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Sadly you cannot choose to take the higher save which can be more advantageous, like Necron Dispersion shields that cannot choose to take the higher save to use their deflection abilities, if their armor save is better.

You don't have to be a maths major to work out that 1/3 * 1/3 (1/9) chance of failing is better than a 1/6 chance of failing!


Automatically Appended Next Post:
Not coming down on one side or the other here. Just commenting on the maths major comment.

Poly Ranger wrote:
You don't have to be a maths major to work out that 1/3 * 1/3 (1/9) chance of failing is better than a 1/6 chance of failing!


Automatically Appended Next Post:
Not coming down on one side or the other here. Just commenting on the maths major comment.

You do not have to be a math major to figure that out, but the rules do not account for it.

If they say "better" save then you use it: your choice.
The intent is whatever is the most advantageous.
The author was not intending to increase the odds of the model taking a wound.
If the shot was AP2 you would take the 5+Inv.
The example with the dispersion shields I will take a look at because that wording is a bit different.

 Talizvar wrote:
If they say "better" save then you use it: your choice.
The intent is whatever is the most advantageous.
The author was not intending to increase the odds of the model taking a wound.
If the shot was AP2 you would take the 5+Inv.
The example with the dispersion shields I will take a look at because that wording is a bit different.

Except Better is defined in the rules as lower.

Tails - as per the tenets of the forum, please back up your assertion with rules. Else mark it as hywpi.

The rules state lower is better. Where is your rule allowing you to consider any other factor?

 Talizvar wrote:
If they say "better" save then you use it: your choice.
The intent is whatever is the most advantageous.
The author was not intending to increase the odds of the model taking a wound.

Assumptions based on ... what rules exactly?

If the shot was AP2 you would take the 5+Inv.

Relevance?

The example with the dispersion shields I will take a look at because that wording is a bit different.

It's not different at all actually. The dispersion shields FAQ proves that you cannot pick a more advantageous save if it's a higher number.

But 3+ re-rollable is not technically better. Going from a 3+ to a 3+ re-rollable only reduces the chance of failure by 8.33...%. Going from a 3+ to a 2+ reduces the chance of failure by 16.666..,

The book tells us 2+ is better because 2+ is actually better.

 DJGietzen wrote:
But 3+ re-rollable is not technically better. Going from a 3+ to a 3+ re-rollable only reduces the chance of failure by 8.33...%. Going from a 3+ to a 2+ reduces the chance of failure by 16.666..,

The book tells us 2+ is better because 2+ is actually better.

that is some bad maths. the odds of passing a rr3+ is 8/9s or 88.89%

while a 2+ is 5/6s or 83.33%, 5% less then the rr3+

rerolling the 3+ is better

 DJGietzen wrote:
But 3+ re-rollable is not technically better. Going from a 3+ to a 3+ re-rollable only reduces the chance of failure by 8.33...%. Going from a 3+ to a 2+ reduces the chance of failure by 16.666..,

The book tells us 2+ is better because 2+ is actually better.

A re-rollable 3+ is absolutely "better" than a 2+, in the sense that it has a lower chance to fail as pointed out above. 1/9 chance of failure vs. 1/6.

Unfortunately the rules have defined better as being strictly a lower number, and not a higher chance of success. So what would be the plain English definition (Most likely to work) and the rulebook definition are no longer aligned when re-rolls get involved.

No the chance of rolling 2d6 and having at least one of them come up 3+ is 88.99%. That is not what is going on here.

You roll 1 die. If it comes up 1 or 2 you can roll it again. You however are not allowed to roll it again if it comes up 3 or better. This means there a 16 possible outcomes for this roll.
1 re-rolls to a 1
1 re-rolls to a 2
1 re-rolls to a 3
1 re-rolls to a 4
1 re-rolls to a 5
1 re-rolls to a 6
2 re-rolls to a 1
2 re-rolls to a 2
2 re-rolls to a 3
2 re-rolls to a 4
2 re-rolls to a 5
2 re-rolls to a 6
3 stays
4 stays
5 stays
6 stays
4 out of 16 are failures. That is 25% chance to fail, a 75% chance to succeed.

With a 2+ there are only 6 possible outcomes and only 1 is a failure. Thats a 16.666% chance to fail and a 83.333% chance to succeed.

With a 3+(no rerolls) there are only 6 possible outcomes and 2 are failures. Thats a 33.333% chance to fail and a 66.666% chance to succeed.

You have a 33% chance to fail. You then have a 66% chance to succeed.
66% of 33% is 22% plus the original 66% is .. 88%.

I have to admit you had me scratching my head, DJGietzen, but I believe you're confusing probability with possibility (one of the most common misconceptions regarding combinatorics).

The formula to determine the probability of a certain outcome with rerollable dice is to take the chance of the first roll's success and add it to the chance of success on the second roll (taking into account the the second roll only occurs if the first roll fails).

I think about it like this:
If P is the probability of success in general (e.g. 2/3 or 66% for a 3+ roll), then it is the chance for success on the first roll and 1-P is the chance for failure on the first roll.
Since you only need to reroll if the first roll is a failure, 1-P x (P) is the probability of success on the second roll.
Then X = ((1-P) * P) + P = the chance of success for both rolls.

ex) Reroll a 5+ save
A 5+ = 2/6 (or 1/3) success. That gives you a 4/6 (or 2/3) chance for failure. Of the failed rolls (2/3) you will have success with 1/3 of them on the second roll, giving you 2/9 success (1/3 * 2/3 = 2/9).
Add 2/9 (success on the second roll) to 1/3 (or 3/9, the success of the first roll) and you get 5/9 (or approx 56%).

The same is true for a rerollable 3+ save:

X = ((1-P) * P) + P
X = ((1-2/3) * 2/3) + 2/3
X = (1/3 * 2/3) + 2/3
X = 2/9 + 2/3
X = 2/9 + 6/9
X = 8/9 or ~89%

You are correct that of the 16 possible outcomes of a rerollable 3+ scenario, 4 are indeed failures, giving you 12/16 or 75% success. That, however, does not give you the probability of failure, which is 4/36, giving you 32/36 or 89% success.

DoW

EDIT: Rigeld beat me to it!

Also, for comparison:

6+ = 17% vs. rr6+ = 31%
5+ = 33% vs. rr5+ = 56%
4+ = 50% vs. rr4+ = 75%
3+ = 66% vs. rr3+ = 89%
2+ = 83% vs. rr2+ = 97%

 DJGietzen wrote:
No the chance of rolling 2d6 and having at least one of them come up 3+ is 88.99%. That is not what is going on here.

You roll 1 die. If it comes up 1 or 2 you can roll it again. You however are not allowed to roll it again if it comes up 3 or better. This means there a 16 possible outcomes for this roll.
1 re-rolls to a 1
1 re-rolls to a 2
1 re-rolls to a 3
1 re-rolls to a 4
1 re-rolls to a 5
1 re-rolls to a 6
2 re-rolls to a 1
2 re-rolls to a 2
2 re-rolls to a 3
2 re-rolls to a 4
2 re-rolls to a 5
2 re-rolls to a 6
3 stays
4 stays
5 stays
6 stays
4 out of 16 are failures. That is 25% chance to fail, a 75% chance to succeed.

With a 2+ there are only 6 possible outcomes and only 1 is a failure. Thats a 16.666% chance to fail and a 83.333% chance to succeed.

With a 3+(no rerolls) there are only 6 possible outcomes and 2 are failures. Thats a 33.333% chance to fail and a 66.666% chance to succeed.

You are ignoring that on the 3-6 results, they also would get a 2nd dice and there for 6 possibilities per roll, not 1. Just that the 2nd roll is arbitrary because to already meet the requirement, but it still factors into probabilty. Ergo there are 36 possible results, of which 4 are failures so 4/36 = 1/9 failures = 8/9 success rate = 88.89% which is what i said earlier

Don't believe me? Base on your deduction, 12 of 16 dice rolls are 1s and 2s, while only 4 out of 16 are 3-6. That is wrong

Thank you all for proving my point with a math discussion.

A 2+ is better than a 3+RR because the lower numeric is the better save, so sayeth the rules.

 Kommissar Kel wrote:
Thank you all for proving my point with a math discussion.

A 2+ is better than a 3+RR because the lower numeric is the better save, so sayeth the rules.

While I can certainly appreciate self-aggrandizing at the best of times, I'm afraid it was Rigeld's point long before it was yours, good sir:

rigeld2 wrote:
It's best numerical save.
Oblits have a 2+ iirc so they cannot choose to take the 3++ rerollable.

DoW

 DogOfWar wrote:
I have to admit you had me scratching my head, DJGietzen, but I believe you're confusing probability with possibility (one of the most common misconceptions regarding combinatorics).

Yup, I was. For any one else still confused. The odds of getting a specific number on a d6 are 1 in 6, or 16.666% chance. The odds of you getting a specific number on a d6, picking it up and getting another specific number are 1 in 6 in 6, or 2.777%.
1 re-rolls to a 1, with a 2.777...% chance of this happening.
1 re-rolls to a 2, with a 2.777...% chance of this happening.
1 re-rolls to a 3, with a 2.777...% chance of this happening.
1 re-rolls to a 4, with a 2.777...% chance of this happening.
1 re-rolls to a 5, with a 2.777...% chance of this happening.
1 re-rolls to a 6, with a 2.777...% chance of this happening.
2 re-rolls to a 1, with a 2.777...% chance of this happening.
2 re-rolls to a 2, with a 2.777...% chance of this happening.
2 re-rolls to a 3, with a 2.777...% chance of this happening.
2 re-rolls to a 4, with a 2.777...% chance of this happening.
2 re-rolls to a 5, with a 2.777...% chance of this happening.
2 re-rolls to a 6, with a 2.777...% chance of this happening.
3 stays, with a 16.666...% chance of this happening.
4 stays, with a 16.666...% chance of this happening.
5 stays, with a 16.666...% chance of this happening.
6 stays, with a 16.666...% chance of this happening.

When you add up the odds of all 12 possible successes you get 88.888...%
When you add up the odds of all 4 possible failures you get 11.111...%

I'd go with whichever is statistically more likely to pass, regardless of which player the save is for... Other than that I'd look to GW manager/TO/Dice roll to see which way to take it.

 Selym wrote:
I'd go with whichever is statistically more likely to pass, regardless of which player the save is for... Other than that I'd look to GW manager/TO/Dice roll to see which way to take it.

Honestly I think that slows the game down unnecessarily. Unlikely though it may be, you can have odd situations like the following:

Ex) You have a Space Marine in Terminator Armour behind an ADL. Additionally, he has a special rule allowing him to reroll his failed invulnerable saves (but only the first failed save), however the AP2 weapons shooting him receive an IG order that requires him to reroll successful cover saves. He receives 2 wounds, how do you roll saves?

A player could spend a minute (or longer, depending on their understanding of probabilities) figuring out which is the statistically more likely chance of saving each wound in turn, or you could just use the numerically best save (as the book describes), taking into account the AP and/or cover negation effects of the weapon, and move on with the game. Adding in multiple types of weapon wounds, ID, and other effects only complicates matters further.

Some people might really enjoy figuring out exactly how best to save their model but, I can assure you, your enemy will not share that enjoyment.

DoW

Easy, all on the Invulnerable based on Statistics. A re-roll failures X+ is always better than a straight (X-1)+ but not a (X-2)+. Conversely a re-roll successes X+ is always worse than a straight (X+1)+ but not an (X+2)+. So if the Terminator isn't Going to Ground, his 5++ is going to be better than the re-rolled ADL 4+ save. If he is going to ground the cover save is going to be better in spite of the re-roll.

EDIT: I figured I better come back and make it clear that I in no way think the rules give you the choice. In this case the rules would dictate Cover all the way, even though it's more likely to get the model killed.

Chrysis wrote:
Easy, all on the Invulnerable based on Statistics. A re-roll failures X+ is always better than a straight (X-1)+ but not a (X-2)+. Conversely a re-roll successes X+ is always worse than a straight (X+1)+ but not an (X+2)+. So if the Terminator isn't Going to Ground, his 5++ is going to be better than the re-rolled ADL 4+ save. If he is going to ground the cover save is going to be better in spite of the re-roll.

EDIT: I figured I better come back and make it clear that I in no way think the rules give you the choice. In this case the rules would dictate Cover all the way, even though it's more likely to get the model killed.

I'm glad you took the time to figure it out, but I have to admit that that was the most 'complicated' example I could come up with on the fly. I'm sure there are more potentially confusing scenarios out there that would stagnate the game somewhat.

I agree with your view on the RAW and I appreciate you taking the time to edit your post and reflect that. I'll add that I consider myself fairly average when it comes to mathematical ability so—considering the varied ages, backgrounds, and aptitudes of 40k players—even if the rules were ambiguous regarding statistical calculations of success rates on saves, I think it would be imprudent to require each and every player to calculate the correct odds and roll accordingly.

Then again, it might be a reasonable house-rule to make but, as I mentioned earlier, I think that might open up the door for abuse regarding 'tactical' or 'strategic' use of saves (rather than simple numerics).

DoW

The only more complicated situation I can think of is only re-rolling specific results, at which point the effect gets more pronounced as options trend towards those being the only results. So "re-roll 1s" has more effect when you are rolling a 2+ than when you're rolling a 6+. I don't feel like checking where the crossover for that is, as that will require doing more actual math. I suspect the crossover is actually at 2+, because a straight re-roll is only marginally better than a +1 improvement anyway.

Chrysis wrote:
The only more complicated situation I can think of is only re-rolling specific results, at which point the effect gets more pronounced as options trend towards those being the only results. So "re-roll 1s" has more effect when you are rolling a 2+ than when you're rolling a 6+. I don't feel like checking where the crossover for that is, as that will require doing more actual math. I suspect the crossover is actually at 2+, because a straight re-roll is only marginally better than a +1 improvement anyway.

You underestimate GW's ability to make up sillier and sillier rules!

But really, I stand by my original point. You, in particular, may have no problem calculating probabilities in your head in seconds (the same amount of time it would take to choose the numeric best), but I would consider you abnormal in that regard, especially considering some of the younger 40k players out there.

DoW

 Nem wrote:
IMO, 'better' under page 2 is not a rule, it's an explanation, the comparative is against 2 armour saves of different values the lower value is better. This will always be true, a 5+ armour save will always be better than a 6+ save, this explanation scope does not include variant scope of multiple options for a save, it only handles 1 alone option. For this reason I am reluctant to apply it to situations outside its scope, and prefer 'best' save to be played at the players discretion

Which leaves you with no rules to use when deciding what the better armour save is. Which breaks the game at this point.

RAW the 2+ is the better save. It's not HIWPI for, but RAW it is the 2+.

Actualy, if we are going to get technical about it, RAW the lower the armor save the better it is. RAW also tells us the lower the cover save the better it is, There is No RAW to describe the best invulnerable save, or if a 2+ cover save is better then a 3+ armor save. The game requires the player to connect the dots in these situations. Its also fair to say the game allows the player to decide what save is better in these situations.

Actually it doesn't, As for invulnerable saves it states how they differ from armour, and how it is better is not one of them. The rules then state out of the choice of saves which is better