Plus or minus 3.325. On average.
That's the statistical impact of D&D Next's all-purpose mechanic to replace circumstance bonuses on d20 rolls: advantage (roll 2d20 and take the higher) and disadvantage (take the lower). But the impact across all possible chances is where this mechanic really shines.
The chart below plots out the effective bonus given by "advantage" across all possible chances to succeed against a given DC with a given bonus, from 1 in 20 to 19 in 20. I compare it against the flatter bonus given by the impossible but statistically equal +3.325.
At the same time, the advantage system doesn't favor long odds like the bonus system does, over on the left. And it makes it nearly impossible to fail when high skill and advantage coincide, with a final chance approaching 20 once added up, on the right.
It's styling, but most importantly, it's simple. One bonus fits all, is some good Old School mentality.
Probably the best rule to come out of d&dn.
ReplyDeleteThe Advantage/disadvantage system gives me a warm fuzzy. I can't wait to see how it works in play.
ReplyDelete- Ark
This is a great breakdown. Let's hope the stuff we see from D&D 5 is more like this than the dissociated stuff that's more prevalent in the playtest.
ReplyDeleteIt played really well at the table for me last night. I've always liked this mechanic, ever since I saw it in Philotomy's OD&D house rules for two-weapon fighting.
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So far, it seems they are consciously avoiding the dissociated design. The only possible exception is the use of some saving throws, like undead making wisdom saves to resist turning. That seems to be mechanics before meaning, to me.
Games Workshop has been using a similar mechanic for years now; granting the ability to re-roll failures. I think I prefer re-rolls because it allows the DM to grant advantage after the player rolls his die (in the case where he either forgot about it or the player can make a convincing argument that he should get it). Rerolling also lets you roll dice for multiple combatants at the same time without forcing you to pair up dice.
ReplyDeleteThese two methods would be identical as long as there isn't any sort of level of success mechanic.
The only pitfall of rerolls is that it cheats the roller out of potential critical hits they might have scored had they actually rolled 2 dice when they had advantage.
ReplyDeleteHow does a re-roll avoid criticals? If they get a 20 on either die, that's a critical, no, even if the second roll is deferred? What am I missing?
DeleteThe probability of rolling any one particular number increases when multiple dice are rolled at the same time as opposed to one die being rolled and then re-rolled. With a single die being rolled twice, your chances are 1 in 20 both times. However, with two dice rolled at the same time, you have a 1 in 20 chance on both dice, plus the possibility of both dice rolling the same result. So your chances of rolling a particular result actually increase. I know the math sounds funny, but I started looking into dice probability at one point and it's true.
DeleteThis feels like a misapplication of Monty Hall. If you're re-rolling, there's a 1/20 shot you hit a 20 and don't re-roll, and a 19/400 shot that you do re-roll and hit 20, so your crit chance is 39/400. If you roll both simultaneously, there's a 361/400 chance that neither hits 20, leaving a 39/400 chance that you hit 20 at least once. What am I missing?
DeleteThis depends, I guess, on whether you reroll only on a miss. I'd just play it as rolling two dice simultaneously, though.
DeleteCharlatan75, you're right that rolling both simultaneously gives a 39/400 chance of crit, i.e 9.75%.
DeleteBut you're missing that you aren't re-rolling every non-crit, you're just re-rolling every miss. So say for example that the combination of modifiers, AC etch is such that you hit on an 8+ (which not uncommon).
That means you only reroll if the first die is 7 or lower, so your chance of crit is a little under 6.67 percent.
So Monty Hall is very much relevant.
The math for rolling both simulateously is:
1 - 19/20 * 19/20 = 9.75%
For rolling one after the other on a 8+ to hit is:
1 - 19/20 * (1 - 7/20 * 1/20)
This is not the biggest reason I have for not granting rerolls after the fact. I dislike it because it feels jarring to me. First you fail, and then, whoops, you succeeded after all. (Never was that sold on the "Fortunue in the Middle"-idea.)
I forgot to finish this equation:
Delete1 - 19/20 * (1 - 7/20 * 1/20) = 533/8000 < 6.66%
I forgot about criticals (as I don't particularly care for them in the first place). However, I would still suggest the DM use the reroll method for packs of identical monsters. I don't think anyone will be too upset if a horde of goblins misses out on a few criticals.
ReplyDeleteI really don't like the rule - it's just bonuses for the sake of bonuses to end combat faster, which, if you are coming from a slow edition is a good thing but if you already have fast combat then there's nothing to see here.
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