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Probability Distribution of Dice
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<blockquote data-quote="LazarusLong42" data-source="post: 779185" data-attributes="member: 9620"><p>Heh, that one's *easy* <img src="https://cdn.jsdelivr.net/joypixels/assets/8.0/png/unicode/64/1f642.png" class="smilie smilie--emoji" loading="lazy" width="64" height="64" alt=":)" title="Smile :)" data-smilie="1"data-shortname=":)" /> As follows:</p><p></p><p>[code][COLOR=silver]</p><p>3 1 0.4630 0.4630 100.000</p><p>4 3 1.3889 1.8519 99.5370</p><p>5 6 2.7778 4.6296 98.1481</p><p>6 10 4.6296 9.2593 95.3704</p><p>7 15 6.9444 16.2037 90.7407</p><p>8 21 9.7222 25.9259 83.7963</p><p>9 25 11.5741 37.5000 74.0741</p><p>10 27 12.5000 50.0000 62.5000</p><p>11 27 12.5000 62.5000 50.0000</p><p>12 25 11.5741 74.0741 37.5000</p><p>13 21 9.7222 83.7963 25.9259</p><p>14 15 6.9444 90.7407 16.2037</p><p>15 10 4.6296 95.3704 9.2593</p><p>16 6 2.7778 98.1481 4.6296</p><p>17 3 1.3889 99.5370 1.8519</p><p>18 1 0.4630 100.000 0.4630</p><p>[/COLOR][/code]</p><p></p><p>Column one is the roll of 3d6; column 2 is the number of rolls (out of 216 possible) that will produce that result. Column three is the percent of rolls that produce that result. Column 4 is the percent of rolls with a result equal to that number or less; column 5 is the percent equal to that number of higher.</p><p></p><p>So, 74.0741% of 3d6 rolls will be 12 or lower, and the same percentage will be 9 or higher.</p><p></p><p>Someone floated results for 4d6 drop lowest a while ago, and I have them somewhere, but they can't be calculated using the formulae in this thread.</p></blockquote><p></p>
[QUOTE="LazarusLong42, post: 779185, member: 9620"] Heh, that one's *easy* :) As follows: [code][COLOR=silver] 3 1 0.4630 0.4630 100.000 4 3 1.3889 1.8519 99.5370 5 6 2.7778 4.6296 98.1481 6 10 4.6296 9.2593 95.3704 7 15 6.9444 16.2037 90.7407 8 21 9.7222 25.9259 83.7963 9 25 11.5741 37.5000 74.0741 10 27 12.5000 50.0000 62.5000 11 27 12.5000 62.5000 50.0000 12 25 11.5741 74.0741 37.5000 13 21 9.7222 83.7963 25.9259 14 15 6.9444 90.7407 16.2037 15 10 4.6296 95.3704 9.2593 16 6 2.7778 98.1481 4.6296 17 3 1.3889 99.5370 1.8519 18 1 0.4630 100.000 0.4630 [/COLOR][/code] Column one is the roll of 3d6; column 2 is the number of rolls (out of 216 possible) that will produce that result. Column three is the percent of rolls that produce that result. Column 4 is the percent of rolls with a result equal to that number or less; column 5 is the percent equal to that number of higher. So, 74.0741% of 3d6 rolls will be 12 or lower, and the same percentage will be 9 or higher. Someone floated results for 4d6 drop lowest a while ago, and I have them somewhere, but they can't be calculated using the formulae in this thread. [/QUOTE]
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