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<blockquote data-quote="Lonely Tylenol" data-source="post: 3816704" data-attributes="member: 18549">I actually did some calculations on the back of a napkin a few months ago regarding this very question, and came up with this: the chance of rolling any particular number (in this case, 1) on an n-sided die over n trials approaches ~63% as n approaches infinity.&nbsp; Having only basic finite math and calculus, I can't tell you why 63% in particular, but that's the number I got.&nbsp; I didn't bother to actually calculate the limit, to determine whether it's actually asymptotic or not, or figure out the actual value of the limit.&nbsp; ~63% is what came back for a d1000000, and all other arbitrarily large values I tried, so that's good enough for me.Anyway, if a 1 comes up in 20 trials about 63% of the time, then rolling a 1 in 14 trials 51% of the time seems like a pretty reasonable estimate.Edit:I ran the numbers again in Excel, using the formula that the chance of rolling 1 on ndn is equal to 1-((n-1)/1))^n.&nbsp; I got the following:[code]die&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; chance4&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 0.6846&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 0.6658&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 0.65610&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 0.65112&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 0.64820&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 0.64230&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 0.638100&nbsp; &nbsp; &nbsp; &nbsp; 0.6341000&nbsp; &nbsp; &nbsp;&nbsp; 0.63210000&nbsp; &nbsp;&nbsp; 0.632100000&nbsp;&nbsp; 0.632etc.[/code]edit again: I also used my formula to double check your calculations, and they're all correct.</blockquote>

[QUOTE="Lonely Tylenol, post: 3816704, member: 18549"] I actually did some calculations on the back of a napkin a few months ago regarding this very question, and came up with this: the chance of rolling any particular number (in this case, 1) on an n-sided die over n trials approaches ~63% as n approaches infinity. Having only basic finite math and calculus, I can't tell you why 63% in particular, but that's the number I got. I didn't bother to actually calculate the limit, to determine whether it's actually asymptotic or not, or figure out the actual value of the limit. ~63% is what came back for a d1000000, and all other arbitrarily large values I tried, so that's good enough for me. Anyway, if a 1 comes up in 20 trials about 63% of the time, then rolling a 1 in 14 trials 51% of the time seems like a pretty reasonable estimate. Edit: I ran the numbers again in Excel, using the formula that the chance of rolling 1 on ndn is equal to 1-((n-1)/1))^n. I got the following: [code] die chance 4 0.684 6 0.665 8 0.656 10 0.651 12 0.648 20 0.642 30 0.638 100 0.634 1000 0.632 10000 0.632 100000 0.632 etc.[/code] edit again: I also used my formula to double check your calculations, and they're all correct. [/QUOTE]

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