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A Seer Council has Fortune, re-rolling its 4++. It fails to deny Misfortune, thus having to re-roll all successful saves. My brother (the Eldar) insisted that these two cancelled out. While this does seem to make sense and be easy, after some quick mathhammer I decided that there should always be two dice rolls, rather than just one.
(Edit: been thinking about this all morning and realised that my math was wrong, but I don't know how to fix it!)
Observe:
.5 chance to pass; Misfortune makes a re-roll: .5 (pass)*.5(fail)=.25
.5+.25=.75 chance to pass
.5 chance to fail; Fortune makes a re-roll: .5 (fail)*.5(pass)=.25
.5+.25=.75 chance to fail

I then realised that this math doesn't add up, because you can't have only 150%.

Could anyone explain, using stats, why it either is or is not significant to roll all the saves twice. It seems sillier in a batch of 15 saves (roll dice, don't bother looking at them, roll them again), but when it's a single Str6 save against the Farseer, when he passes it I'd like him to roll again. And I'm sure that if he failed, he'd like the chance to roll it again.

It's actually reasonably easy:

Roll saves (say... 10). 4 pass, 6 fail.
The 4 passes get re-rolled due to Misfortune. The 6 fails get re-rolled due to Fortune.
You can never re-roll a re-roll.

So basically, roll all saves first. Then pick them all up and roll them a second time. Ignore first results, second results stand.

{Edit: To save time, many players will agree to simply have the first rolls stand, effectively 'cancelling' the two powers. However, it is important to remember that the re-rolls have been used and the dice can't re re-rolled from other effects.

Statistically it should make no difference.}

To be fair, it could make a difference.

In the event of the 2 powers being in effect, if you get 1 pass and 9 fails, i'd want to pick up those dice and suffer the effects of having to reroll my one pass!

it could make a difference yes but since one is a reroll of successfull and the other is a reroll of failed, and the key reroll of not rerolling rerolls, i believe but can't remember the wording and not at home so no rule book to hand this would come under the rule of rolling a d6 and seeing which rule takes precendence

Bloodhorror wrote:
To be fair, it could make a difference.

In the event of the 2 powers being in effect, if you get 1 pass and 9 fails, i'd want to pick up those dice and suffer the effects of having to reroll my one pass!

Fine, but then equally 9 pass and 1 fail, you'd still re-roll them.
If you want to save time and skip the first roll, discuss with your opponent before the first roll.

Elric - dice are the definition of independent events. Picking up all the dice again and rolling them, vs just rolling one set, yields the same likelihood of success or failure.

IIRC the old Eldar FAQ had a question about the swarmlord vs rolling failed saves. (I cannot find it atm) The answer was that if you have a set of contradicting powers, that you stick with the initial roll.

nosferatu1001 wrote:
Elric - dice are the definition of independent events. Picking up all the dice again and rolling them, vs just rolling one set, yields the same likelihood of success or failure.

I realise this, I just can't seem to wrap my head around the statistics.
A BS4 TL weapon, for example, has an 89% chance to hit. (.666+[.333*.666])
But if the initial result never stands, how would this be expressed in a formula?

Does misfortune still make you reroll deny the witch? If not than atleast fortune lets you reroll your deny the witch.

The dice have no memory.
The first roll in your scenario is meaningless, only the second roll will count, so you might as well only roll them once.

Ailideon wrote:
Does misfortune still make you reroll deny the witch? If not than atleast fortune lets you reroll your deny the witch.

DTW is not a save.

 Elric Greywolf wrote:

nosferatu1001 wrote:
Elric - dice are the definition of independent events. Picking up all the dice again and rolling them, vs just rolling one set, yields the same likelihood of success or failure.

I realise this, I just can't seem to wrap my head around the statistics.
A BS4 TL weapon, for example, has an 89% chance to hit. (.666+[.333*.666])
But if the initial result never stands, how would this be expressed in a formula?

Each save you take has a 50% chance to pass, which you then have to reroll, and the reroll has a 50% chance to pass and a 50% chance to fail.
Similarly, each save has a 50% chance to fail, which you then have to reroll, and again the reroll has a 50% chance to pass and a 50% chance to fail.

So you have:
Pass, then Pass: 0.5*0.5 = 0.25 Pass
Pass, then Fail: 0.5*0.5 = 0.25 Fail
Fail, then Pass: 0.5*0.5 = 0.25 Pass
Fail, then Fail: 0.5*0.5 = 0.25 Fail

For a total of:

0.5 (50%) Pass
0.5 (50%) Fail

Which, as noted above, is exactly the same as just rolling once and not wasting time with rerolling everything.

 Elric Greywolf wrote:
I realise this, I just can't seem to wrap my head around the statistics.
A BS4 TL weapon, for example, has an 89% chance to hit. (.666+[.333*.666])
But if the initial result never stands, how would this be expressed in a formula?

There are two ways to make a passing save: To pass, and then pass again on the re-roll; or to fail, and then pass on the re-roll. The odds of that are (0.5*0.5)+(0.5*0.5)= 50%.

Odds of failing, by similar reasoning, is also 50%.

In other words, if powers are in effect you may as well forego the re-rolls. The odds are exactly the same.

Edit: Son of a... ninja'd!

They cancel out.

Look at it like this.


I roll 5 4+ invuln saves. I am the target of Fortune and Misfortune.


My 5 rolls are, 1, 3, 4, 2, and 6.

I must reroll the 1, 3, and 2 because of Fortune, and I must reroll the 4 and 6 because of Misfortune.

So no matter what I roll on the first roll, I must reroll the dice.

Now we cut out the first roll to save time, so effectively the 2 cancel out and you only make a single dice roll.

The only thing you can do, mathematically, is to calculate the likelihood that the second set of rolls will be better or worse than the first set once you know the results of the first set (but if you apply the "cancel all re-rolls" or "re-roll all the dice" universally as you should, this calculation is moot). Like everyone says, the second set of rolls are in no way connected to the first.

As everyone as said, the rulebook is quite clear that you can't re-roll a re-roll, so Fortune + Misfortune means you just re-roll all of the saves once. Or, to save time, you could just agree with your opponent to just roll once and re-roll none of them.

Fragile wrote:

Ailideon wrote:
Does misfortune still make you reroll deny the witch? If not than atleast fortune lets you reroll your deny the witch.

DTW is not a save.

No, it's not, but the new version of Fortune in the new codex also allows DtW to be re-rolled.

They are opposing rules, they just cancel eachother out guys. This is really simple.