D&D 5E Advantage vs. re-rolls

[Nagol]

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"

5E is mostly pass/fail. I've seen house rules where amount over/under matters and even the base game has a few (critical hits, for example).

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

Your post is the reason I decided to post the math.

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.

No it doesn't.

In both cases, you roll up to 2 dice.. With advantage, you get the best of the lot. With reroll, you only roll again when you need to and if you need to then are committed to keeping the second roll. This isn't a big deal if you already know your first roll is a failure; it is why the math gets trickier when the roller has to guess whether its worth rolling again if the outcome remains uncertain before the choice is made.

So, with reroll if you succeed on the first roll, you're done, yay! If you don't succeed on the first roll, it's all down to the 2nd. If the 2nd roll is high enough to succeed then you pass. Yay! If, not, you fail. Boo!

Now for the sake of argument imagine you rolled both the dice at the same time and are looking at them individually. If the first die you look at is high enough, you pass, yay! It doesn't matter what's n the second die: you're already guaranteed a pass. If it isn't high enough then it's all down to the second die. If the 2nd roll is high enough to succeed then you pass. Yay! If, not, you fail. Boo! That's the advantage system.

With advantage you always roll 2 dice, but because you have the choice of result it's functionally the same as rolling one die, determining success, and choosing to roll a second if and only if you need a better number.

 

[Nagol]

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.

Rerolls do increase your chance to crit as you point out. Advantage increases it more since you get the reroll even if the first die is sufficient to hit..

 

[CapnZapp]

5E is mostly pass/fail. I've seen house rules where amount over/under matters and even the base game has a few (critical hits, for example).




Your post is the reason I decided to post the math.



No it doesn't.

In both cases, you roll up to 2 dice.. With advantage, you get the best of the lot. With reroll, you only roll again when you need to and if you need to then are committed to keeping the second roll. This isn't a big deal if you already know your first roll is a failure; it is why the math gets trickier when the roller has to guess whether its worth rolling again if the outcome remains uncertain before the choice is made.

So, with reroll if you succeed on the first roll, you're done, yay! If you don't succeed on the first roll, it's all down to the 2nd. If the 2nd roll is high enough to succeed then you pass. Yay! If, not, you fail. Boo!

Now for the sake of argument imagine you rolled both the dice at the same time and are looking at them individually. If the first die you look at is high enough, you pass, yay! It doesn't matter what's n the second die: you're already guaranteed a pass. If it isn't high enough then it's all down to the second die. If the 2nd roll is high enough to succeed then you pass. Yay! If, not, you fail. Boo! That's the advantage system.

With advantage you always roll 2 dice, but because you have the choice of result it's functionally the same as rolling one die, determining success, and choosing to roll a second if and only if you need a better number.

Oh boy - we really need to sort this out because this sounds just like a major misunderstanding.

That last description of yours - of advantage - is eerie, because I could have used those exact words to describe a re-roll!

So, here goes. Step by step. From the definition of our check and the difference between the chance to use a reroll and the reroll itself, to a detailed walkthrough of what I mean by advantage and rerolls.

---

First off, let's only discuss regular "pass/fail" checks. Sure there are exceptions, but for maximum clarity I beg you to not even mention these in your reply. Please let us focus 100% on the archetypical case, where if you reach the DC, you succeed, if you don't, you fail.

Now the set-up. You have one bennie (a poker chip say). In the first case it's a free advantage. In the second case it's a free re-roll. Each time you're faced with a check you get to decide whether to use it for this check, or to save it for the next one.

Now, advantage: You decide to use your advantage. You roll two dice as instructed. You roll both dice at the same time. Then you must pick one. Obviously you pick the highest one. Your bennie is then used up.

If the success rate was 50%, you've increased this to 75% at the cost of your bennie.

Then, reroll: You make your check, rolling a single die. If you succeed, you save your bennie. If you fail, you decide to use your bennie. Then you re-roll the same die, taking this latter result. And your bennie is used up.

If the success rate was 50%, mathematically the probability has increased to 75% here too. But there's a 50% chance you still have your bennie. So the cost is half a bennie.


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.

Now, Nagol, feel free to dispute any of my findings, but so far I haven't been able to understand where exactly we differ and what you don't like about my evaluation. So please quote the exact phrase when you do. I am not a math wizz, so please explain exactly where I went wrong and why. Thank you.

 

[CapnZapp]

Rerolls do increase your chance to crit as you point out. Advantage increases it more since you get the reroll even if the first die is sufficient to hit..

You mean, advantage increases it more since you normally don't force the re-roll if the first die is sufficient to hit, yes?

(If you're hell-bent on maximising your crit chance, rerolls and advantage increase the crit chance equally. That assumes that you take the reroll even if the first die is a success, in other words that you're prepared to risk failure just to match the crit chance of advantage)

 

[Sorcerers Apprentice]

(double post)

 

[Sorcerers Apprentice]

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.

The effect minor though, nothing like doubling the chance of a crit with advantage.

 

[Enevhar Aldarion]

Rerolls do increase your chance to crit as you point out. Advantage increases it more since you get the reroll even if the first die is sufficient to hit..

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.

 

[Nagol]

Oh boy - we really need to sort this out because this sounds just like a major misunderstanding.

That last description of yours - of advantage - is eerie, because I could have used those exact words to describe a re-roll!

So, here goes. Step by step. From the definition of our check and the difference between the chance to use a reroll and the reroll itself, to a detailed walkthrough of what I mean by advantage and rerolls.

---

First off, let's only discuss regular "pass/fail" checks. Sure there are exceptions, but for maximum clarity I beg you to not even mention these in your reply. Please let us focus 100% on the archetypical case, where if you reach the DC, you succeed, if you don't, you fail.

Now the set-up. You have one bennie (a poker chip say). In the first case it's a free advantage. In the second case it's a free re-roll. Each time you're faced with a check you get to decide whether to use it for this check, or to save it for the next one.

Now, advantage: You decide to use your advantage. You roll two dice as instructed. You roll both dice at the same time. Then you must pick one. Obviously you pick the highest one. Your bennie is then used up.

If the success rate was 50%, you've increased this to 75% at the cost of your bennie.

Then, reroll: You make your check, rolling a single die. If you succeed, you save your bennie. If you fail, you decide to use your bennie. Then you re-roll the same die, taking this latter result. And your bennie is used up.

If the success rate was 50%, mathematically the probability has increased to 75% here too. But there's a 50% chance you still have your bennie. So the cost is half a bennie.


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.

Now, Nagol, feel free to dispute any of my findings, but so far I haven't been able to understand where exactly we differ and what you don't like about my evaluation. So please quote the exact phrase when you do. I am not a math wizz, so please explain exactly where I went wrong and why. Thank you.

I was discussing the comparison of having advantage on a roll or having a reroll on the same roll. If you achieve the circumstance where advantage is activated or a reroll is active the expected value achieved from either mechanic is the same. The original question didn't indicate any form of consumable. The effect on probability of offering a reroll once the player knows the failure and offering advantage upfront is the same. For example, saying flanking offers a free reroll vs. flanking offers advantage confers no advantage to the flanking attacker or relief to the victim flanked.

For a situation where you have a consumable resource to either grant advantage upfront or force a reroll on demand once the failure is determined, the ultimate effective probability to achieve a pass is the same once the bennie is spent (though now that part of the probability is known, there is a P chance of success from the reroll since the failure is already "spent"), but the reroll offers greater flexibility in that a there is a P chance the bennie is unneeded and can be kept, yes.

 

[Nagol]

You mean, advantage increases it more since you normally don't force the re-roll if the first die is sufficient to hit, yes?

(If you're hell-bent on maximising your crit chance, rerolls and advantage increase the crit chance equally. That assumes that you take the reroll even if the first die is a success, in other words that you're prepared to risk failure just to match the crit chance of advantage)

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.

 

[Nagol]

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.

Yep. I'm just discussing the effect on probability of rolling with advantage vs. rerolling on failure. For simple pass/fail results, the probabilities of a pass -- before any dice are rolled -- are identical under the two regimes, namely 2P minus P-squared where P is the base probability of achieving a pass.