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Relevant: Does Indomitable let you reroll Saving Throws with Advantage?

There's a line that comes up a lot in class abilities that seems out of place, and I don't know what the difference is between it and using the established "Advantage" in fifth edition.

It usually says something like this:

If you fail a saving throw, you can reroll it, and you must use the new roll.

Compared to (Dis)Advantage which is

Use the higher of the two rolls if you have advantage, and use the lower roll if you have disadvantage

Based on the linked post, I have found out that these do not stack.

What's the difference between the first quote and just having advantage for that saving throw roll?

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  • \$\begingroup\$ Are you asking for the mathematical difference or the theoretical difference? \$\endgroup\$ – NautArch Jul 26 '18 at 16:34
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    \$\begingroup\$ I suppose theoretical, as it's likely to receive more reference in play. \$\endgroup\$ – Daniel Zastoupil Jul 26 '18 at 16:36
  • \$\begingroup\$ How do you mark a specific answer when there's 3 valid answers that address the question? \$\endgroup\$ – Daniel Zastoupil Jul 26 '18 at 16:57
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    \$\begingroup\$ If you don't think there's a single answer, you don't have to select one. I'd also (as always) suggest you wait awhile for other answers to come in, for answers to be updated/edited as comments roll in, etc. I generally wait about 24 hours before selecting an answer (if I feel one should be selected.) \$\endgroup\$ – NautArch Jul 26 '18 at 17:03
  • \$\begingroup\$ I removed Statistics as a tag and reference in the wording given your statement above that you're not looking for statistics but theoretical difference. \$\endgroup\$ – NautArch Jul 26 '18 at 17:18
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Advantage and rerolling are statistically equivalent, except for interaction with each other and a few specific game mechanics.

For many rolls you only need to roll the target number or higher to succeed, and it the margin by which you succeed or fail doesn't particularly matter. You have nothing to lose by rerolling a fail, and (except for the slim chance of a critical hit) it's not worth the risk of rerolling a success.

In this situation, at the most basic level, advantage and rerolling are functionally the same: you succeed if at least one of two dice roll a success. We can model this scenario using logic gates:

  • The truth table for Advantage is an or gate: You succeed as long as at least one of the rolls is a success.
  • The truth table for Reroll is also effectively the same as an or gate, except that the results True/True and True/False are invalid and collapse down to True. If the first roll succeeds, the result is a success, and there is no need to use the reroll, so the second roll is irrelevant. If the first roll fails, and the reroll succeeds, then you pass.

In either case, you only fail on two failed rolls, and all other possible results are a success. The two are functionally equivalent for simple cases of boolean success or failure.

However, there are a few complications, in practice:

  • The benefit of a reroll-based ability is that you may have both a reroll and another source of advantage, which is better than just advantage; whereas you cannot stack two sources of advantage.
  • The benefit of Advantage is that it will cancel disadvantage, and certain abilities may trigger on advantage, such as a rogue's sneak attack.
  • In some cases, such as those monster attacks which have an even worse effect if you fail by 5 or more, the reroll can actually make things worse. You'd much rather have advantage in this scenario.
  • Critical hits will happen slightly more often with advantage than with rerolls, since you'll rarely reroll an attack which hits.

Advantage is generally slightly better since its only drawback is that it can't stack with advantage, and lots of things already give advantage. Conversely, and to answer your question directly, a reroll's main benefit is that it stacks with advantage, and lots of things give advantage.

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  • \$\begingroup\$ Would the reroll gain advantage as well? \$\endgroup\$ – Daniel Zastoupil Jul 26 '18 at 16:38
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    \$\begingroup\$ The reroll wouldn't, but the first one would, so they can still stack because you're effectively getting 3 chances to make the save. Two from advantage and an additional from the reroll. \$\endgroup\$ – Blake Steel Jul 26 '18 at 16:51
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    \$\begingroup\$ You just gave several examples that show they are not effectively the same. Edge cases or not, they are cases and their degree of edge is variable and dependent on the situation. \$\endgroup\$ – NautArch Jul 26 '18 at 16:58
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    \$\begingroup\$ @QuadraticWizard I think it may have to do with the fact that your answer originally said "None" for the difference, which was a noticeable difference from your current one, and they likely downvoted for the original answer and never reviewed it later to fix their opinion. Also, while it is cleaned up now, the summary about the Advantage gate was a bit disorienting a few revisions ago, and was a bit difficult to follow along. Either way, the answer you have now is excellent. \$\endgroup\$ – Daniel Zastoupil Jul 27 '18 at 14:54
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    \$\begingroup\$ I think that one other advantage of reroll rather than advantage is timing; an ability that grants advantage may have to be activated before your roll, while a reroll can be used once you know what come up on the first one. \$\endgroup\$ – Elia Jul 27 '18 at 19:59
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It's about being able to take the Higher, and only advantage gives you that.

Advantage lets you use the higher die, while rerolling and keeping the 2nd roll does not. You may roll lower on your 2nd roll and you'd be stuck with that value.

Saving Throws

In the case of saving throws, there are some saving throws that cause additional effects depending on the result.

An example is the Ghost's Horrifying Visage:

Each non-undead creature within 60 feet of the ghost that can see it must succeed on a DC 13 Wisdom saving throw or be frightened for 1 minute. If the save fails by 5 or more, the target also ages 1d4 × 10 years. A frightened target can repeat the saving throw at the end of each of its turns, ending the frightened condition on itself on a success.

In this case, you may have failed by 3 but want to reroll to try and save. Your reroll fails by 5 and you now suffer the aging effect which you wouldn't have done with the saving throw rolled with advantage; that would have let you choose the fail by 3.

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    \$\begingroup\$ It might also be worth sharing an example of rolling a save, such as a death save, where you probably wouldn't want to use a reroll for an 18 but advantage gives you an extra chance at a 20 without the risk of the reroll. The danger of your reroll coming up as a 1 on a death save is similar to your Horrifying Visage example. \$\endgroup\$ – Nick Brown Jul 27 '18 at 0:06
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The only time there's a difference between these two methods would be if you can critically succeed (i.e. a higher roll than just the success/fail mark is actually better).

For saving throws, that's an irrelevant difference since a higher roll than a success doesn't do you any good (e.g. DC 15, it doesn't matter if you roll 16 or 26, they're effectively the same).

If the other rule (not Advantage) was applied in other cases, like Attack Rolls, then it'd be slightly less good. The reason for this is that Advantage gives you 2 chances to roll a natural 20 for a critical hit, regardless of the other die's roll. However, the "reroll if fail" method has the margin where you hit but didn't get a critical hit, where you wouldn't get another die to possibly get a critical hit. In that case, the statistical difference depends on the number on the die you need to roll to hit (if you need to roll a 20 to hit at all, there's no difference, whereas if you hit on a 2 there's a huge difference between the methods).

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It's not Advantage (which doesn't stack with itself) so you can use both functions. If you fail a roll with Advantage (or Disadvantage) you still have the ability to reroll it, using such class features.

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  • \$\begingroup\$ True, although you will only be able to reroll one die, not two. \$\endgroup\$ – Gandalfmeansme Jul 26 '18 at 19:02
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    \$\begingroup\$ In the grand scheme of things, rerolling only one die is still good: if you were disadvantaged, now you aren't! If you are advantaged (and still failed!) it's still a third die. Pretty much only benefits. \$\endgroup\$ – Draco18s Jul 27 '18 at 0:41
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Several people have already laid out the advantages of advantage - critical hits, triggering abilities, cancelling disadvantage - as well as the benefit of having both together - they stack. There is one big advantage to a reroll (as a limited-use ability), though: you only use it when you need it.

Say I give myself advantage on a save, and roll my two dice one at a time. If the first die is a success, then I have wasted my ability - my original roll would have been a success, so I didn't need the second one. On the other hand, with a reroll, I roll my second die only after seeing the result of the first one, so it is always capable of making a difference

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