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<blockquote data-quote="orsal" data-source="post: 3534227" data-attributes="member: 16016">10.5, actually.An individual result can only be a whole number; the same is not true for the average.Why the next? Even if the average had to be an integer (which it clearly doesn't), why smallest one greater than the simple average of a single die?Look at it this way: You roll a die, then get to increase your result by rolling again, but with no loss if your reroll is less than your original roll. Suppose instead you were doing this with d1000s. Do you really think the reroll, which has approximately 50% chance of increasing your result, but if it does could increase it by up to 999, would on average increase it by less than 1?Captain Murphy would have the average as significantly less than 10. For example, any time you make an important roll that needs 5 or higher to succeed, Murphy would guarantee you a result no higher than 4. Unless you only make rolls with relatively low probabilties of success, there's no way Murphy's Law can be consistent with such results.</blockquote>[/QUOTE]

[QUOTE="orsal, post: 3534227, member: 16016"] 10.5, actually. An individual result can only be a whole number; the same is not true for the average. Why the next? Even if the average had to be an integer (which it clearly doesn't), why smallest one greater than the simple average of a single die? Look at it this way: You roll a die, then get to increase your result by rolling again, but with no loss if your reroll is less than your original roll. Suppose instead you were doing this with d1000s. Do you really think the reroll, which has approximately 50% chance of increasing your result, but if it does could increase it by up to 999, would on average increase it by less than 1? Captain Murphy would have the average as significantly less than 10. For example, any time you make an important roll that needs 5 or higher to succeed, Murphy would guarantee you a result no higher than 4. Unless you only make rolls with relatively low probabilties of success, there's no way Murphy's Law can be consistent with such results.[/QUOTE] [/QUOTE]

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