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<blockquote data-quote="Dr. Harry" data-source="post: 3841165" data-attributes="member: 5468">I kind of picked this post to respond to randomly, so no offense is meant anywhere ...The odds of ending up with a score of x is y (for an individual score).x&nbsp; &nbsp; &nbsp;&nbsp; y (%)3&nbsp; &nbsp; &nbsp;&nbsp; 0.084&nbsp; &nbsp; &nbsp;&nbsp; 0.315&nbsp; &nbsp; &nbsp;&nbsp; 0.776&nbsp; &nbsp; &nbsp;&nbsp; 1.627&nbsp; &nbsp; &nbsp;&nbsp; 2.938&nbsp; &nbsp; &nbsp;&nbsp; 4.789&nbsp; &nbsp; &nbsp;&nbsp; 7.0210&nbsp; &nbsp; &nbsp; 9.4111&nbsp; &nbsp;&nbsp; 11.4212&nbsp; &nbsp;&nbsp; 12.8913&nbsp; &nbsp;&nbsp; 13.2714&nbsp; &nbsp;&nbsp; 12.3515&nbsp; &nbsp;&nbsp; 10.1116&nbsp; &nbsp; &nbsp; 7.2517&nbsp; &nbsp; &nbsp; 4.1718&nbsp; &nbsp; &nbsp; 1.62&nbsp; If anyone is curious about my methodology, I use brute force, as well as copy, paste, and fill down to set up a table of all 1,296 possible results in Excel.&nbsp; The odds of rolling six 18's in this way is (0.0162)^6, as I make it, or 1.81 x 10^(-11).&nbsp; We should expect to see all 18's come up 1.8 times for every hundred billion sets of rolls.&nbsp; This does not account for other influences, such as:1) This roll does not count because the dice is touching that piece of paper/book/bit of cheeto.&nbsp;or2) Rolling the dice consecutively and aiming the throw of a later die to hit and effectively reroll a previous, less desired result.or others.&nbsp; Maybe it would be a fun thread to collect as many dice rationalizations as possible.&nbsp; That might even overtake the Hive Mind thread <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&nbsp; &nbsp; :)"&nbsp; data-smilie="1"data-shortname=":)" />There is a 1.34% chance that someone could &quot;roll without rationalizations&quot; and get no scores lower than 13.&nbsp; If the player rolled ten characters and only kept the best one, there is a 12.7% chance that at least one of them has no scores lower than 13.&nbsp; For twenty characters, the odds of &quot;success&quot;, (if you want to call it that) go up to 23.7%The odds of a character getting at least one 18 are 9.30 out of 100, or 9.30%If I have done the math correctly (just flying off the top of my head) the odds of a character getting at least two 18's would be this 9.30% for one score to be 18 out of six times the chance that one of the five remaining scores is an 18, or 0.73 %.&nbsp; The odds of three 18's would be 0.046 %.(Looking at it like this gives me a chance of getting six 18's as a more common one in one hundred million, as opposed to one in one hundred billion, so I think that the numbers in the previous paragraph trend high.&nbsp; Why? I haven't got time to sort it out right now.</blockquote>

[QUOTE="Dr. Harry, post: 3841165, member: 5468"] I kind of picked this post to respond to randomly, so no offense is meant anywhere ... The odds of ending up with a score of [i]x[/i] is [i]y[/i] (for an individual score). x y (%) 3 0.08 4 0.31 5 0.77 6 1.62 7 2.93 8 4.78 9 7.02 10 9.41 11 11.42 12 12.89 13 13.27 14 12.35 15 10.11 16 7.25 17 4.17 18 1.62 If anyone is curious about my methodology, I use brute force, as well as copy, paste, and fill down to set up a table of all 1,296 possible results in Excel. The odds of rolling six 18's in this way is (0.0162)^6, as I make it, or 1.81 x 10^(-11). We should expect to see all 18's come up 1.8 times for every hundred billion sets of rolls. This does not account for other influences, such as: 1) This roll does not count because the dice is touching that piece of paper/book/bit of cheeto. or 2) Rolling the dice consecutively and aiming the throw of a later die to hit and effectively reroll a previous, less desired result. or others. Maybe it would be a fun thread to collect as many dice rationalizations as possible. That might even overtake the Hive Mind thread :) There is a 1.34% chance that someone could "roll without rationalizations" and get no scores lower than 13. If the player rolled ten characters and only kept the best one, there is a 12.7% chance that at least one of them has no scores lower than 13. For twenty characters, the odds of "success", (if you want to call it that) go up to 23.7% The odds of a character getting at least one 18 are 9.30 out of 100, or 9.30% If I have done the math correctly (just flying off the top of my head) the odds of a character getting at least two 18's would be this 9.30% for one score to be 18 out of six times the chance that one of the five remaining scores is an 18, or 0.73 %. The odds of three 18's would be 0.046 %. (Looking at it like this gives me a chance of getting six 18's as a more common one in one hundred million, as opposed to one in one hundred billion, so I think that the numbers in the previous paragraph trend high. Why? I haven't got time to sort it out right now. [/QUOTE]

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