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Message: <blockquote data-quote="Steveyd" data-source="post: 4438818" data-attributes="member: 61233">[FONT=&quot]The success of the d20 roll is binary; a roll of a certain number or above is a success and a lower than that is failure.  There's not just a simple effective bonus because the bonus will change depending on the target number.Let's say you need a 12 or better to hit the monsters Armor Class.  The probability of a success is .45 on the first dice, and probability of failure is .55.  Now of those failures, the second dice has a probability of bailing you out of .45.  Thus the total probability of a failure on the first and a success on the second is .45*.55 = .2475, close to an effective +5 bonus, total possibility to succeed .6975.That changes though as AC increases, because the second dice also has a lower probability to roll high enough.  Say you need a 16 or better to hit, then P(Success) = .25, P(Failure)=.75, and P(Failure then Success) = .1875, an effective bonus of 3.75.  Total Success would be .4375.if you were really looking to give a bonus to eliminate dice rolling (though why is rolling 2 dice at once any harder?) you could look over the range of rolls typically needed and just go with something in there you feel appropriate.  +4 over the range of 14-17 on the dice required to hit the target number might be appropriate, though you are actually giving them a little bit better bonus against harder things and slightly shortchanging them against easier things.  If the BBEG that they need a 19-20 to actually hit shows up, then you are giving them a huge effective bonus to hit them if you stay with the keep 4.  I suggest just having them roll both dice at once.[/FONT][FONT=&quot] Of course, this is only to hit at all.  Factoring in criticals on 20 and automiss on 1 skews to having many more criticals and practically 0 critical misses in a session. [/FONT]  Here's the table:[ATTACH]36349[/ATTACH]</blockquote>

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