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Evil Space Elves
Ollelta
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Scorpion
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PostSubject: To all math genii   To all math genii I_icon_minitimeMon Jul 08 2013, 13:33

Is there a math difference if you have to make a 2+ save 12 times and you roll all the dices at same time or one at the time??


There is a huge discussion going on in our group about that. I just need some proof to show them that there is or isn't a difference.

Please help.

The thing was that my opponent had an HQ with one wound left and a 2+ save. He had 12 wounds he had to save. He rolled the dices one at the time instead of rolling them at the same time. Did he had better chances of making it rolling one D6 at the time ?

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Count Adhemar
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PostSubject: Re: To all math genii   To all math genii I_icon_minitimeMon Jul 08 2013, 13:58

Mathematically it's the same but it's bloody annoying!

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PostSubject: Re: To all math genii   To all math genii I_icon_minitimeMon Jul 08 2013, 15:51

It's the same mathematically, but I have to say it always seems to be luckier if you roll one at a time.
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Ollelta
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PostSubject: Re: To all math genii   To all math genii I_icon_minitimeMon Jul 08 2013, 16:06

I'm sad to say that it's not necessarily mathematically the same. And for reasons that affect us very much on this forum.

It depends on if this save was for a Shadow field. In which case you're specifically instructed to roll them one at a time as the first failed roll destroys the field, and then all unsaved wounds to that point must be made on whatever the next best save is.

If you roll them all at once you take, on average, two wounds. (12*1/6)

However, if you roll them sequentially then each wound has a 1/6 chance to destroy the field, so your odds are somewhat worse. You in fact have a 1/6 chance to take all 12 wounds, which sucks. On average.. well, lets see if i can work this out.. Assuming you have no other saves available, each wound total has the following averages:

0.1666 - 12 wounds
0.1388 - 11 wounds
0.1157 - 10 wounds
0.0964 - 9 wounds
0.0803 - 8 wounds
0.0669 - 7 wounds
0.0558 - 6 wounds
0.0465 - 5 wounds
0.0387 - 4 wounds
0.0323 - 3 wounds
0.0269 - 2 wounds
0.0225 - 1 wounds
0.1121 - 0 wounds

Which I think puts the average as 7.5 wounds (the sum of the multiples of all the above probabilities). Though my maths memory may be failing me at this point..
Either way, you can see its definitely a lot worse than the above 2 wounds for rolling all at once.

Of course, if this wasn't a "destroy the field if failed save", then he was just being a nuisance and it is mathematically the same.

So, was it a Shadow field? Or have I just done all that maths for no reason?
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Evil Space Elves
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PostSubject: Re: To all math genii   To all math genii I_icon_minitimeMon Jul 08 2013, 16:12

@Scorpion wrote:

The thing was that my opponent had an HQ with one wound left and a 2+ save. He had 12 wounds he had to save.

Since it had only one wound left it wouldn't have been a model with a Shadowfield unless it had taken wounds from something that ignored invulnerable saves, or if the opponent was just buck-wild crazy and took armor saves instead for no good reason Razz 

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Ollelta
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PostSubject: Re: To all math genii   To all math genii I_icon_minitimeMon Jul 08 2013, 16:15

It's just about possible it could have gone to ground for some sort of 2+ cover save to avoid risking the shadow field, but I suspect you are right.. Nevermind, it was good practice for my brain..
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Mushkilla
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PostSubject: Re: To all math genii   To all math genii I_icon_minitimeMon Jul 08 2013, 16:35

@Ollelta wrote:
It depends on if this save was for a Shadow field. In which case you're specifically instructed to roll them one at a time as the first failed roll destroys the field, and then all unsaved wounds to that point must be made on whatever the next best save is.

I don't think the OP was talking about shadow fields. As the rules for shadow fields specifically tell you to roll one save at a time (for the reason you mentioned).

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Ollelta
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PostSubject: Re: To all math genii   To all math genii I_icon_minitimeMon Jul 08 2013, 16:42

Aye, I suspect on balance you're probably right, just thought it was worth making the point that it's not necessarily mathematically the same, depending on the circumstances. It strikes me as the sort of thing an unscrupulous player might accidentally-on-purpose forget if they had a large number of incoming shots on their shadow field.. Roll them all at once and a 3 wound model survives on average (at least for another turn) sequentially, and you're probably going to get splatted.
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Count Adhemar
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PostSubject: Re: To all math genii   To all math genii I_icon_minitimeMon Jul 08 2013, 16:44

I honestly can't remember the last time my Archon failed a Shadow Field save that didn't instantly kill him.

/sad panda

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PostSubject: Re: To all math genii   To all math genii I_icon_minitimeMon Jul 08 2013, 17:00

^^ that ^^ No 
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PostSubject: Re: To all math genii   To all math genii I_icon_minitimeMon Jul 08 2013, 18:42

It was a Tau commander with one wound left... So yeah, my opponent was very annoying! He passed all the saves, one by one. Even though I asked him to take them all at same time.
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Thor665
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PostSubject: Re: To all math genii   To all math genii I_icon_minitimeMon Jul 08 2013, 19:05

Officially under the rules of 40k 6th edition he is obligated to take the saves one at a time.

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PostSubject: Re: To all math genii   To all math genii I_icon_minitimeMon Jul 08 2013, 19:10

Wow... thank you! what page??
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Thor665
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PostSubject: Re: To all math genii   To all math genii I_icon_minitimeMon Jul 08 2013, 19:38

Page 16-17.

You roll saves individually (1 at a time) or you roll saves for as many models have a given save in the wound group (which, in the above example, would be 1 Tau Commander, so 1 at a time). Then you roll the save and remove one wound for a failed save.

It's perfectly reasonable to expect and even request that he do them all at once if it's a one model unit. Most players do this, because it makes painful sense.

That said - it's not the way the rules tell you to do it, so it's certainly reasonable for him to insist doing it singly if he feels it will help his chances.

The only thing I would be worried about is if you think he has practiced controlled rolling - but generally speaking unless he's rolling on a smooth surface and not hitting anything (like the side wall of a dice rolling area) then he is almost assuredly being fair and just has gambler's fallacy about his luck.

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PostSubject: Re: To all math genii   To all math genii I_icon_minitimeMon Jul 08 2013, 22:45

Quote :
It's the same mathematically, but I have to say it always seems to be luckier if you roll one at a time.
This, and it is advantageous if hes using a single dice repeatedly. My approach if rolling one at a time is to throw a different dice each time or at least hold 3 in hand each time I throw a random one.. takes away the feeling of something shady going on.

Also fast dice are optional, while single rolls are obligated depending on circumstance as thor stated but my reading is he still has the option of one at a time even if not obligated.
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Dogmar
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PostSubject: Re: To all math genii   To all math genii I_icon_minitimeMon Jul 08 2013, 23:09

Thor pretty much got everything covered.

The only way to increase his chances is to "practice" rolling single dice, which I think is possible as long as you always use the same dice and the same surface to roll on and don't collide with anything. Well or he has a weighed dice. I'd call both cheating, but I don't like accusing people so let's put that aside, he might just be superstitious with his dice Very Happy.

Other than that the expected result of 12 2+ saves regardless of rolling one at a time or rolling them together is 2 wounds through. Completely the same mathematically unless it's a shadow field, but we got that covered.

And yes, if the commander is in a unit he must(!) roll saves one at a time because I'd assume the commander to have a better armor save than the unit. If the commander is on his own, rolling the dice separately is pretty silly, but he still has the right to do it.
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