Ascalaphus wrote:Dice analysis above (I've posted link) shows that average roll on "2d20 take best" is 15.
Actually it's closer to a +2.5 on the roll, based on a million trials. Taking the best od 2d20 will give you an average of 13.
Yeah, I checked out those links and ran some experiments myself. It's actually doable to test this without any random trials, because it's easy to just enumerate all the possible results of rolling 2d20. That's only 20 x 20 = 400 combinations. So you take the average of max(A, B) for all the possible results of dice A and B, and that's 13. Compared to the average result of rolling just die A and getting a 10.5, that's just a +2.5 bonus.
Where it's sweet however is in the probability distribution. If you roll 1d20 you have a perfectly flat distribution. Your chance of rolling average or bad is the same. By rolling more dice however, the chance of outliers decreases.
One of the other articles referenced in the article you quoted does a much better job of explaining that (with the nice graph) than the one you quoted. LINK
Basically, rolling more dice means you're more likely to have a "normal" performance instead of an occasional extreme failure. If you needed to roll a 11 to save, that's 50% chance on 1d20, but 75% chance on 2d20 drop lowest. (Exactly.) That's where his "+5" comes from. It's not really a +5 bonus, because if the DC is higher it doesn't help quite so much.
Suppose you need to roll a 18 to save. That's a 15% chance of success. With two dice it's 27.75% chance of success; more like a +3. And if you need a 20 to save then it's 5% vs. 9.75%, so only a +1.
(I generated the probabilities through enumerating all the possibilities, rather than through simulation like he did. The numbers are close but not exactly the same. These are my probabilities of getting at least X, using 2 dice: [1.0, 0.9975, 0.99, 0.9775, 0.96, 0.9375, 0.91, 0.8775, 0.84, 0.7975, 0.75, 0.6975, 0.64, 0.5775, 0.51, 0.4375, 0.36, 0.2775, 0.19, 0.0975])
On the low DC front: suppose you needed only a 4 to save (85%). With two dice that's a 97.75% chance, so again a +3. If you only needed a 2 to save (because a 1 always fails), you go from 95% to 99.75%, so only a +1.
TL;DR - this item does something different from just giving a +5 bonus. It reduces randomness. If you could probably make the check, now you're much more likely to. If it was a long shot anyway, it becomes only a little bit more likely that you'll succeed.
On the whole, it's a very good item. It's good protection against midrange enemies, not so much against the end boss.