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Message: <blockquote data-quote="Agback" data-source="post: 886815" data-attributes="member: 5328">None of them. We are talking about the expected value, which is like a mean but subtlely different.The expectation of a discrete distribution (like 4d6) is calculated by multiplying each possible outcome by its probability of occurring, and then adding together the products.If you roll 4d6 n times, sum the n rolls, and divide by n, you will have the mean of those particular rolls. For given n, that will be sometimes more and sometimes less: it will be a random variable (it is called the sample mean, and its symbol is an X with a bar across the top). But if you make n really big, the chances are very small that X-bar will be very far from mu, where mu is the expected value. (For discrete distributions, the expected value corresponds to a thing called the population mean, but the point is not extensible to continuous distributions, and tends not to get a lot of attention in real statistics.)Example:2d6 has eleven possible outcomes (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12). Their probabilities are (1/36, 1/ 18, 1/12, 1/9, 5/36, 1/6, 5/36, 1/9, 1/12, 1/18, 1/36). Multiply each possible outcome by its own probability and you get (2/36, 6/36, 12/36, 20/36, 30/36, 42/36, 40/36, 36/36, 30/36, 22/36, 12/36). Add those up and you get 252/36 = 7. The expectation of 2d6 is 7.Now I roll 2d6 eleven times and get (5, 4, 7, 11, 3, 8, 3, 9, 7, 8, 7). That sample has a mean of 6 6/11 (and it has a median of 7 and a mode of 7), but it doesn't have an expectation because it is a sample, not a distribution. Meanwhile, 2d6 has an expectation of 7, doesn't have a mean, and doesn't have a median, because it is a distribution, not a sample. (A distribution does have a mode, but in a slightly different sense from that in which a sample does. The mode of 2d6 is 7.)Regards,Agback</blockquote>

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