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<blockquote data-quote="iwatt" data-source="post: 1012465" data-attributes="member: 11085"><p>Tessarel, you said:</p><p></p><p> </p><p></p><p>This is slightly OT, but the chances of succes in an opposed check can be found if you know your rivals check modifier. For the complete math background, you can check my post midway down this <a href="http://enworld.cyberstreet.com/showthread.php?s=&threadid=53892" target="_blank">thread</a> </p><p></p><p>What you have to understand is taht an opposed roll check between characters A and B can be characterized as:</p><p></p><p>d20_A + CM_A v/s d20_B + CM_B</p><p></p><p>CM_A (is character A's check modifier including circumstance bonus). The same goes for CM_B. Now the random variable is the substarction of two uniform variables. </p><p> </p><p></p><p>Here you have to set some ground rules. What happens in cas of a tie. I decree that the initiator of the opposed check wins on a tie. So let's assume that A initiates the check. A will win when</p><p></p><p>d20_A-d20_B >= CM_B-CM_A</p><p></p><p>In the above thread I do the math if you want to check it, but believe me that the</p><p>OCD = d20_A-d20_B (Opposed Check Difference)</p><p>is a random variable with a triangular probability density function with OCD ranging from -19 to +19. The cumulative density function becomes:</p><p></p><p>P(OCD<= N)=.125*(20+N)(21+N) -19<=N<=0</p><p>P(OCD<= N)=100-.125*(20-N)(19-N) 0<=N<=+19</p><p></p><p> That means that you can find the chance to succed from the following:</p><p></p><p>P(OCD>=CM_B-CM_A) = 100-P(OCD<=CM_B- CM_A- 1) </p><p></p><p>I know this seems a bit complicated, but here you have a table. </p><p></p><p>if we define N = CM_B-CM_A-1 </p><p>Or if you want you can simply define X= CM_A-CM_B (positive values indicates A is better than B.</p><p></p><p> N____% succes___X</p><p></p><p>-20_____100_____19</p><p>-19_____99,75___18</p><p>-18_____99,25___17</p><p>-17_____98,5____16</p><p>-16_____97,5____15</p><p>-15_____96,25___14</p><p>-14_____94,75___13</p><p>-13_____93______12</p><p>-12_____91______11</p><p>-11_____88,75___10</p><p>-10_____86,25___9</p><p>-9______83,5____8</p><p>-8______80,5____7</p><p>-7______77,25___6</p><p>-6______73,75___5</p><p>-5______70______4</p><p>-4______66______3</p><p>-3______61,75___2</p><p>-2______57,25___1</p><p>-1______52,5____0</p><p>0_______47,5____-1</p><p>1_______42,75___-2</p><p>2_______38,25___-3</p><p>3_______34______-4</p><p>4_______30______-5</p><p>5_______26,25___-6</p><p>6_______22,75___-7</p><p>7_______19,5____-8</p><p>8_______16,5____-9</p><p>9_______13,75___-10</p><p>10______11,25___-11</p><p>11______9_______-12</p><p>12______7_______-13</p><p>13______5,25____-14</p><p>14______3,75____-15</p><p>15______2,5_____-16</p><p>16______1,5_____-17</p><p>17______0,75____-18</p><p>18______0,25____-19</p><p>19______0_______-20</p><p></p><p>Which basically means you need to have a +19 better than the character youa are trying to beat to insure 100% effectiveness. But with "only" a +11 you are beating him 91% of the time. If you are evenly matched (X=0, N=-1) you beat him 52,5% of the time (because ties favor you).</p><p></p><p>You can easily make an excel sheet to calculate your succes rates, or just print out the above table.</p></blockquote><p></p>
[QUOTE="iwatt, post: 1012465, member: 11085"] Tessarel, you said: This is slightly OT, but the chances of succes in an opposed check can be found if you know your rivals check modifier. For the complete math background, you can check my post midway down this [URL=http://enworld.cyberstreet.com/showthread.php?s=&threadid=53892]thread[/URL] What you have to understand is taht an opposed roll check between characters A and B can be characterized as: d20_A + CM_A v/s d20_B + CM_B CM_A (is character A's check modifier including circumstance bonus). The same goes for CM_B. Now the random variable is the substarction of two uniform variables. Here you have to set some ground rules. What happens in cas of a tie. I decree that the initiator of the opposed check wins on a tie. So let's assume that A initiates the check. A will win when d20_A-d20_B >= CM_B-CM_A In the above thread I do the math if you want to check it, but believe me that the OCD = d20_A-d20_B (Opposed Check Difference) is a random variable with a triangular probability density function with OCD ranging from -19 to +19. The cumulative density function becomes: P(OCD<= N)=.125*(20+N)(21+N) -19<=N<=0 P(OCD<= N)=100-.125*(20-N)(19-N) 0<=N<=+19 That means that you can find the chance to succed from the following: P(OCD>=CM_B-CM_A) = 100-P(OCD<=CM_B- CM_A- 1) I know this seems a bit complicated, but here you have a table. if we define N = CM_B-CM_A-1 Or if you want you can simply define X= CM_A-CM_B (positive values indicates A is better than B. N____% succes___X -20_____100_____19 -19_____99,75___18 -18_____99,25___17 -17_____98,5____16 -16_____97,5____15 -15_____96,25___14 -14_____94,75___13 -13_____93______12 -12_____91______11 -11_____88,75___10 -10_____86,25___9 -9______83,5____8 -8______80,5____7 -7______77,25___6 -6______73,75___5 -5______70______4 -4______66______3 -3______61,75___2 -2______57,25___1 -1______52,5____0 0_______47,5____-1 1_______42,75___-2 2_______38,25___-3 3_______34______-4 4_______30______-5 5_______26,25___-6 6_______22,75___-7 7_______19,5____-8 8_______16,5____-9 9_______13,75___-10 10______11,25___-11 11______9_______-12 12______7_______-13 13______5,25____-14 14______3,75____-15 15______2,5_____-16 16______1,5_____-17 17______0,75____-18 18______0,25____-19 19______0_______-20 Which basically means you need to have a +19 better than the character youa are trying to beat to insure 100% effectiveness. But with "only" a +11 you are beating him 91% of the time. If you are evenly matched (X=0, N=-1) you beat him 52,5% of the time (because ties favor you). You can easily make an excel sheet to calculate your succes rates, or just print out the above table. [/QUOTE]
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