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Message: <blockquote data-quote="Esker" data-source="post: 7620983" data-attributes="member: 6966824">I think your conclusion -- that Lucky helps about as much when you have advantage as when it doesn't, on average -- is more or less right, but I think the reasoning is missing some pieces. On most rolls the number you get doesn't particularly matter, only whether you meet the DC or not (or, in the case of an attack, whether you crit). So rerolling a 1 and getting a 2 technically increased your roll, but isn't going to make any difference outside the easiest of easy rolls.    On a straight-up roll (no advantage or disadvantage) with a baseline success chance of p, Lucky increases the success chance to p + 0.05 * p, that is by 5% of the baseline success chance. For a typical case where the success chance is around 60% or so, that's an increase of 3%.    For the same DC but with advantage, the non-halfling has a 1 - (1 - p)^2 success chance (for the 60% case without advantage, that's 84%). Applying Lucky, we typically only care about rerolls when we otherwise failed (on attack rolls we can still reroll for another chance at a crit, but that's a separate case). The chance that the first die shows a 1 and the second die is low enough for a failure is 0.05 * (1 - p). The chance that the second die shows a 1 and the first is low enough for a failure is (1 - p) * 0.05. So the chance that we get to reroll in a situation where we would have failed otherwise is approximately 0.10 * (1 - p). (We technically need to reduce that by 0.05^2 since we're double counting the double ones case, but let's set that aside for simplicity). Then, the chance that the reroll nets us a success is just p. So we have a marginal benefit of 0.10*(1-p)*p.   This represents an extra factor of 2 * (1 - p) compared to the non-advantage case.   That means for rolls where we need a natural 11 or better to succeed, it's the same benefit that we have without advantage (well, 0.25% less). For more difficult rolls, the benefit is more than that; for easier ones, less. Taking 60% as a typical case, that means the halfling actually benefits slightly less from Lucky when they have advantage, if we measure in terms of the additive increase to the chance of success.    The increase to crit chance is simpler: 0.05^2 in the straight-roll case, and a bit less than twice that in the advantage case. Since going from a miss to a hit is worth more than going from a hit to a crit, the extra 0.05^2 ish crit chance we get with advantage doesn't balance the 0.05^2 that we ignored for simplicity above.</blockquote>

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