D&D 5E Advantage vs. re-rolls

[Enevhar Aldarion]

Yep. If a player rolls a 16 and hits, he is unlikely to force a reroll hoping for a critical. Now, if he knows he hits on a 1, he probably will since it can't hurt.

Well, since rolling a 1 in combat is an auto-miss, no matter the amount of pluses you add, you may want to say "if he knows he hits on a 2". Because if you roll a 1 on the first roll, and you have a re-roll available, you are going to use it.

Now, if you are talking anything other than combat and death saves, then yes, there is a chance of success when rolling a 1.

 

[guachi]

I don't get why Zapp has invented the idea that the reroll or advantage costs something. Nowhere in the OP does he mention it.

As far as I'm aware, no poster was responding to Zapp's invention of the reroll/advantage costing something. And yet, Zapp proceeded to insult people who correctly responded to the OP by saying that in a strict pass/fail there is no difference between reroll and advantage.

Now, if you had to spend some resource to either reroll or get advantage then of course reroll is better. But that's obvious enough it's not worth asking the question.

 

[Shiroiken]

I don't get why Zapp has invented the idea that the reroll or advantage costs something. Nowhere in the OP does he mention it.

Because if there's no cost, advantage is always better, which doesn't fit the OP ("how much better is re-roll"). My original comment mentioned the assumption that an opportunity cost was present (such as x/day).

 

[Shiroiken]

Maybe I am just misunderstanding the way people are writing things, but you do know Advantage is not a re-roll. With Advantage, and Disadvantage, you roll both d20s at the same time, not one and then the other.

You can do either, which was part of the point of the system (if you forget you have advantage, you can just roll another die). When I play, I normally have a "standard" d20 and "(dis)advantage" d20 so that I know if the advantage helped or if the disadvantage hurt.

 

[CapnZapp]

Okay then.

Seems like everything's straightened out, even though it looked thorny there for a while

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[CapnZapp]

I don't get why Zapp has invented the idea that the reroll or advantage costs something. Nowhere in the OP does he mention it.

As far as I'm aware, no poster was responding to Zapp's invention of the reroll/advantage costing something. And yet, Zapp proceeded to insult people who correctly responded to the OP by saying that in a strict pass/fail there is no difference between reroll and advantage.

Now, if you had to spend some resource to either reroll or get advantage then of course reroll is better. But that's obvious enough it's not worth asking the question.

A few easy asks of you, Guachi.

If you want to talk to me, I'm here. No need to mention me in the third person as if I wasn't here.

If I have insulted someone, let that party call it out. Don't invent controversies.

As for your main question, you have gotten an answer. (Thanks Shiroiken) There was no need to get conspiratorial. I was just trying to help.



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[Yunru]

A re-roll is at best equal to advantage. That is, if you get to re-roll after knowing the outcome, and the outcome would be a failure. Or if you're re-rolling dice with which you had advantage.

Advantage is roll 2, pick the one you want best.
As such, advantage will always net you the best of the rolls.

Re-roll is roll 1, then decide if you want that one. If not, roll again.
As such, re-rolling will only net you the roll you choose, whether or not it's better.


There is an edge case:
Advantage doesn't stack, while re-rolling does.

 

[Ilbranteloth]

Mathematically there's no difference in the isolated case.

Of course a reroll is better in that you get to see the first roll before deciding to use it.

So, assuming 50% chance of success, one free advantage (such as the one from Inspiration) is worth +25%.

The reroll is the same, except you get to keep it half the time ( and still succeed).

Ergo, you could say in this case the reroll is twice as good as the advantage, on average.

It should be easy to see that while the numeric advantage of both advantage and reroll decreases as your probability of success goes up, the relative benefit of the reroll also go up (since you're more likely to not have to use it, ie keep it).

Whether the decrease in actual utility is matched by the relative utility (of the reroll over the advantage) we need math to tell us.

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Yes, it's exactly the same unless you are expending a resource. Then the re roll is better since you won't have to spend the resource if you succeed on the first roll.

 

[Ilbranteloth]

If the result is a simple pass/fail where the level of success or failure doesn't matter then advantage and reroll on failure offer the same benefit assuming you get to choose which result from the reroll to accept. If the probability of a pass is P then the probability of a fail is 1 - P.

reroll
X1 --> pass (P)
X1 --> fail X2 --> pass (1-P)*P
            X2 --> fail (1-P)*(1-P)

The sum of the above probabilities must equal 1

sum = P + (P - PP) + (1 - P - P + PP)  (PP represents P squared)
        = 1

Probability of success = 2P - PP

versus

advantage
X1, X2 --> (pass, pass) (PP)
         --> (pass, fail)   (P*(1-P)   ( these two combined are the same probability as X1 --> pass above,  PP + P - PP == P )
         -->(fail, pass) ((1-P)*P  (this is the same as X1-->fail, X2 pass, above)
         -->(fail, fail) (1-P)*(1-P)

sum PP + (P - PP) + (P - PP) + ( 1 - P - P + PP) = 1
  
success probability is 2P - PP, as above

If the level of success/failure matters things get somewhat trickier. Advantage is still preferable though. Rerolling ends up either worse (if you must take the second result) or the same (if you choose which result to accept). It also gets a bit trickier if you have to make the choice of reroll before determining success.

At its best, reroll and advantage at the same. Constraints on reroll make it somewhat worse -- how much worse depends on the constraints.

Good point, if you have to take the second roll, then the math changes.

 

[Sword of Spirit]

This makes me say a bennie re-roll is roughly twice as valuable as an advantage bennie. The actual re-roll is just as valuable as actual advantage, though.

This is the conclusion I ended up with.

The original question didn't indicate any form of consumable.

Woops! Apparently [MENTION=12731]CapnZapp[/MENTION] was reading my mind, because a limited resource was intended. I guess I made the subconscious assumption that since pretty much all re-rolls in 5e are limited resources re-roll implies limited resource.

The best example of what I was wondering about might be the fighter's Indomitable (limited uses, reroll only a known failure). I believe we've worked out that while the value on any particular roll is the same as advantage, the overall value is twice that of advantage do to not needing to use it half the time. I ended up verifying it with a table.