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<blockquote data-quote="Morrus" data-source="post: 6233664" data-attributes="member: 1">Sorry guys; I know I keep asking for help with this stuff.&nbsp; I want to get it right!So I'm writing a page in my RPG which delves a bit into the maths.&nbsp; Only slightly, and many readers will skip it, but for those interested it can be an interesting insight, I think. So I figured why not include it? So here's what I have so far.&nbsp; It's a very basic look at basic dice d6 dice pools.&nbsp; But I want to be sure I have it all correct.&nbsp; As you can see, I've also been unable to incorporate the exploding dice into the maths, meaning that the last two tables, especially, are showing figures which are too low.&nbsp;This short section of the rulebook contains a little math and probability theory. You can skip it, though reading it may prove useful when it comes to assigning difficulty values.&nbsp; &nbsp; A look at the statistics will assist the GM in assigning appropriate difficulty values. Consider the following facts:&nbsp; &nbsp;<ul>
<li data-xf-list-type="ul">&nbsp; &nbsp;&nbsp; The average human attribute&nbsp; &nbsp;&nbsp; (without skill bonuses) is 4. </li>
<li data-xf-list-type="ul">&nbsp; &nbsp;&nbsp; This means that an average human&nbsp; &nbsp;&nbsp; adult will tend to roll between 4-24 on 4d6, with the most common&nbsp; &nbsp;&nbsp; result being 14. </li>
<li data-xf-list-type="ul">&nbsp; &nbsp;&nbsp; Because 4d6 is a bell-curve, the&nbsp; &nbsp;&nbsp; results will tend towards the average, and half of the time the&nbsp; &nbsp;&nbsp; average human will roll between 12 and 16. </li>
<li data-xf-list-type="ul">&nbsp; &nbsp;&nbsp; The exploding dice will tend to&nbsp; &nbsp;&nbsp; increase these odds, putting the 'average' roll at 16 on 4d6, rather&nbsp; &nbsp;&nbsp; than 14 with an average range of 14-18. </li>
</ul>&nbsp; &nbsp; So if you want a difficulty value that the average person would succeed at half the time (perhaps breaking down a regular door), you should set it at 16.&nbsp; Some significant “landmarks” are as follows:&nbsp; <table style='width: 100%'><tr><td>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; 4 
&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; </td><td>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; Lowest possible roll 
&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; </td><td>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; Trivially easy;&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; success guaranteed 
&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; </td></tr><tr><td>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; 12 
&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; </td><td>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; Low end of most rolls 
&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; </td><td>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; 
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 
&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; </td></tr><tr><td>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; 16 
&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; </td><td>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; Average roll 
&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; </td><td>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; Routine; about 50%&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; success rate 
&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; </td></tr><tr><td>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; 18 
&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; </td><td>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; High end of most&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; rolls 
 
&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; </td><td>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; 
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 
&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; </td></tr><tr><td>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; 24 
&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; </td><td>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; Highest possible roll 
&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; </td><td>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; Incredibly difficult;&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; success unlikely 
&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; </td></tr></table>&nbsp; The same average difficulty for someone with basic training (taken the skill once, gaining +1d6) is 19, and for someone well-trained (taken it twice) is 23, and for someone specialised (gaining 3d6 or more on the check) is 27 or higher.&nbsp; Setting the value at higher than 24 means that the average person with no additional training or bonuses from elswhere will be very unlikely to succeed (barring a lucky string of exploding dice), but someone with a couple of ranks in that skill has a reasonable chance of doing so.&nbsp;&nbsp; &nbsp; <table style='width: 100%'><tr><td>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; Average untrained&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; person succeeds half the time, trained person succeeds most times 
&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; </td><td>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; 16 
&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; </td></tr><tr><td>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; Average untrained&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; person likely fails, but someone with basic training succeeds half&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; the time 
&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; </td><td>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; 19 
&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; </td></tr><tr><td>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; Average untrained&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; person likely fails, but well-trained person succeeds half the&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; time 
 
&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; </td><td>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; 23 
&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; </td></tr><tr><td>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; Trained person likely&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; fails, but specialized person succeeds half the time 
&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; </td><td>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; 27 
&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; </td></tr></table>&nbsp; Here are the average die rolls for varying sized dice pools. This is a good guide as to what is a difficult or easy target value for a given sized dice pool.&nbsp; <table style='width: 100%'><tr><td>1d6 
 
</td><td>2d6 
</td><td>3d6 
</td><td>4d6 
</td><td>5d6 
</td><td>6d6 
</td><td>7d6 
</td><td>8d6 
</td><td>9d6 
</td><td>10d6 
</td></tr><tr><td>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; 3.5 
 
&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; </td><td>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; 7 
&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; </td><td>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; 10.5 
&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; </td><td>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; 14 
&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; </td><td>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; 17.5 
&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; </td><td>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; 21 
&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; </td><td>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; 24.5 
&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; </td><td>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; 28 
&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; </td><td>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; 31.5 
&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; </td><td>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; 35 
&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; </td></tr></table>Finally, here's a look at the performance of an average, untrained human (i.e. one rolling 4d6) and his likelihood of hitting certain difficulty values.&nbsp;<table style='width: 100%'><tr><td>4 
 
</td><td>5 
</td><td>6 
</td><td>7 
</td><td>8 
</td><td>9 
</td><td>10 
</td><td>11 
</td><td>12 
</td><td>13 
</td><td>14 
</td></tr><tr><td>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; 100% 
&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; </td><td>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; 99.9% 
 
&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; </td><td>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; 99.6% 
&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; </td><td>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; 98.4% 
&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; </td><td>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; 97.3% 
&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; </td><td>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; 94.6% 
&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; </td><td>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; 90.2% 
&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; </td><td>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; 84.1% 
&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; </td><td>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; 76.1% 
&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; </td><td>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; 66.4% 
&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; </td><td>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; 55.6% 
&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; </td></tr><tr><td>15 
 
</td><td>16 
</td><td>17 
</td><td>18 
</td><td>19 
</td><td>20 
</td><td>21 
</td><td>22 
</td><td>23 
</td><td>24 
</td><td>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; 
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 
&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; </td></tr><tr><td>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; 44.4% 
&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; </td><td>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; 33.6% 
&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; </td><td>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; 23.9% 
&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; </td><td>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; 15.9% 
&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; </td><td>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; 9.7% 
&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; </td><td>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; 5.4% 
&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; </td><td>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; 2.7% 
&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; </td><td>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; 1.2% 
&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; </td><td>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; 0.4% 
&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; </td><td>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; 0.1% 
&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; </td><td>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; 
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 
&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; </td></tr></table>Exploding dice add about 15% (on average) to those chances, although less so at the higher extremes.</blockquote>

[QUOTE="Morrus, post: 6233664, member: 1"] Sorry guys; I know I keep asking for help with this stuff. I want to get it right! So I'm writing a page in my RPG which delves a bit into the maths. Only slightly, and many readers will skip it, but for those interested it can be an interesting insight, I think. So I figured why not include it? So here's what I have so far. It's a very basic look at basic dice d6 dice pools. But I want to be sure I have it all correct. As you can see, I've also been unable to incorporate the exploding dice into the maths, meaning that the last two tables, especially, are showing figures which are too low. This short section of the rulebook contains a little math and probability theory. You can skip it, though reading it may prove useful when it comes to assigning difficulty values. A look at the statistics will assist the GM in assigning appropriate difficulty values. Consider the following facts: [LIST] [*] The average human attribute (without skill bonuses) is 4. [*] This means that an average human adult will tend to roll between 4-24 on 4d6, with the most common result being 14. [*] Because 4d6 is a bell-curve, the results will tend towards the average, and half of the time the average human will roll between 12 and 16. [*] The exploding dice will tend to increase these odds, putting the 'average' roll at 16 on 4d6, rather than 14 with an average range of 14-18. [/LIST] So if you want a difficulty value that the average person would succeed at half the time (perhaps breaking down a regular door), you should set it at 16. Some significant “landmarks” are as follows: [TABLE] [TR] [TD] 4 [/TD] [TD] Lowest possible roll [/TD] [TD] Trivially easy; success guaranteed [/TD] [/TR] [TR] [TD] 12 [/TD] [TD] Low end of most rolls [/TD] [TD] [/TD] [/TR] [TR] [TD] 16 [/TD] [TD] Average roll [/TD] [TD] Routine; about 50% success rate [/TD] [/TR] [TR] [TD] 18 [/TD] [TD] High end of most rolls [/TD] [TD] [/TD] [/TR] [TR] [TD] 24 [/TD] [TD] Highest possible roll [/TD] [TD] Incredibly difficult; success unlikely [/TD] [/TR] [/TABLE] The same average difficulty for someone with basic training (taken the skill once, gaining +1d6) is 19, and for someone well-trained (taken it twice) is 23, and for someone specialised (gaining 3d6 or more on the check) is 27 or higher. Setting the value at higher than 24 means that the average person with no additional training or bonuses from elswhere will be very unlikely to succeed (barring a lucky string of exploding dice), but someone with a couple of ranks in that skill has a reasonable chance of doing so. [TABLE] [TR] [TD] Average untrained person succeeds half the time, trained person succeeds most times [/TD] [TD] 16 [/TD] [/TR] [TR] [TD] Average untrained person likely fails, but someone with basic training succeeds half the time [/TD] [TD] 19 [/TD] [/TR] [TR] [TD] Average untrained person likely fails, but well-trained person succeeds half the time [/TD] [TD] 23 [/TD] [/TR] [TR] [TD] Trained person likely fails, but specialized person succeeds half the time [/TD] [TD] 27 [/TD] [/TR] [/TABLE] Here are the average die rolls for varying sized dice pools. This is a good guide as to what is a difficult or easy target value for a given sized dice pool. [TABLE] [TR] [TD]1d6 [/TD] [TD]2d6 [/TD] [TD]3d6 [/TD] [TD]4d6 [/TD] [TD]5d6 [/TD] [TD]6d6 [/TD] [TD]7d6 [/TD] [TD]8d6 [/TD] [TD]9d6 [/TD] [TD]10d6 [/TD] [/TR] [TR] [TD] 3.5 [/TD] [TD] 7 [/TD] [TD] 10.5 [/TD] [TD] 14 [/TD] [TD] 17.5 [/TD] [TD] 21 [/TD] [TD] 24.5 [/TD] [TD] 28 [/TD] [TD] 31.5 [/TD] [TD] 35 [/TD] [/TR] [/TABLE] Finally, here's a look at the performance of an average, untrained human (i.e. one rolling 4d6) and his likelihood of hitting certain difficulty values. [TABLE] [TR] [TD]4 [/TD] [TD]5 [/TD] [TD]6 [/TD] [TD]7 [/TD] [TD]8 [/TD] [TD]9 [/TD] [TD]10 [/TD] [TD]11 [/TD] [TD]12 [/TD] [TD]13 [/TD] [TD]14 [/TD] [/TR] [TR] [TD] 100% [/TD] [TD] 99.9% [/TD] [TD] 99.6% [/TD] [TD] 98.4% [/TD] [TD] 97.3% [/TD] [TD] 94.6% [/TD] [TD] 90.2% [/TD] [TD] 84.1% [/TD] [TD] 76.1% [/TD] [TD] 66.4% [/TD] [TD] 55.6% [/TD] [/TR] [TR] [TD]15 [/TD] [TD]16 [/TD] [TD]17 [/TD] [TD]18 [/TD] [TD]19 [/TD] [TD]20 [/TD] [TD]21 [/TD] [TD]22 [/TD] [TD]23 [/TD] [TD]24 [/TD] [TD] [/TD] [/TR] [TR] [TD] 44.4% [/TD] [TD] 33.6% [/TD] [TD] 23.9% [/TD] [TD] 15.9% [/TD] [TD] 9.7% [/TD] [TD] 5.4% [/TD] [TD] 2.7% [/TD] [TD] 1.2% [/TD] [TD] 0.4% [/TD] [TD] 0.1% [/TD] [TD] [/TD] [/TR] [/TABLE] Exploding dice add about 15% (on average) to those chances, although less so at the higher extremes. [/QUOTE]

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