Multiple Rerolls, How do they stack?

[Elricaltovilla]

So this question came up tonight when I was talking with my gaming friends. If say, you have a stalker with murderous insight (roll twice, take the better result) attacking a stalker with Combat Precognition (creatures attacking you must roll twice and take the worse result) how do those two abilities interact? How many dice would you roll?

I started thinking about it further, what if you added the Witch Hexes Fortune (roll twice take the better) and Misfortune (roll twice and take the worse) to the mix? How many such reroll abilities can we stack like this and what would be the end result? I'm probably just tired, but I'm not really able to puzzle it out. Thoughts?

[holywhippet]

I'd say four dice. Your insight lets you roll twice for a given attack, their precognition makes you roll twice. So you'd roll two dice, then two dice again. For each pair of dice rolled you'd take the better result, but for the final result you'd take the worse of those two.

eg. Say you roll 10 and 13 for the first set of rolls, then 3 and 18 for the second. You take the best of each roll so you end up with 13 and 18. But their ability makes you take the worse result so you end up with 13.

I'd not expect reroll abilities to stack, but if they do you'd keep doubling the number of dice rolled.

[Lord Vukodlak]

I'd rule they cancel each other out and you roll normally.

[grarrrg]

Another option!
For every "roll extra and take worst" you roll one extra die and ignore a High result.
For every "roll extra and take best" you roll one extra die and ignore a Low result.

So if you have 2 "Fortunes" and one "Misfortune", you'd roll 4 dice, ignore the 2 lowest due to Fortune, and ignore the highest due to Misfortune.

[Andreaz]

You guys overcomplicate. Just have them cancel out, no need to roll 478382 times per normal roll. And favorable stacking goes similar to crits: 2 roll-twice-take-better become a roll-thrice-take-better.

[Elricaltovilla]

You guys overcomplicate. Just have them cancel out, no need to roll 478382 times per normal roll. And favorable stacking goes similar to crits: 2 roll-twice-take-better become a roll-thrice-take-better.

But it doesn't say anywhere that the abilities cancel out. There's no ruling on the interaction between such abilities at all, and no general rule about spell-like or supernatural abilities cancelling each other out. In fact, it usually takes specific wording (like with Enlarge Person and Reduce Person) to note that opposed abilities cancel each other out.

[upho]

But it doesn't say anywhere that the abilities cancel out. There's no ruling on the interaction between such abilities at all, and no general rule about spell-like or supernatural abilities cancelling each other out. In fact, it usually takes specific wording (like with Enlarge Person and Reduce Person) to note that opposed abilities cancel each other out.Which makes me believe the only RAW way to deal with this is as described by holywhippet:
I'd say four dice. Your insight lets you roll twice for a given attack, their precognition makes you roll twice. So you'd roll two dice, then two dice again. For each pair of dice rolled you'd take the better result, but for the final result you'd take the worse of those two.Insight transforms a single roll into "roll twice, take best", while precognition forces you to take the worst of two such "roll twice, take best" rolls. Can't see any other solution being RAW.

EDIT: Which of course also means that multiple reroll effects multiplies the number of rolls (rather than simply adding one additional reroll à la crit multiplier). If this comes up a lot, I would probably houserule it to having such abilities cancel each other out if the players are fine with it.

[Qwertystop]

I think four might be wrong because it means that one of the abilities is being applied to two different rolls. I'd say roll twice, take the best, roll once more, take the worse of the two. Or the other order. Not sure if the odds are different from each other, or from roll three, take median.

[Deadkitten]

Lets see... as to the most re-rolls you can get on a character...

Witch with the Misfortune Hex, Ill Omen, Pugwampi's Grace, And a Pugwampi Braid (its crafted with bestow curse for some reason) would be 4 instances of re-rolls right there. There might be a few more I am missing cause I seem to think I got up to like 7 re-roll effects on a theoretical build once.

[Djinn_in_Tonic]

Which makes me believe the only RAW way to deal with this is as described by holywhippet:Insight transforms a single roll into "roll twice, take best", while precognition forces you to take the worst of two such "roll twice, take best" rolls. Can't see any other solution being RAW.

This doesn't work at all. How do you determine which effect takes "final" precedence? The worst of (2 @ best of 2) is statistically better than the best of (2 @ worst of 2), for example. The former has a high chance of being two >10 rolls, while the latter has a high chance of being two <10 rolls.

There's no written RAW for this, but simple cancellation produces what I feel is the obvious intended effect.

[upho]

I think four might be wrong because it means that one of the abilities is being applied to two different rolls. I'd say roll twice, take the best, roll once more, take the worse of the two. Or the other order. Not sure if the odds are different from each other, or from roll three, take median.Hmm... Looking at both abilities again, I see you could be correct, but I think the RAW makes a slightly better case for the "roll four times" interpretation. Murderous insight applies to all attack rolls for 1 + wis rounds, and the second forced combat precognition "take worse" roll is, in itself, an "attack roll" AFAICT (my emphasis):
Combat Precognition (http://www.d20pfsrd.com/path-of-war/classes/stalker#TOC-Stalker-Arts)...forces opponents who attack the stalker to roll their attack rolls twice and take the worse of the two results...Of course, this is just reading a meaning into the term "attack roll" that most likely wasn't intended. :smallconfused:

I propose the player rolls a d20 every time this situation comes up; a roll >10 means the player takes the worst of two "roll twice, take best", and <11 means the player gets the worst of one "roll twice, take best" and one single roll. More rollplay FTW! :smallbiggrin:

[upho]

This doesn't work at all. How do you determine which effect takes "final" precedence? The worst of (2 @ best of 2) is statistically better than the best of (2 @ worst of 2), for example. The former has a high chance of being two >10 rolls, while the latter has a high chance of being two <10 rolls.First in first served, as other non-cancelling effects?

EDIT: In this particular case, murderous insight would of course always take precedence to produce the "worst of (2 @ best of 2)" when attacking a foe with precognition, since murderous insight requires a swift action which only affects the stalker, not the target.


There's no written RAW for this, but simple cancellation produces what I feel is the obvious intended effect.Rules quote supporting that "obvious intended effect"? While I don't think the devs ever saw this (much less that their "obvious intentions" on how to solve it can be found in any rules text), I agree that it would be good houserule.

[Djinn_in_Tonic]

Rules quote supporting that "obvious intended effect"? While I don't think the devs ever saw this (much less that their "obvious intentions" on how to solve it can be found in any rules text), I agree that it would be good houserule.

I did mention that there wasn't any RAW ruling to my knowledge. Sometimes "obvious intended effect" is something you have to figure out based on your own design knowledge. In this case, roll twice choose best is clearly a "get the better roll." Roll twice choose worst is clearly "get the worse roll." Pick Higher clearly is the opposite of Pick Lower, so Roll Normally seems like a really obvious break between the two.

[Barstro]

While I think RAW (though relatively silent) is against it, having the rolls negate and just become a single roll seems best.

Roll Twice take the Better/Worse is a dice way of dealing with increased or decreased luck and is close to a +4 or so, depending on what the actual dice roll needed is. In my limited use of a Witch, I found that Roll Twice and take the Worse was very powerful, but Roll Twice and take the Best was of limited use. But all of that is beside the point.

If time and fun were not an issue, I'd do it as follows;
Assuming has a Roll Twice going both ways
Good 1) Roll once. If it hits, go to step Bad 1.
Good 2) Roll the second time. If that also misses, we are done. MISS
Bad 1) Roll once. If that still hits, it is a hit and we are done. HIT
Bad 2) (The good reroll of the bad reroll). This is the deciding roll.

I just ran the numbers. With 50% hit odds, the final result is a 50% hit odd. Somehow, my math shows it stays at 50% if you do the Bad Luck first, but there are six combinations instead of eight. I assume I messed up somewhere.

Anyway, since I'm tired of dealing with this spreadsheet, I'll add my vote to "opposing rerolls cancel"

[Elricaltovilla]

I did mention that there wasn't any RAW ruling to my knowledge. Sometimes "obvious intended effect" is something you have to figure out based on your own design knowledge. In this case, roll twice choose best is clearly a "get the better roll." Roll twice choose worst is clearly "get the worse roll." Pick Higher clearly is the opposite of Pick Lower, so Roll Normally seems like a really obvious break between the two.

As a game designer I'd likely rule that the effects cancel each other out, but in terms of my playing/DMing preference I'd at least want to see how many nested rerolls I could pull off.

[upho]

I did mention that there wasn't any RAW ruling to my knowledge. Sometimes "obvious intended effect" is something you have to figure out based on your own design knowledge.I meant rules quotes on anything similar to this or from the related abilities that could support this interpretation, not actual RAW specifically dealing with stacking "roll attack twice"-abilities. The closest I get is cancelling spells like haste/slow, and those aren't really comparable IMO.


In this case, roll twice choose best is clearly a "get the better roll." Roll twice choose worst is clearly "get the worse roll."Yes.


Pick Higher clearly is the opposite of Pick Lower,Mathematically, in terms of relative impact on hit probability, this is only true if the probability for the attack to hit is exactly equal to it's probability to miss. For example, if the attacker has a 90% hit chance, a "pick higher" increases the hit chance to 91% (approx. 1.1% difference), but a "pick lower" decreases the hit chance to 81% (a whopping 10% difference). The actual meaningful impact of "pick lower" is almost ten times greater than "pick higher" in this case.

EDIT: Disregard the above, I was being stupid. Feel free to laugh at my obvious lack of mathematical comprehension though... :smallredface:


so Roll Normally seems like a really obvious break between the two.I agree with Elricaltovilla on this, from a game designer perspective this would be the obvious solution. But going by the current RAW, it would most certainly be houserule.

[Barstro]

Mathematically, in terms of relative impact on hit probability, this is only true if the probability for the attack to hit is exactly equal to it's probability to miss. For example, if the attacker has a 90% hit chance, a "pick higher" increases the hit chance to 91% (approx. 1.1% difference), but a "pick lower" decreases the hit chance to 81% (a whopping 10% difference). The actual meaningful impact of "pick lower" is almost ten times greater than "pick higher" in this case.

Don't cherry-pick your stats.:smallwink:
If the To-Hit is 10%, then the stats work the other way. On average, they have the same effect and can cancel.

Please don't force me to do an even larger spreadsheet with percentages involved.

For the record, that was in before the redaction.

[upho]

For the record, that was in before the redaction.Sorry 'bout that. I hope my pathetic cognitive abilities offered some compensatory entertainment... :smallfrown:

[Jormengand]

I'd do it the way Warhammer did it with Cold-Blooded and the Light of Death - you roll two extra dice and drop the highest and the lowest. However, as people have said, there's no clear RAW answer.

[grarrrg]

I am firmly against "roll double the dice each ability" for a few reasons. I will admit that the reasoning is decent, but the in game execution is flawed.

1: the results are not 'consistent'. There is a bit of difference whether you "take best then take worst" or "take worst then take best" (and who decides which is first?)
If dice are paired 5/10 15/20
Best then Worst you'll have a 10
Worst then Best you'll have a 15

If dice are paired 5/15 10/20
Best then Worst you'll have a 15
Worst then Best you'll have a 10

If dice are paired 5/20 10/15
Best then Worst you'll have a 15
Worst then Best you'll have a 10
Doing Best then Worst leads to slightly higher rolls, Worst then Best leads to slightly lower rolls.
If you have 3 or more "roll extra, drop one" abilities the problem is compounded.


2: Speaking of 3 or more "roll extras", you'll quickly be rolling a LOT of dice.


3: If "Take Best" doubles the dice, and "Take Worst" doubles the dice, then what about TWO "Take Bests"?
You'd roll _4_ dice and get the best out of the bunch, whereas rolling 3 seems more reasonable.


My vote is for what I suggested earlier (roll 1 extra die and then ignore a high/low), or the cancel out approach.

[Andreaz]

or the cancel out approach.It's the best approach, because individually both Rerollers have the same statistical significance, and this way you only roll once instead of FOUR times.

Remember, people, the PLAYERS are doing the rolls. Do you really want to waste the time to roll and count 4 dice instead of 1, when the final result is supposed to be the same as 1?

[Elricaltovilla]

I'm not interested in the "best" way to handle it. I'm interested in the RAW.

And what if the players do want to roll 4 or more d20s? If it's about the players, then that possibility still has to be considered.

[With a box]

I'm not interested in the "best" way to handle it. I'm interested in the RAW.

And what if the players do want to roll 4 or more d20s? If it's about the players, then that possibility still has to be considered.

There is no RAW about that.
It's like asking RAW answer for how much a macbook cost in pathfinder world.

[Barstro]

There is no RAW about that.
It's like asking RAW answer for how much a macbook cost in pathfinder world.

Oh, I think that one can come up with RAW. There is just no place to say "How multiple double rolls work". You have to piece a bunch of stuff together from different areas. And since there is no specific rule that says "rerolls of opposite effects cancel", you have to go the long way around.

TL:DR;
"Roll X, Take Best" is how many dice are rolled each time. "The Group"
"Roll X, Take Worst" is how many times you roll the Group.
You then select the worst die among all the best from each group.

Example
So, Roll 4, take best along with a Roll Twice, take worse results in rolling 4 dice (take best) twice, and taking the worse of those two rolls.
(18, 1, 5, 7)=18
(15, 17, 7, 16)=16
Result is 16

But, Roll Twice, take best, along with a Roll 4, take worse results in rolling two dice (take best) four times, and taking the worse of those four rolls.
(18, 1)=18
(5, 7)=7
(15, 17)=17
(7, 16)=16
Result is 7
----------------------------

Now, the Too Long part of this;

One way of thinking that makes this easier is that each "roll twice - better" is considered just a single roll where you drop the lower.
Then, each "roll twice - worse" is a new reroll of those two dice.

Each step gets its particular set of rerolls.

Person making the rolls goes first.

Example;
PC needs to roll a 15 to hit an enemy and is under the effect of Roll Twice - Better (RTB) and Roll Twice - Worse (RTW).
1) PC rolls two dice (RTB), both miss - Done. He Missed.
2) PC rolls two dice (RTB), at least one hits. His reroll section caused a hit, move on.
2b) PC now under effect of RTW and rolls two dice (RTB of reroll)

NOTE: if PC has "RTB twice" (from multiple sources), just roll however many dice (the group) each time.
Likewise, TRW multiple times just changes how many TIMES the PC rolls "the group"

If I do the above with a d4, I get the following;

4 Needed to hit (25% normally)
9/16 is a miss on the first double, no need to reroll
7/16 is a 4, need to reroll. 7/16 of reroll is a hit. Making a Hit every 19%)

3 Needed to hit (50% normally)
1/4 is a miss on first double
3/4 is a hit, need to reroll, 3/4 of reroll is a hit. 56%

2 Needed to hit (75% normally)
1/16 is a miss on first double
15/16 is a hit, reroll is, again, 15/16
89% chance to hit.

The result of all of this is that it transforms the straight line of a single roll into the bell curve of multiple rolls, making a middle distribution much more likely than extreme highs or lows. Crits will almost never happen. Since the Mean roll of a d20 is 10.5, 10 or lower gets closer to a guarantee, while 11 or higher becomes much less likely.

[Andreaz]

Oh, I think that one can come up with RAW. There is just no place to say "How multiple double rolls work". You have to piece a bunch of stuff together from different areas. And since there is no specific rule that says "rerolls of opposite effects cancel", you have to go the long way around.

TL:DR;
"Roll X, Take Best" is how many dice are rolled each time. "The Group"
"Roll X, Take Worst" is how many times you roll the Group.
You then select the worst die among all the best from each group.
And, of course, there's nothing that forces you to do it this way instead the other way around: Take Worsts as the "Group" and Take Bests as the number of Groups. As posted before...the results change.

[Barstro]

And, of course, there's nothing that forces you to do it this way instead the other way around: Take Worsts as the "Group" and Take Bests as the number of Groups. As posted before...the results change.

True. I chose that the "best" is the "Group" simply because the person making the roll is the subject of the sentence and I normally look at bonuses first. I think either way is fine and not too time consuming.

[Andreaz]

True. I chose that the "best" is the "Group" simply because the person making the roll is the subject of the sentence and I normally look at bonuses first. I think either way is fine and not too time consuming.
They really do differ. The final result is +0.7 or -0.7 around the average number (which, of course, means if you do both over time it cancels out to the usual 10,5 average). Lower of 2 Highs affords an average of 11.2, while Higher of 2 Lows affords an average of 9.8

Also either way natural 1s and 20s more or less disappear. With Ho2L you get 0.0095 chance of rolling a nat1, and a 0.005 chance of rolling a nat20. With Lo2H it's the opposite(1s are 10 times less likely, 20s are 5 times less likely). Either way is far below the usual .05 chance of a single roll and is consistent with the average loss as well.
http://anydice.com/program/5e36

[Stegyre]

Interesting.

Cancelling out strikes me as the simplest approach, but not how I would rule it, were it up to me:

1. Each re-roll adds one d20. Thus, the OP situation of one "re-roll take best" and one "re-roll take worst" would be 3d20, not 4.

2. From the middle, each "take the best" means one step up, and each "take worst" is one step down. Thus, if only a single effect applied ("take best"), you roll 2d20 and take a step up to the higher die -- exactly as you would do by RAW. When you have a step up and a step down, they cancel out and you take the middle d20.
I did not read too closely to see if this was already covered, but this is very different from cancelling out to only roll 1d20: it gives a bell curve result, instead of a flat result, significantly changing the odds of the extreme rolls.

A worked example: two "take worst" and one "take best":

1. roll 4d20.

2. From the middle, you go down a net one, so use the result of the second-lowest d20.

Not RAW, because there is no RAW. But this approach makes each effect actually have an effect, rather than simply nullifying a contrary effect. FWIW.

[lsfreak]

Stegyre's method is exactly what I'd do; honestly I didn't post it cuz I figured if it hadn't been posted yet there was a problem I didn't foresee. The main one being if there's Immediate action rerolls that come into play after some of the rolls have already been made, but I'm not sure those exist and I'm not sure they're really a problem for that method anyways.

[Djinn_in_Tonic]

Ooh. Interesting thing I forgot, that's really important here.

"Rolling Twice" is a doubling of your number of rolls, pretty explicitly.

The rule for D&D is that two doubling effects equal a tripling. This is most apparent in damage multiplication, but we see it a few other places as well.

So 2 "roll twice" effects ends up as a "roll three dice" effect.

Of course, RAW this gets odd, since we can be forced to take both the lowest and highest results.

I think that's about as RAW as you can get though.

[Stegyre]

"Rolling Twice" is a doubling of your number of rolls, pretty explicitly.

The rule for D&D is that two doubling effects equal a tripling. This is most apparent in damage multiplication, but we see it a few other places as well.

So 2 "roll twice" effects ends up as a "roll three dice" effect.
Exactly.

Of course, RAW this gets odd, since we can be forced to take both the lowest and highest results.
In a way, we are: we are simultaneously taking the highest of the bottom d20s and the lowest of the top d20s. That is essentially what the step-up and step-down process does.


Small sidetrack, because my personal preference is for the 3d6: I think you can do something similar with 3d6, having each effect add an additional d6 and then netting out the appropriate 3, so one up and one down would be 5d6 taking the middle 3.

[grarrrg]

1. Each re-roll adds one d20. Thus, the OP situation of one "re-roll take best" and one "re-roll take worst" would be 3d20, not 4.
...I did not read too closely to see if this was already covered


Stegyre's method is exactly what I'd do; honestly I didn't post it cuz I figured if it hadn't been posted yet there was a problem I didn't foresee.

Great, now I feel like chopped liver (for context, please see the 3rd reply to the thread).

"Add a die, drop one" is the simplest method that follows the spirit of the abilities, and still has an effect.
Canceling out is the simplest.
Anything else gets needlessly complicated pretty quickly.

[Stegyre]

Great, now I feel like chopped liver (for context, please see the 3rd reply to the thread).
True. The rest of us should have read more carefully. But,

1. Rules of forum posting require that a certain minimum of posts be made before a "best" answer is posted, and

2. Posts with numbered lists, ftw.

[upho]

And, of course, there's nothing that forces you to do it this way instead the other way around: Take Worsts as the "Group" and Take Bests as the number of Groups. As posted before...the results change.No, as posted before, like other effects it's "first in first served". Don't see any RAW reason you should treat this differently. Meaning:

Example situation 1:
A. You're the target of Fortune: roll twice, take best.
B. A moment later, you're also the target of Misfortune: take worst of 2 x (roll twice, take best).

Example situation 2:
A. You're the target of Misfortune: roll twice, take worst.
B. A moment later, you're also the target of Fortune: take best of 2 x (roll twice, take worst).

Yes, it may result in a damn s**tload of dice to be rolled, and yes, it's far from the greatest solution. If we add Djinn_in_Tonic's good find...


The rule for D&D is that two doubling effects equal a tripling....which is referring to:
Core Rulebook (4th printing), page 12: "Multiplying: When you are asked to apply more than one multiplier to a roll, the multipliers are not multiplied by one another. Instead, you combine them into a single multiplier, with each extra multiple adding 1 less than its value to the first multiple. For example, if you are asked to apply a ×2 multiplier twice, the result would be ×3, not ×4."...then the most RAW working solution must be that for every "roll twice, take best", you add 1 d20 roll and choose the best, and for every "roll twice, take worst" you do the same, but if you get both effects as the example above, you'd actually multiply the rolls. For example:

A. You're the target of Fortune: roll twice, take best.
B. You're also using Murderous Insight: roll thrice, take best.
C. A moment later, you're also the target of Misfortune: take worst of 2 x (roll thrice, take best).

I think there's a somewhat decent argument for this being in accordance with the above quoted RAW on multiplying, namely that "roll twice, take best" and "roll twice, take worst" are two different conditional multipliers, not your standard flat unconditional one (which without doubt was the only type of multiplier the devs could think of when creating the quoted rule more than five years ago).

...


However...

If I were to speculate on the RAI of the above quoted rule, I'd say it only applies to rolls where you add the results together (as in "determine amount of X"-rolls like damage), not to rolls where you pick one result (as in "determine success or failure"-rolls like attacks). The reason of course being that the RAW simply does not work if it applies to the "pick one" type of "multipliers". I also wonder whether these types of rolls can/should even be considered "multipliers" by RAW...

[upho]

"Add a die, drop one" is the simplest method that follows the spirit of the abilities, and still has an effect.
Canceling out is the simplest.
Anything else gets needlessly complicated pretty quickly.Yeah, I still agree with the "follows the spirit of the abilities" and all that (and would use this solution myself), but IMO it doesn't match very well with RAW. Which is what Elricaltovilla wanted to know, after all.