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Power Levels in AeriadorAeriador is a fantastical world full of various races and professions. There are many powerful people that dwell here and I count myself blessed to be an acquaintance to many of them. The “Wise” might say power is knowledge, but there is also a less arbitrary way to count the powerful in the realms. &nbsp;I have categorized power levels into the chart below and applied a rarity to it. Each higher level is about half as common as the one before it (an exponential/“geometric” rarity).Using a total population of 60,000,000, here are both the exact-by-level counts and the at-least-this-level counts.<h3>Rarity by Level (q = 0.5 per level)</h3>Each level up halves the headcount. P(exact L) = 0.5^L, P(≥L) = 0.5^(L-1).“Legendary” (≥11): ~1 in 1,024 people“Pinnacle” (≥20): ~1 in 524,288 peopleUsing a total population of 60,000,000, here are both the exact-by-level counts and the at-least-this-level counts.<figure class="table"><table><tbody><tr><td>Level &nbsp;&nbsp;</td><td>1-in-n (exact)</td><td>Count exact &nbsp;</td><td>1-in-n (≥)</td><td>Count ≥</td></tr><tr><td>1</td><td>1 in 2.0</td><td>30000000</td><td>1 in 1.0</td><td>60000000</td></tr><tr><td>2</td><td>1 in 4.0</td><td>15000000</td><td>1 in 2.0</td><td>30000000</td></tr><tr><td>3</td><td>1 in 8.0</td><td>7500000</td><td>1 in 4.0</td><td>15000000</td></tr><tr><td>4</td><td>1 in 16.0</td><td>3750000</td><td>1 in 8.0</td><td>7500000</td></tr><tr><td>5</td><td>1 in 32.0</td><td>1875000</td><td>1 in 16.0</td><td>3750000</td></tr><tr><td>6</td><td>1 in 64.0</td><td>937500</td><td>1 in 32.0</td><td>1875000</td></tr><tr><td>7</td><td>1 in 128.0</td><td>468750</td><td>1 in 64.0</td><td>937500</td></tr><tr><td>8</td><td>1 in 256.0</td><td>234375</td><td>1 in 128.0</td><td>468750</td></tr><tr><td>9</td><td>1 in 512.0</td><td>117188</td><td>1 in 256.0</td><td>234375</td></tr><tr><td>10</td><td>1 in 1,024</td><td>58594</td><td>1 in 512.0</td><td>117188</td></tr><tr><td>11</td><td>1 in 2,048</td><td>29297</td><td>1 in 1,024</td><td>58594</td></tr><tr><td>12</td><td>1 in 4,096</td><td>14648</td><td>1 in 2,048</td><td>29297</td></tr><tr><td>13</td><td>1 in 8,192</td><td>7324</td><td>1 in 4,096</td><td>14648</td></tr><tr><td>14</td><td>1 in 16,384</td><td>3662</td><td>1 in 8,192</td><td>7324</td></tr><tr><td>15</td><td>1 in 32,768</td><td>1831</td><td>1 in 16,384</td><td>3662</td></tr><tr><td>16</td><td>1 in 65,536</td><td>916</td><td>1 in 32,768</td><td>1831</td></tr><tr><td>17</td><td>1 in 131,072</td><td>458</td><td>1 in 65,536</td><td>916</td></tr><tr><td>18</td><td>1 in 262,144</td><td>229</td><td>1 in 131,072</td><td>458</td></tr><tr><td>19</td><td>1 in 524,288</td><td>114</td><td>1 in 262,144</td><td>229</td></tr><tr><td>20</td><td>1 in 1,048,576</td><td>57</td><td>1 in 524,288</td><td>114</td></tr><tr><td>21</td><td>1 in 2,097,152</td><td>29</td><td>1 in 1,048,576</td><td>57</td></tr><tr><td>22</td><td>1 in 4,194,304</td><td>14</td><td>1 in 2,097,152</td><td>29</td></tr><tr><td>23</td><td>1 in 8,388,608</td><td>7</td><td>1 in 4,194,304</td><td>14</td></tr><tr><td>24</td><td>1 in 16,777,216</td><td>4</td><td>1 in 8,388,608</td><td>7</td></tr><tr><td>25</td><td>1 in 33,554,432</td><td>2</td><td>1 in 16,777,216</td><td>4</td></tr><tr><td>26</td><td>1 in 67,108,864</td><td>1</td><td>1 in 33,554,432</td><td>2</td></tr><tr><td>27</td><td>1 in 134,217,728</td><td>~0</td><td>1 in 67,108,864</td><td>1</td></tr><tr><td>28</td><td>1 in 268,435,456</td><td>~0</td><td>1 in 134,217,728</td><td>~0</td></tr><tr><td>29</td><td>1 in 536,870,912</td><td>~0</td><td>1 in 268,435,456</td><td>~0</td></tr><tr><td>30</td><td>1 in 1,073,741,824</td><td>~0</td><td>1 in 536,870,912</td><td>~0</td></tr></tbody></table></figure>

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