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Message: <blockquote data-quote="Pbartender" data-source="post: 2002254" data-attributes="member: 7533">The probability of success does not depend on the actual results of the rolls, only the distribution of the probabilities...  Which are identical and independent for both rollers, since they are using two independent but identical dice.  In such an instance (and ignoring any other modifiers to the score), the probability of success for either player is always 50%, with small adjustments for how ou treat a tie.Trust me, I got full marks on that exam question.   <img src="https://cdn.jsdelivr.net/joypixels/assets/8.0/png/unicode/64/1f609.png" class="smilie smilie--emoji" loading="lazy" width="64" height="64" alt=";)" title="Wink    ;)"  data-smilie="2"data-shortname=";)" />No it's not.  You're looking at it wrong.  You are not rolling 2d20, you are two 1d20's and comparing the results.  You don't have one bell curve (2d20 wouldn't be a bell curve anyway, but that's beside the point), you have two linear curves that are identical.  The real point is that the shape of the curves don't make a difference, so long as both players are using the same probability curve, and result of one playr's roll doesn't affect the result his opponent's roll.</blockquote>