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<blockquote data-quote="Nathan" data-source="post: 355241" data-attributes="member: 1342">I am very sorry about me having mistyped the formula when I posted it for the first time and thus confusing you.You are asking what kind of math is required... Hmm. I think the most important thing to deduce such a formula is your own brain and some logic. On the other hand, it is of course important to have some knowledge of the integers and basic probability theory (Laplace's notion of probability). And, one should have a good practice in manipulating formulas.I can recommend the following book:Graham, Knuth, Patashnik: &quot;Concrete Mathematics&quot;.If you have read (and worked with) this book, you should have developed a good skill manipulating numbers, formulas and deducing your own ones.Or, better: study maths, as I did <img src="https://cdn.jsdelivr.net/joypixels/assets/8.0/png/unicode/64/1f642.png" class="smilie smilie--emoji" loading="lazy" width="64" height="64" alt=":)" title="Smile&nbsp; &nbsp; :)"&nbsp; data-smilie="1"data-shortname=":)" />Now let's get a little bit more specific:And now some ideas I had developing the formula:Fix n, k, s. The experiment is rolling a die n times.How many possible outcomings does this experiment have? Answer: For every roll of a die, there are s outcomings. Therefore, we have s^n = s * s * ... * s (n times) in total.The next step is to divide the set of all outcomings. For every outcoming of our experiment lets us denote by t the value of the lowest die among the highest k ones in all n dice. Okay?Of course, t can have the following values: 1, 2, ..., s.Example (n = 5, k = 3, s = 6):Rolls: 1, 5, 6, 5, 2,: -&gt; corresponding t is 5.Rolls: 4, 2, 5, 1, 1 : -&gt; corresponding t is 2.Therefore we have divided the set of all results of our experiment (rolling n die) into s subsets parametrised by t.This will lead to summation over t in my above formula.Have you understood everything up to now?</blockquote>

[QUOTE="Nathan, post: 355241, member: 1342"] I am very sorry about me having mistyped the formula when I posted it for the first time and thus confusing you. You are asking what kind of math is required... Hmm. I think the most important thing to deduce such a formula is your own brain and some logic. On the other hand, it is of course important to have some knowledge of the integers and basic probability theory (Laplace's notion of probability). And, one should have a good practice in manipulating formulas. I can recommend the following book: Graham, Knuth, Patashnik: "Concrete Mathematics". If you have read (and worked with) this book, you should have developed a good skill manipulating numbers, formulas and deducing your own ones. Or, better: study maths, as I did :) Now let's get a little bit more specific: And now some ideas I had developing the formula: Fix n, k, s. The experiment is rolling a die n times. How many possible outcomings does this experiment have? Answer: For every roll of a die, there are s outcomings. Therefore, we have s^n = s * s * ... * s (n times) in total. The next step is to divide the set of all outcomings. For every outcoming of our experiment lets us denote by t the value of the lowest die among the highest k ones in all n dice. Okay? Of course, t can have the following values: 1, 2, ..., s. Example (n = 5, k = 3, s = 6): Rolls: 1, 5, 6, 5, 2,: -> corresponding t is 5. Rolls: 4, 2, 5, 1, 1 : -> corresponding t is 2. Therefore we have divided the set of all results of our experiment (rolling n die) into s subsets parametrised by t. This will lead to summation over t in my above formula. Have you understood everything up to now? [/QUOTE]

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