D&D 5E Advantage vs. re-rolls

[Sword of Spirit]

Does anyone know how much better a re-roll on failure is than advantage?

And then of course there are the in-betweens 5e includes, like re-rolling after you see your roll but before you know if it succeeds, and either taking the best or taking the new one.

 

[Shiroiken]

I don't have the math, but a re-roll on a failure is a pretty big deal (assuming it's a limited resource). You don't know if advantage will actually help or not (about half the time the first die will be higher anyway), so you'd only use it when you really needed to ensure success (or needed a Rogue Sneak Attack). Even if you don't know the result before you choose, you'd just always wait until you roll really low (~4 or less), since the odds of turning a success into a failure is really low (you probably failed anyway). Re-rolling and getting the better result simply has a higher minimum (~6 or less), or is good for thinks that are REALLY important (save or die/suck kinda thing).

 

[CapnZapp]

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.

Sent from my C6603 using EN World mobile app

 

[Yunru]

As a side note, being able to reroll one of a "pick higher" set (such as Elven Accuracy) basically only adds another die to choose from, as you only reroll the one that's not as beneficial.

 

[Nagol]

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.

 

[Rhenny]

I like using re-roll instead of advantage for when players chose to use inspiration. This way, the player doesn't need to waste the inspiration if he/she knows that he's already rolled high enough to succeed. My players like that too. I even remember hearing Chris Perkins, Mike Mearls or Rodney Thompson (I can't remember who since it was a long time ago) saying that allowing that choice was a good one.

 

[Sorcerers Apprentice]

Re-roll on a failure is slightly worse than advantage, since re-rolling doesn't increase your chance of a critical hit, while advantage does.

 

[CapnZapp]

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.

I'm having a hard time following you. Are you new to 5th edition, Nagol?

"Advantage" means: roll two dice, pick the best.
A "re-roll" means: roll a die, decide whether to re-roll. If you re-roll, you must keep the second roll.

The context is on ability checks, attacks and saves. In almost every case, all that matters if you reach the "Difficulty Class" or DC, which is just a target number. (There are examples where it gets more complicated than that, such as specific ability checks where something extra bad happens if you fail the DC by five or more, but the OP didn't ask for that).

This is a friendlier way to say "of course it's a simple pass/fail - this is D&D"

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

I'd like you to read my post, and ask you how we could reach so disparate conclusions:

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

What I mean by that is that in both cases, you get to roll two dice.

But in the case of advantage you need to commit before you see the results of either.

While in the case of the reroll, you get to see the first result before committing.

If you have a 50% chance of success (the level where advantage grants a maximum benefit), you also have a 50% chance of not having to spend your reroll at all (simply because the first roll succeeded).

In sweeping terms, this makes me say a free reroll is roughly twice as good as a free advantage.

 

[Blue]

Does anyone know how much better a re-roll on failure is than advantage?

And then of course there are the in-betweens 5e includes, like re-rolling after you see your roll but before you know if it succeeds, and either taking the best or taking the new one.

It depends on the frequency and if it's an attack roll vs. some other roll. I'm also assuming standard succeed/fail - do I hit the AC, make the save, and the like. I'm not considering degrees of success.

With unlimited uses and attack rolls, advantage wins. Simply because more crits. Do you want to reroll a hit and risk a miss for s achnce for a crit?

With unlimited uses and non-attack rolls, it's exactly the same. You need one of (up to two) dice to succeed. You don't care which, and no benefit from both succeeding.

With practically limited uses, reroll wins because you can decided to apply it after seeing the first die while advantage you need to apply before rolling. So mathematically it's the same, but rerolls are more efficient resource management.

 

[ccs]

Re-roll on a failure is slightly worse than advantage, since re-rolling doesn't increase your chance of a critical hit, while advantage does.

Re-rolling on a miss absolutely does increase my odds of a crit.
I go from 0% chance - because I missed - to an all new roll to hit with a 1/20 chance of scoring a crit.