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<blockquote data-quote="EzekielRaiden" data-source="post: 6877894" data-attributes="member: 6790260">Exactly. Rerolling happens 0% of the time that you roll an acceptable value, and 100% of the time that you roll an unacceptable value. Therefore, the probability of rerolling is conditional upon what the result of the original roll was.Or, putting it very, VERY simply: The probability of flipping a fair coin and getting heads is 0.5. The probability of flipping two coins and getting at least one head is 0.75. This is equivalent to getting exactly ONE re-flip if the first doesn't work. The probability of flipping n coins and getting at least one head is (1-2^n); this is equivalent to getting n re-flips, stopping as soon as you get a head. The probability of getting a head if you flip an infinite number of coins is 1, because lim(n-&gt;infinity) 1-2^-n = 1; this is equivalent to flipping coins until you get a head.This exact same process applies to non-uniform distributions, it's just more complex to determine their probabilities. If the odds of getting a rejectable result on an unmodified roll are, say, 10%, then the infinite series for getting a non-rejectable result is lim(n-&gt;infinity) 1-10^-n = 0.999999... = 1. And so on.</blockquote>

[QUOTE="EzekielRaiden, post: 6877894, member: 6790260"] Exactly. Rerolling happens 0% of the time that you roll an acceptable value, and 100% of the time that you roll an unacceptable value. Therefore, the probability of rerolling is [I]conditional[/I] upon what the result of the original roll was. Or, putting it [I]very, VERY[/I] simply: The probability of flipping a fair coin and getting heads is 0.5. The probability of flipping two coins and getting [I]at least one[/I] head is 0.75. This is equivalent to getting exactly ONE re-flip if the first doesn't work. The probability of flipping [I]n[/I] coins and getting at least one head is (1-2^n); this is equivalent to getting [I]n[/I] re-flips, stopping as soon as you get a head. The probability of getting a head if you flip an infinite number of coins is 1, because lim(n->infinity) 1-2^-n = 1; this is equivalent to flipping coins until you get a head. This exact same process applies to non-uniform distributions, it's just more complex to determine their probabilities. If the odds of getting a rejectable result on an unmodified roll are, say, 10%, then the infinite series for getting a non-rejectable result is lim(n->infinity) 1-10^-n = 0.999999... = 1. And so on. [/QUOTE]

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