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<blockquote data-quote="TeeSeeJay" data-source="post: 680609" data-attributes="member: 9969">For any n-sided die (1dn), the following is true:1/n * 100 = % chance of rolling any number from 1 to nFor a roll of 2dn in which the results are summed, the following is true:The total number of combinations is n^2The median, mode, and mean of 2dn = n+1The % chance to roll the mode value is 1/n * 100The number of possible rolls equal to the mode is nTherefore,A roll of 2d8 is 12.5% likely to result in a value of 9, which is the same chance of rolling any given number on 1d8. There are 64 different combinations, 9 of which sum to 9. 9 is also the median value and the average value of these 64 combinations.I'm posting this because I'm generally not very good with statistics and probability and just want to make sure I understand this correctly.Is there any similar patterns to easily determine the various probablities of larger rolls, like 3dn? Probably not, since the numbers get very large.The mode of 3d6 = 10The mode of 3d4 = 7The mode of 3d2 = 4The pattern is mode(3dn)=mode(2dn)+(n/2)So, that would mean mode(3d8)=9+4=13mode(3d10)=11+5=16mode(3d12)=13+6=19mode(3d20)=21+10=31I'm not about to verify these the hard way. Can anyone point me to relevant web sites that might have such formulas available? I wasn't able to find anything helpful through my own searches.My head hurts now.</blockquote>

[QUOTE="TeeSeeJay, post: 680609, member: 9969"] For any n-sided die (1dn), the following is true: 1/n * 100 = % chance of rolling any number from 1 to n For a roll of 2dn in which the results are summed, the following is true: The total number of combinations is n^2 The median, mode, and mean of 2dn = n+1 The % chance to roll the mode value is 1/n * 100 The number of possible rolls equal to the mode is n Therefore, A roll of 2d8 is 12.5% likely to result in a value of 9, which is the same chance of rolling any given number on 1d8. There are 64 different combinations, 9 of which sum to 9. 9 is also the median value and the average value of these 64 combinations. I'm posting this because I'm generally not very good with statistics and probability and just want to make sure I understand this correctly. Is there any similar patterns to easily determine the various probablities of larger rolls, like 3dn? Probably not, since the numbers get very large. The mode of 3d6 = 10 The mode of 3d4 = 7 The mode of 3d2 = 4 The pattern is mode(3dn)=mode(2dn)+(n/2) So, that would mean mode(3d8)=9+4=13 mode(3d10)=11+5=16 mode(3d12)=13+6=19 mode(3d20)=21+10=31 I'm not about to verify these the hard way. Can anyone point me to relevant web sites that might have such formulas available? I wasn't able to find anything helpful through my own searches. My head hurts now. [/QUOTE]

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