Reply to thread

Message: <blockquote data-quote="Yaarel" data-source="post: 9192647" data-attributes="member: 58172">The following experiment is to understand the nature of dice rolls.Rethink the point buy costs.Here, the goal is a point buy method whose costs are proportional to the dice roll results.The costs are weighted according to the 4d6-Lowest dice roll.To determine the costs, determine the statistical chance of rolling a score, when using the 4d6-Lowest method. Here, there is a 1.000 (namely a 100%) chance that the score will be at least 3. Thus a 3 is least valuable. However, a score that is at least a 17 is much rarer and much more valuable, at a 0.0579 (namely a 5.79%) chance.Then the inverse of the chance is the proportional cost. For example, to improve a score of 16 to 17 costs about 17 points: 17.27 = 1 / 0.0579.Here the default score is 10. The 10 is given for free. The scores higher cost incrementally more upwards from 10.<table style='width: 100%'><tr><td>SCORE</td><td>Chance of at least (x)</td><td>Inverse (1/x)</td><td>Rounded cost for each improvement</td><td>POINT COST</td></tr><tr><td></td><td></td><td></td><td></td><td></td></tr><tr><td>18</td><td>.0162</td><td>61.73</td><td>62</td><td>99</td></tr><tr><td></td><td></td><td></td><td></td><td></td></tr><tr><td>17</td><td>.0579</td><td>17.27</td><td>17</td><td>37</td></tr><tr><td>16</td><td>.1304</td><td>7.669</td><td>8</td><td>20</td></tr><tr><td></td><td></td><td></td><td></td><td></td></tr><tr><td>15</td><td>.2315</td><td>4.320</td><td>4</td><td>12</td></tr><tr><td>14</td><td>.3549</td><td>2.818</td><td>3</td><td>8</td></tr><tr><td></td><td></td><td></td><td></td><td></td></tr><tr><td>13</td><td>.4877</td><td>2.050</td><td>2</td><td>5</td></tr><tr><td>12</td><td>.6165</td><td>1.622</td><td>2</td><td>3</td></tr><tr><td></td><td></td><td></td><td></td><td></td></tr><tr><td>11</td><td>.7307</td><td>1.369</td><td>1</td><td>1</td></tr><tr><td>10</td><td>.8248</td><td>1.212</td><td>1</td><td>DEFAULT</td></tr><tr><td></td><td></td><td></td><td></td><td></td></tr><tr><td>9</td><td>.8951</td><td>1.117</td><td>1</td><td>−1</td></tr><tr><td>8</td><td>.9429</td><td>1.061</td><td>1</td><td>−2</td></tr><tr><td></td><td></td><td></td><td></td><td></td></tr><tr><td>7</td><td>.9722</td><td>1.029</td><td>1</td><td>−3</td></tr><tr><td>6</td><td>.9884</td><td>1.012</td><td>1</td><td>−4</td></tr><tr><td></td><td></td><td></td><td></td><td></td></tr><tr><td>5</td><td>.9961</td><td>1.004</td><td>1</td><td>−5</td></tr><tr><td>4</td><td>.9992</td><td>1.001</td><td>1</td><td>−6</td></tr><tr><td></td><td></td><td></td><td></td><td></td></tr><tr><td>3</td><td>1.000</td><td>1.000</td><td>1</td><td>−7</td></tr></table>As the table demonstrates, a natural 18 is very rare and very valuable. It costs far more than the point buy method can ever afford. When the dice roll method actually rolls an 18, it by itself is worth far more than the entire standard array.The average array for the 4d6-Lowest dice roll is: 16, 14, 13, 12, 10, 9This array is worth 35 points.Other arrays that are worth 35 points include:16, 15, 12, 10, 10, 1016, 15, 11, 11, 11, 1016, 14, 13, 11, 11, 1016, 14, 12, 12, 11, 1015, 15, 14, 12, 10, 1015, 14, 14, 13, 11, 1115, 14, 14, 12, 12, 1115, 14, 13, 13, 13, 1014, 14, 14, 14, 12, 1014, 14, 14, 13, 13, 11All of these equivalents of the 4d6-Lowest method are worth more than the standard array.But if the dice roll method happens to roll an 18, the actual value of its array is worth vastly more than the standard array.And because players discard low rolls, the actual average of 4d6-Lowest is worth many more points.The scores of the 4d6-Lowest dice roll are equivalent to many free feats at level 1.</blockquote>

Verification