[Gen] 2D6 Probability

[FerociousBeast]

Already put the re-roll thing in. As for why the average is slightly higher, I don't know for sure, but it's probably got something to do with the one divot face being heavier and causing it to settle to the bottom just VERY slightly more often than any other face. Every die is weighted

EDIT: oh, you're talking about the program results above. I have no idea.

[PenitentMan]

well he was using a program to get the results so the actual effect of the die divot holes (remember the weight of the paint in each ) wouldn't be included.
As for the reason wouldn't it be because of the effect of actual probability? I can't remember the name of it but it's something to do with the distribution of results and how the more squewed the probability is the greater the effect will be (on any sample short of the infinite)

A rough example being:
52% probability results in finite samples showing ~52.1%
while
86% probability results in samples ~90%

Disclaimer: the above numbers are just made up numbers to get the idea across

[Snake1311]

I can't believe this conversation hasn't moved on to provide something useful, but is full of mathematical arguements. Pick up a statistics textbook, ones aimed at the respective level of education in any country for 16-17 year olds should have your basics on tree diagrams.

To summarize:

Chance to hit with TL weapon:

(chance to hit) + [(chance to miss)*(chance to hit)]

So for BS2 its (1/3)+(2/3)*(1/3) = 5/9 = 55%

There can be NO arguement about this. It's the way it works, and understanding it will probably be easier from another medium rather than warhammer forums .

________________________________________

Now, the contributing part

I prefer to work with probability in fractions, so....in ascending order of chance to hit:

BS 1........ 6/36
BS 1 TL ..11/36
BS 2 ......12/36
BS 3 ......18/36
BS 2 TL.. 20/36
BS 4 ......24/36
BS 3 TL ..27/36
BS 5 ......30/36
BS 4 TL ..32/36
BS 5 TL ..35/36


We can see that generally, TL a weapon is better for increasing accuracy than upping the BS by 1. The exception being the pitiful BS1, which is pretty rare (the only entry i can think of is tyranid rippers). So we can ignore that, and say that, in all cases:

TL > +1 BS

The benefit of Tling reaches its peak at BS3 and drop evenly on both sides.
As in, benefit of TL is equal for BS 1 and 5; and BS 4 and 3.
BS3 and BS4 benefit almost double than BS1 and BS5, whilst BS3 gains only marginally more than BS3 and BS4.

So the conclusion here is don't TL BS5 unless its dirt-cheap. My lone example of BS1 comes with a Tl weapon anyway, so meh.

To end on a question....what's the purpose of BS higher than 5? seems to be a lot of it in the eldar codex.

[moleytov]

In case of modifiers that would lower it, I suspect, not that I can think of any off the top of my head.

[Snake1311]

In case of modifiers that would lower it, I suspect, not that I can think of any off the top of my head.

yeah, thats how far I got too .

There must be something which affects them still in play, because the eldar codex is brand new...

[Orkanik]

I just roll. I do a little dance when I get good rolls. I do a frowny face when I don't. It's supposed to be a fun game with A LOT of Fluff and the other half is math (adding and subracting points and frag counts). Just go with the flow. Chant "It's all in the wrist." and roll your dice. Because a book nor a computer can roll them for you.

[moleytov]

I don't say anything, murphy's law can be measured fairly accurately using a profanitometer.
The dice really do hear you when you say "anything but a ..."

[FerociousBeast]

To end on a question....what's the purpose of BS higher than 5? seems to be a lot of it in the eldar codex.

I don't remember any BS higher than 5, but if there is one, I can only assume it is put in there in anticipation either of a rules update or an advanced rules supplement.

[Snake1311]

Phoenix lords and Autarchs, including Yriel. Its in the ref. sheet. Rules update / supplement sounds like fun

[[Vertigo]]

Vertigo, I just want to say that my simple example, which you continuously ignored because it went against what you wanted to believe, told you exactly that.

I rolled 100 dice and got closer to 48%. Yes, I did ignore your example. In fact I have a very badly done MS paint that Vertigo got me to do, to help me visulize the math. No I don't have the picture anymore.

ICQ con.

[14:34] Vertigo: Imagine it this way (heee)
[14:35] Vertigo: Imagine a bar. The fullness of the bar is your chance to hit. EMpty = 0%. Full = 100%
[14:35] Vertigo: (Fill in the bar based on percentages)
[14:35] Vertigo: 1 to 0 probabilitiy
[14:35] Vertigo: (right, I'm using visuals to make it easier)
[14:35] [Vertigo]: kk
[14:35] Vertigo: First roll... 1/3 chance, right?
[14:35] [Vertigo]: hmmm
[14:35] Vertigo: Fill in 1/3 of the bar.
[14:35] [Vertigo]: that's where I am starting to think something is off
[14:36] Vertigo: "move" the remaining bar downwars.
[14:36] Vertigo: repeat on the smaller bar
[14:36] Vertigo: 1/3 chance, right?
[14:36] Vertigo: Now, slide them back together
[14:36] Vertigo: What total percentage has been filled?
[14:36] Vertigo: (1/3) from the first roll
[14:36] Vertigo: (1/3) of (2/3) from the second roll
[14:36] Vertigo: =5/9
[14:37] [Vertigo]: actually I am horrible at mental visulization
[14:37] [Vertigo]: if I can't see it I am lost
[14:37] [Vertigo]: too much crap running through my head
[14:37] Vertigo: Sorry. I'm highly visual, and I draw out bars and boxes to do probability match.
[14:37] Vertigo: Draw it out, then.
[14:37] Vertigo: Won't take long.
[14:38] [Vertigo]: ms paint FTW!
[14:39] Vertigo: The probablity is lower because the 2nd "1/3" doesn't contribute as much to the filling as the first 1/3.
[14:39] [Vertigo]: this is where I got stuck origonally
[14:39] [Vertigo]: after the first roll then what?
[14:40] Vertigo: Do this. Draw lines straight down from the bar.
[14:40] [Vertigo]: i see what you say
[14:41] [Vertigo]: it's ugly but I can see it
[14:41] Vertigo: Draw them from the ends of the empty part
[14:41] [Vertigo]: hold
[14:41] [Vertigo]: I drew a line
[14:41] [Vertigo]: divied it into thirds
[14:41] [Vertigo]: after the first 1/3
[14:41] [Vertigo]: I divied it into thirds again
[14:42] Vertigo: same thing
[14:42] Vertigo: right. first part was 1/3
[14:42] Vertigo: 2/3 was left
[14:42] Vertigo: you divided that into 1/3
[14:42] [Vertigo]: yeah
[14:42] Vertigo: math: 1/3 * 2/3
[14:42] [Vertigo]: added that to 1/3
[14:42] Vertigo: Add it back together: 1/3 + ( 1/3 * 2/3 )
[14:43] Vertigo: = 5/9
[14:44] Vertigo: intuition can be a serious burden in complex probability. It's easy to "lose" event space.
[14:44] Vertigo: In probability, you ALWAYS roll ALL the dice. Kinda weird.

I hope you'll understand if I'm a bit irked at this. Did it not occur to you that some of us have had some formal training in probability?

All humans are fallible, even me. I hope you can understand that. Just because I argue doesn't mean I think your wrong or right it means I want to know more! N0z3 and Moleytov almost had me convinced but then I started thinking again.

[n0z3k1ll3r]

Vert can you please stick the [ and ] around your name in those chatlogs?

[MooFreaky]

I rolled 100 dice and got closer to 48%. Yes, I did ignore your example. In fact I have a very badly done MS paint that Vertigo got me to do, to help me visulize the math. No I don't have the picture anymore.

I didn't roll 100 dice. I just used percentages.
IE 33% hit of the first 100 rolled, then 33% of the 67 re-rolls.

33+22 = 55

55/100=55%

[Azmodael]

Erm guys. People need a fast formula to calculate the chances in their mind while playing. Instead of providing long and confusing formulas as well as numorous examples you should give something simple. Example:

I have a Fortuned Squad of Harlies which is under fire from 10 Guardsmen with lasguns. They are using rapid fire. I wonder how many will survive...

1. 10 GM x 2 Shots means they will shoot 20 times.
2. My harlies save on a 5 or a 6, meaning there is exactly 33,3% chance for them to save.
3. 1/3 from 20 is between 6 and 7, that means they will take probably 12 or 13 casualties
4. HOWEVER! They are fortuned. The failed saves are rerolled, 1/3 from 12 is 4 meaning I will take about 8 casualties.
5. Conclusion -> I shouldnt let my Harlies go under such a heavy fire


Of course there are always factors that change the probabilities. Like someone said the standart d6 dice has the numbers drilled in so there is slightly more chance for a 6 to roll then for 1, because the side that has the single dot in it is heavier and therefore the dice is a bit more likely to land on it. Fortunately for us these interferences are small and we can't do anything about them so they are best ignored. They do play their part tho. Just look at a rulette table, even if you play Red/Black or Even/Odd in the long run you will always loose due to the presence of 0 on the table. Statistically it is the same. While at a certain game your rolling sucked and at another you rolling rocked the overall good/bad rolls you rolled during your while life EVEN in number


Oh yeah, about the 2d6 rolls. It is wrong to rely on a 7 as well. Yes, 7 WILL be rolled most of the time. But the chances of rolling a 6 and 8, even 5 and 9 are not small either. When relying on certain abilities always assume that a 9/10 or 5/4 will roll. This way you back yourself up with some really high chance of success. 11 will roll on only 2 occasions - a 5 and a 6 or a 6 and a 5, 12 will roll only on a double 6. That gives you a 3/26->1/13 for about a 7% chance of failure.

[Doohicky]

Ummm.. you kind of forgot about the guardsmen hitting and wounding.

20 shots ----> 10 hit ------> 5 wound

Then 3 or 4 failed saves, but re-roll = only 2 or 3 failed saves.

Conclusion... why the heck did you let guardsmen into rapid fire range?? LOL...

[Azmodael]

Rofl stupid me I assumed everything hit and caused a wound

[cfoley]

Oh yeah, about the 2d6 rolls. It is wrong to rely on a 7 as well. Yes, 7 WILL be rolled most of the time.

Actually, 7 will only be rolled 16.67% of the time. That's hardly most and explains why you can't rely on it.

[Azmodael]

Well maybe I said it wrong. The chance to roll a 7 is higher then any other chance for a different number. It DOES mean that 7 will be rolled more times then any other number taken alone, but it DOESN'T mean that it will be rolled more often then all other number taken as a whole goup.

[n0z3k1ll3r]

No, but generally you either want a seven or more, or a seven or less, in which case the odds are somewhat in your favour.

[[Vertigo]]

"Vert can you please stick the [ and ] around your name in those chatlogs?"

Done and done.

[PenitentMan]

@Moo: you want vertigo to apologise for ignoring you and trying to figure it out on his own? wth?

[MooFreaky]

No, he was talking about it rolling it out rather than following percentages.
Just wondering if there was a reason its logic wasn't convincing