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Average Damaged By Different Dice?
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<blockquote data-quote="Plane Sailing" data-source="post: 158183" data-attributes="member: 114"><p>Since nobody else has explicitly mentioned this aspect, I might as well bring it up.</p><p></p><p>When rolling 2d6 your chance of getting minimum damage (or maximum damage) is 1 in 36. i.e. two 1's or two 6's respectively. With 1d12 on the other hand your chance of getting minimum or maximum damage is 1 in 12.</p><p></p><p>Thus the single die as a greater chance of getting to one of the extremes of damage.</p><p></p><p>In fact, with a single d12 there is an equal chance of any of the numbers from 1 to 12 coming up (1 in 12).</p><p></p><p>With 2d6 you get a "distribution curve". There is one way of rolling 12 (6 & 6), two ways of rolling 11 (6 & 5 or 5 & 6) through to six ways of rolling 7 (6&1, 5&2, 3&4, 1&6, 2&5, 4&3). The 2d6 weapon has a significantly higher chance of getting its "average" damage on any particular roll than of getting its maximum (or minimum) damage.</p><p></p><p>The more dice which are rolled, the harder it is to get the maximum. The chance of getting 60 damage from a 10d6 fireball is astonishingly tiny (unless you use Maximise <img src="https://cdn.jsdelivr.net/joypixels/assets/8.0/png/unicode/64/1f609.png" class="smilie smilie--emoji" loading="lazy" width="64" height="64" alt=";)" title="Wink ;)" data-smilie="2"data-shortname=";)" />)</p><p></p><p>--- People still talk about a d8 having an average of 4.5 (for the calculated reasons given above) because over a period of time the total number of d8's that you roll will tend towards a middle number. If you rolled 10d8 you would be much more likely to get a number near 45 than near 80 (for the reasons I explained in the 2d6 example above). Talking about average damage in this way is shorthand for saying "over the length of a campaign when you are rolling a d8 all the time your average roll would be about 4.5 if you added them all up and averaged them".</p><p></p><p>Incidentally this is a practical reason why on critical hits you roll and add the damage for the multiplier rather than just multiply your initial roll. Otherwise an Orc that critically hits you would have a 1 in 12 chance of doing 42 points damage! Since he has to roll each d12 separately he actually has only a 1 in 1728 chance of doing that (three 12's in a row).</p><p></p><p>Cheers</p></blockquote><p></p>
[QUOTE="Plane Sailing, post: 158183, member: 114"] Since nobody else has explicitly mentioned this aspect, I might as well bring it up. When rolling 2d6 your chance of getting minimum damage (or maximum damage) is 1 in 36. i.e. two 1's or two 6's respectively. With 1d12 on the other hand your chance of getting minimum or maximum damage is 1 in 12. Thus the single die as a greater chance of getting to one of the extremes of damage. In fact, with a single d12 there is an equal chance of any of the numbers from 1 to 12 coming up (1 in 12). With 2d6 you get a "distribution curve". There is one way of rolling 12 (6 & 6), two ways of rolling 11 (6 & 5 or 5 & 6) through to six ways of rolling 7 (6&1, 5&2, 3&4, 1&6, 2&5, 4&3). The 2d6 weapon has a significantly higher chance of getting its "average" damage on any particular roll than of getting its maximum (or minimum) damage. The more dice which are rolled, the harder it is to get the maximum. The chance of getting 60 damage from a 10d6 fireball is astonishingly tiny (unless you use Maximise ;)) --- People still talk about a d8 having an average of 4.5 (for the calculated reasons given above) because over a period of time the total number of d8's that you roll will tend towards a middle number. If you rolled 10d8 you would be much more likely to get a number near 45 than near 80 (for the reasons I explained in the 2d6 example above). Talking about average damage in this way is shorthand for saying "over the length of a campaign when you are rolling a d8 all the time your average roll would be about 4.5 if you added them all up and averaged them". Incidentally this is a practical reason why on critical hits you roll and add the damage for the multiplier rather than just multiply your initial roll. Otherwise an Orc that critically hits you would have a 1 in 12 chance of doing 42 points damage! Since he has to roll each d12 separately he actually has only a 1 in 1728 chance of doing that (three 12's in a row). Cheers [/QUOTE]
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