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Wolf Claw maths.

2.2K views 28 replies 9 participants last post by  Winterous  
#1 · (Edited)
The Wolf Claw, coming in the Space Wolves codex, is similar to a Lightning claw.
The difference being that, before any attacks are thrown, you can decide to either re-roll to hit rolls, or to wound rolls.

Which is better to choose?

Long post is long, skip to the bottom if you don't want to read!

I'm here to show you my initial calculations.

----

Ok, if you're comparing two rolls that have an equal comparison, the gain in chance to pass is identical.
For example, a 5+ to hit, and 3+ to wound, both have the same comparison, a 1/3 - 2/3 chance.
However, a 4+ roll will ALWAYS be the best gain in chance, regardless.

Unfortunately, choosing to re-roll to hit gives you a greater benefit, because if you hit, the second roll happens, whereas if you miss, the second roll does not happen, thereby voiding that chance.
I'm not sure how you'd factor that into the calculation without huge working out.

Ultimately, I would say it's only worth re-rolling to wound when you have a 4+ to hit, and 2+/6+ to wound.
I could be wrong, but that's the only likely time that the gain in chance will be better.


For those who actually understand, I'll show the maths.
2+ = 30/36 chance, and 5/6 for the leftover. Gain is 5.
3+ = 24/36, 8/12. Gain is 8.
4+ = 18/36, 9/18. Gain is 9.
5+ = 12/36, 8/24. Gain is 8.
6+ = 6/36, 5/30. Gain is 5.

From that you can see that re-rolling a 4+ gives a greater degree of difference than re-rolling anything else, almost twice the difference of re-rolling a 2+ or 6+.

----

Now, I can't be sure if it is EVER wise to re-roll to wound over to hit (against vehicles excluded obviously) unless I do a bit of a flow chart, but that takes time, and I'm lazy.

Final word?
Always choose to re-roll to hit, unless there are special circumstances.
In most cases regardless of special circumstances, still choose to re-roll the hit!

*edit*
Maths which appear to directly contradict my logic.
:shok:
What??
I went through it, that's all right (well, at least very close to right)

This seems to be illogical...

Ok, reversing the required rolls!

Re-rolling to hit
6+ 4+

30 attacks
6 hit
Re-roll 24, 4 hits, 10 hits total
5 wounds

Re-rolling to wound
6+ 4+

30 attacks
6 hits
3 wounds
Re-roll 3, 1.5
4.5 wounds total


Argh this is ridiculous!



Ok, a fair competition.
4+ for all.

Re-rolling to hit

30
15
Re-roll 7.5, 22.5 hits
11.25 wounds

Re-rolling to wound

30
15
7.5
Re-roll 7.5, 3.75
11.25 wounds


Ok so, that's even, and it would be with other rolls as well I assume.

Alright, 3+ to hit, 4+ to wound.

Re-rolling to hit

30
20
Re-roll 10, 6.66, 26.66 hits
13.33 wounds

Re-rolling to wound

30
20
10
Re-roll 10, 5
15 wounds


Now that outcome I DID anticipate, as the to wound roll has a greater benefit from the re-roll.

Switching the values, 4+ then 3+.

Re-rolling to hit

30
15
RR 7.5, 22.5
15 wounds

Re-rolling to wound

30
15
10, RR 5, 3.33
13.33 wounds


*FACEPALM*

I just realised what I failed to take into account!
The compared value of the initial chance, and the re-rolled gain.
For smaller chances, the gain is less, but higher in proportion, that relationship makes the re-rolled chance comparatively more than the gained chance on the more likely rolls!

FUUUUUUUUUUUUUUUUUUUCK~!

I love maths, and hate it at the same time :laugh:



=-=-=-=-=-=-=-=-=-=-=-=-=

TLDR?
Opt to re-roll the less likely roll, you'll (probably) always come out of it better.

And yes, I did fuck up majorly at the start :p
 
#3 ·
But that's where you're wrong.
If you're hitting on 4+ and wounding on 5+ or 6+, you're STILL better off re-rolling the 4+.

Maths my friend, there's no disproving it.
I imagine there are only a very few situations in the whole game where re-rolling the wound roll is more worthwhile.

Remember, however good your chance to wound is, you don't GET that roll if you don't hit first.
 
#5 ·
i just did some quick math and im sure there is one example in which its better.

if for example you are needing 4+ to hit, and 6+ to wound.


rerolling to hit

4+ to hit 6+ to wound

30 attacks on the charge

15 hits

reroll= 7.5 extra hits

22.5 hits altogether


6+ to wound

3.75 wounds.


reroll to wound

+ to hit 6+ to wound

30 attacks

15 hits

Roll to wound = 2.5 wounds

12.5 Re-roll’s to wound = 2.083

4.583 wounds.

so in this circumstance is is better. (although i could be highly wrong, as i have just finished an 11 hour shift aha)

the reason it is better to reroll to hit, like you mentioned, is because if you dont hit, you dont get the chance to wound, so rerolling to hit is very beneficial. expecially if you fluff it big time.

fin
 
#6 ·
Maths which appear to directly contradict my logic.
:shok:
What??
I went through it, that's all right (well, at least very close to right)

This seems to be illogical...

Ok, reversing the required rolls!

Re-rolling to hit
6+ 4+

30 attacks
6 hit
Re-roll 24, 4 hits, 10 hits total
5 wounds

Re-rolling to wound
6+ 4+

30 attacks
6 hits
3 wounds
Re-roll 3, 1.5
4.5 wounds total


Argh this is ridiculous!



Ok, a fair competition.
4+ for all.

Re-rolling to hit

30
15
Re-roll 7.5, 22.5 hits
11.25 wounds

Re-rolling to wound

30
15
7.5
Re-roll 7.5, 3.75
11.25 wounds


Ok so, that's even, and it would be with other rolls as well I assume.

Alright, 3+ to hit, 4+ to wound.

Re-rolling to hit

30
20
Re-roll 10, 6.66, 26.66 hits
13.33 wounds

Re-rolling to wound

30
20
10
Re-roll 10, 5
15 wounds


Now that outcome I DID anticipate, as the to wound roll has a greater benefit from the re-roll.

Switching the values, 4+ then 3+.

Re-rolling to hit

30
15
RR 7.5, 22.5
15 wounds

Re-rolling to wound

30
15
10, RR 5, 3.33
13.33 wounds


*FACEPALM*

I just realised what I failed to take into account!
The compared value of the initial chance, and the re-rolled gain.
For smaller chances, the gain is less, but higher in proportion, that relationship makes the re-rolled chance comparatively more than the gained chance on the more likely rolls!

FUUUUUUUUUUUUUUUUUUUCK~!

I love maths, and hate it at the same time :laugh:
 
#7 ·
ahahaha, i believe i had took that into consideration =]
dont worry i wasnt nit picking mate.i was just trying to work out myself is the was any benefit to rerolling to wound rather than to hit...lol
 
#9 ·
Ahahaha, I know, I just hate it when I'm wrong on such a grand scale XD

So, your maths show re-rolling the one that is more difficult is the key.
Err, ultimately yes.
It's not OBVIOUS though, and even if you think it is, it's good to have mathematical backing.

It's little things like this that can make all the difference in a game :D
 
#10 ·
Pure Mathhammer- yes its better to re-roll the harder roll. However, in game terms its often better just to re-roll the to-hit roll... sometimes the average result just isnt enough, occasionally you need to throw caution to the winds and just go for broke and try to get lucky.
 
#11 ·
o_õ
I honestly don't understand how reducing your chance could be considered lucky.

I respect your view there, but I can't comprehend it.
I mean yes, there's the whole 'rolling poorly' concept, but ultimately the outcome of the dice is not entirely random, and always subject to minor inconsistencies, as are most things in physics.
But to the best of our knowledge, going with a true random understanding of the roll of the dice is the most logically sound way; considering it otherwise is frankly, both foolish and strange.
That's not to say taking a gamble isn't wise in a lot of situations, going for that 1/6 chance to kill X vehicle can really change the battle, but when taking that gamble, would it not be wise to endeavor for the best chance of a payout?


This whole thing is all on average though.
If I worked out individual attacks with the flowchart method, I'm sure there would be increased merit to re-rolling the hit die in some situations, but it probably wouldn't be a very significant difference.
 
#12 ·
yes tim/steve has nailed it. =]

although you need the reroll for higher T models, it will make jack difference i you choose to reroll to wound, and fluff alot of your hitting dice.=]

so it realy come down to how much faith you have in your dice rolls and the unit your attacking against/with.

from a mathammer point - reroll the hardest dice roll

from a "my dice rolls are terrible" - reroll to hit because atleast it gives you a chance to roll dice and wound =D
 
#14 ·
I was thinking more about ignoring averages when you need to pull out something special- if you have 6 attacks and must cause 3-4 on a fex or it'll kill you then the avarage isnt going to help you (assuming WS4 fex 4+ to hit 6+ to wound = 0.92W average).. so you need to get jammy... personally I would re-roll to hit to try to get 5-6 hits... then hoping the dice gods favour me with a few extra 6s in the to-wound rolls.

In any other situation, I would always go with the Mathhammer best (can normally work it out on the fly).
 
#16 ·
Oh yeah, that makes sense then.
I believe that re-rolling the to hit dice give you a better chance of scoring high, but a lower score on average, so it's really just a bit of logic in situations like that.

take it from me, a heavy tourney gamer, people who dont take chances dont win big Tourneys, now you may argue this point to the death, this is just my opinion..

i have played against people who use mathammer as there "tactic" and to be honest there not that great. although i do use mathammer, i use it for this reason

in fantasy it give you a rough idea of how combats will end up, and many situations.
in 40k it should be realied on as much. your tactic should be how to best the other person, not how many dice should i need to roll to whipe that squad out, because there is so much more chance in 40k.ive had a devilfish not fail a cover save from its launchers before all game, and other times its lastest most of the game, and on a few occasions die very quickly.

yes technically if you roll a dice 6 times you should get 1,2,3,4,5,6 as the results.
likly hood is you wont.and to be honest you know thats true.

hence why his statement is true, people do have bad luck, i know one guy who can not pass his shadow field save for the life of him(once in about 14 games) thats not average... if warhammer came down to averages it would be fun now would it. it would be my men shot take off x amount, you shoot take off x amount. i charge and kill x amount, i loss x amount, you have a 66% chance of passing ld test.

its all about so random elements, like a guard squard shooting 4 marines out of the sky in one turn, or one last remaining lascannon popping a monolith. it adds to the game.

so to get this back on track.

if you've had an accident at work, WAIT, i mean if you have crappy luck, reroll to wound, atleast then you can hit a barn door.

if your not a cronic dice roller, the reroll the more difficult set.

=]

fin
I'm not saying Maths > Tactics, it's just that in a situation like this, where it's as simple as choosing A or B, then tactics has no place.
As Tim mentioned, in some cases this theory goes out the window, but in most situations going by my recommendation will net you a better score in the end.
 
#15 ·
take it from me, a heavy tourney gamer, people who dont take chances dont win big Tourneys, now you may argue this point to the death, this is just my opinion..

i have played against people who use mathammer as there "tactic" and to be honest there not that great. although i do use mathammer, i use it for this reason

in fantasy it give you a rough idea of how combats will end up, and many situations.
in 40k it should be realied on as much. your tactic should be how to best the other person, not how many dice should i need to roll to whipe that squad out, because there is so much more chance in 40k.ive had a devilfish not fail a cover save from its launchers before all game, and other times its lastest most of the game, and on a few occasions die very quickly.

yes technically if you roll a dice 6 times you should get 1,2,3,4,5,6 as the results.
likly hood is you wont.and to be honest you know thats true.

hence why his statement is true, people do have bad luck, i know one guy who can not pass his shadow field save for the life of him(once in about 14 games) thats not average... if warhammer came down to averages it would be fun now would it. it would be my men shot take off x amount, you shoot take off x amount. i charge and kill x amount, i loss x amount, you have a 66% chance of passing ld test.

its all about so random elements, like a guard squard shooting 4 marines out of the sky in one turn, or one last remaining lascannon popping a monolith. it adds to the game.

so to get this back on track.

if you've had an accident at work, WAIT, i mean if you have crappy luck, reroll to wound, atleast then you can hit a barn door.

if your not a cronic dice roller, the reroll the more difficult set.

=]

fin
 
#17 ·
Personally all this math hammer to me as been stated means zilc in the end probabilty suggests one thing, eg: that rolling 6 dice I should get results 1-6, reality suggest another, eg it could two 4's, one 5, and three 2, in the end it comes down to "luck " (using term lightly as I don't really believe in it though in game situation makes a little more sense than coincicdence) something you can't measure. I've had 3 die roll all 6's probability would suggest otherwise, 40k Mathhammer in my opinion useless as we have different CC and shooting rules to fantasy.

WHFB Mathhammer for CC very important in figuring out whether you can survive - though once again saying this I've had 2 wild riders last 3 rounds of CC against a herd of 15 beastmen and whittle them down to 4 beastmen before dying.
 
#19 ·
What people are stuggling to say: if you roll 6 dice you should average 1*1, 1*2, 1*3, 1*4, 1*5 and 1*6 ... but the chance of actually ROLLING the average (ie 1,2,3,4,5,6) is about 1/65 so should rarely be seen.

Using Mathhammer as a 'tactic' isnt a great idea... but knowing what mathhammer suggests is never a bad plan- knowing what shooting/combat options should give what reaslts helps you to make good choices on movement and target allocation (or even charges in WFB) but shouldnt be used blind at the start of the turn- you need the fluidity to adapt to the dice rolls as you play the phase (I always keep a unit or 2 not firing and use them against those targets that I rolled badly against, or to wipe out remnants of squads I did well against).

But yes, as Bob said; sometimes you just need to take risks and hope you roll well- is my 150pt ogre unit going to break that 1000pt deathstar unit? Mathhammer says no but if I get the chance to charge it in the flank Im still gonna do it... its not the MH 'best' but the slight chance of winning or a large chance of messing it up a bit and holding it up for a turn or 2 if enough for me...
Maths never suggests that rolling a 6D6 will on average come up 1-6.
If we consider the number a value rather than a result, then the average value of rolling 6D6 is 3.5, which is the average of 1-6.
You can't get the average of something which isn't a value, it doesn't work that way.

Math shows us that rolling 6D6 in a specific order has an equal chance of the dice showing up in any combination as is does showing up 1 through 6.


And yes Tim, I agree that Maths should not command your tactics.
Maths is an advisor in a tactical situation, not the commander, it should hold some importance in your decision making process, but not the only importance.

All I'm saying in this thread is that re-rolling the lower chance will net you a better end result, whereas re-rolling the higher chance may well give you a better chance of scoring high, but a lower average score.
 
#18 ·
What people are stuggling to say: if you roll 6 dice you should average 1*1, 1*2, 1*3, 1*4, 1*5 and 1*6 ... but the chance of actually ROLLING the average (ie 1,2,3,4,5,6) is about 1/65 so should rarely be seen.

Using Mathhammer as a 'tactic' isnt a great idea... but knowing what mathhammer suggests is never a bad plan- knowing what shooting/combat options should give what reaslts helps you to make good choices on movement and target allocation (or even charges in WFB) but shouldnt be used blind at the start of the turn- you need the fluidity to adapt to the dice rolls as you play the phase (I always keep a unit or 2 not firing and use them against those targets that I rolled badly against, or to wipe out remnants of squads I did well against).

But yes, as Bob said; sometimes you just need to take risks and hope you roll well- is my 150pt ogre unit going to break that 1000pt deathstar unit? Mathhammer says no but if I get the chance to charge it in the flank Im still gonna do it... its not the MH 'best' but the slight chance of winning or a large chance of messing it up a bit and holding it up for a turn or 2 if enough for me...
 
#22 · (Edited)
i've been really busy today, so i made up this spreadsheet. i just goes to show that re-rolls to hit just pip re-rolls to wound at the post, however it really isn't by much. thankfully we don't have to choose which before the game starts, and so can treat it case by case.

ps. i don't have a Codex: Space Wolves, so i've simply written it using some generic numbers that are at least relatively realistic and demonstrate trends.

edit: bugger! you can't upload spreadsheets for some reason. sadly, i can't convert it to a PDF, so if you want to take a look, PM me.
 
#23 ·
TBH all you really need to know is that vs T5,6,7 re-rolling to wound is slightly better. Anything else is just going to go down too easily.