, 44, 53, 62, 71</p><p>9: 18, 27, 36, 45, 54, 63, 72, 81</p><p>10: 19, 28, 37, 46, 55, 64, 73, 82, 91</p><p>11: 10, 29, 38, 47, 56, 65, 74, 83, 92, 01</p><p>12: 20, 39, 48, 57, 66, 75, 84, 93, 02</p><p>13: yay symmetry! same as 9.</p><p></p><p>So the total number of outcomes that fall in this range is 7+8+9+10+9+8 or 51.</p><p></p><p>So in a d20 roll, the chances of the roll falling in the range of 8 to 13 are about 3 in 10, but the same range for 2d10 is more than 5 in 10.</p><p></p><p>EDIT: Holy convenient math error, batman!</p></blockquote><p></p>
[QUOTE="shurai, post: 513233"] Foist of all, the chances of rolling an 11 on 2d10 isn't 0.08 but 0.1, and the chances of rolling a 10 on 2d10 is 0.09. Also, I'm no sure what your definition of 'drastically' is, but the probability of rolling minimally falls from 0.05 to 0.01. For most people that would be a pretty drastic drop. The curve isn't that slight either, at least not to me (though it's a subjective thing so maybe we just disagree about what 'slight' is). Anyway, one thing I can be sure of is the math, so here it is: Sure, for getting an 11 it goes up by 5 percentage points, but if you look at a [i]spread[/i] of values, things get more pronounced. Let's look at the chances of getting a range of values close to the expected value of both rolls, say 8 to 13. For the d20, there's 6 values that equal success, all equally likely, and 20 possible outcomes, so 6/20 or 0.3. For 2d10 it's a bit more complicated. There are 100 possible rolls, all equally likely. Several combinations of rolls will result in any given target result, as follows: 8: 17, 26, 35, 44, 53, 62, 71 9: 18, 27, 36, 45, 54, 63, 72, 81 10: 19, 28, 37, 46, 55, 64, 73, 82, 91 11: 10, 29, 38, 47, 56, 65, 74, 83, 92, 01 12: 20, 39, 48, 57, 66, 75, 84, 93, 02 13: yay symmetry! same as 9. So the total number of outcomes that fall in this range is 7+8+9+10+9+8 or 51. So in a d20 roll, the chances of the roll falling in the range of 8 to 13 are about 3 in 10, but the same range for 2d10 is more than 5 in 10. EDIT: Holy convenient math error, batman! [/QUOTE]
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