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Message: <blockquote data-quote="Gez" data-source="post: 2241217" data-attributes="member: 1328">Three shots with a 20% chance to hit for each shot results in:20% × 20% × 20% chance of all three hitting, so 0.8% of triple damage.(20% × 20% × 80%) + (20% × 80% × 20%) + (80% × 20% × 20%) of two of the shots hitting, so 9.6% of double damage.(80% × 80% × 20%) + (80% × 20% × 80%) + (20% × 80% × 80%) of one of the shots hitting, so 38.4% of single damage.80% × 80% × 80% of none of them hitting, so 51.2% chance of no damage.So, you the average damage will be: (51.2×0 + 38.4×1 + 9.6×2 + 0.8×3)/100Which amounts to 0.6. A 60% chance of dealing single damage, and 40% chance of missing altogether, would yield the same statistical average damage.Indeed, three separate 20% chance of something happening is not the same as a single 60% chance of said thing happening... But that's because you're reasonning in a binary mode, either it happens, or it doesn't. D&D is more quantitative than that, either it doesn't happen, or it does, in a varying number of occurences.Similarly, if you have only two attacks but with a 30% chance to hit (+10 is equivalent to +2 on a d20), then, what do we see?30% × 30% of double damage (09%).(30% × 70%) + (70% × 30%) of single damage (42%).70% × 70% of no damage (49%).(49×0 + 42×1 + 9×2)/100Which amounts to... 60% again...</blockquote>