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<blockquote data-quote="Nathan" data-source="post: 354986" data-attributes="member: 1342">The problem is that I have no sum symbol (the greek letter &quot;Sigma&quot;) on my keyboard. With it, it would have been easier for me to post the formula.And now to your question:1) Yes, you sum up over all possibilities of the triple (t, l, r).However, I made a MISTAKE! One has to sum t from 1 to s, not to k, which doesn't make much sense.2) After summing up everything you divide! IMPORTANT: I made a second mistake when I posted the formula. At the end you have to divide by the number of all possible rolls which is s^n and not s^k! Please correct the formula in this way.3) Why do you have problems with fixed n and k? Just plug them into the formula and you get a new one depending only on s. Of course it is worthy to ask if the new formula can be further simplified.4) MORE Brackets: Put a big &quot;(&quot; after the word &quot;of&quot; and a big &quot;)&quot; before the word &quot;over&quot;. The precendence of the operators &quot;+&quot;, &quot;-&quot;, &quot;*&quot;, &quot;/&quot;, &quot;^&quot; is the usual one, i.e. &quot;^&quot; binds more the &quot;*&quot; and &quot;/&quot;, &quot;*&quot;, &quot;/&quot; bind more than &quot;+&quot;, &quot;-&quot;. Otherwise, everything is to be read from left to right.5) Example: n = 2, k = 1 (i.e. better die of two rolls):We have to sum t from 1 to s, l from 0 to 1 and r from 1 to 1, i.e. is fixed and no summing needed.Plug these values (n = 2, k = 1, r = 1) in the big summand and you will get a formula without n, k and r which is to be summed over t from 1 to s and over l from 0 to 1 (which you can write with an ordinary &quot;+&quot; sign).Please note three things: 0! = 1 by definition, x^0 = 1 by definition and1+2+3+4+5+6+...+x = x*(x+1)/2 which can be of use for the case E(2,1,s).Evaluating the formula, I'll get:E(2, 1, s) = (4*s^3+3*s^2-s)/(6*s^2).(I summed up analytically.)For example E(2, 1, 6)= 4,47...If you are still interested in the topic I will explain this in further detail.</blockquote>

[QUOTE="Nathan, post: 354986, member: 1342"] The problem is that I have no sum symbol (the greek letter "Sigma") on my keyboard. With it, it would have been easier for me to post the formula. And now to your question: 1) Yes, you sum up over all possibilities of the triple (t, l, r). However, I made a MISTAKE! One has to sum t from 1 to s, not to k, which doesn't make much sense. 2) After summing up everything you divide! IMPORTANT: I made a second mistake when I posted the formula. At the end you have to divide by the number of all possible rolls which is s^n and not s^k! Please correct the formula in this way. 3) Why do you have problems with fixed n and k? Just plug them into the formula and you get a new one depending only on s. Of course it is worthy to ask if the new formula can be further simplified. 4) MORE Brackets: Put a big "(" after the word "of" and a big ")" before the word "over". The precendence of the operators "+", "-", "*", "/", "^" is the usual one, i.e. "^" binds more the "*" and "/", "*", "/" bind more than "+", "-". Otherwise, everything is to be read from left to right. 5) Example: n = 2, k = 1 (i.e. better die of two rolls): We have to sum t from 1 to s, l from 0 to 1 and r from 1 to 1, i.e. is fixed and no summing needed. Plug these values (n = 2, k = 1, r = 1) in the big summand and you will get a formula without n, k and r which is to be summed over t from 1 to s and over l from 0 to 1 (which you can write with an ordinary "+" sign). Please note three things: 0! = 1 by definition, x^0 = 1 by definition and 1+2+3+4+5+6+...+x = x*(x+1)/2 which can be of use for the case E(2,1,s). Evaluating the formula, I'll get: E(2, 1, s) = (4*s^3+3*s^2-s)/(6*s^2). (I summed up analytically.) For example E(2, 1, 6) = 4,47... If you are still interested in the topic I will explain this in further detail. [/QUOTE]

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