Misstating the Odds, why I started this blog.

Here is a line from a resent post on resevering on 3++, "Statistically only half of your army is coming in on Turn 2 which …" which mathematically is not exactly true.  For any one unit this is true, but for the whole army it is not. By the way the odds are better then this.

Let me say that the article is a decent sort, it just the off hand statistical errors that I want to address.

 Let me first show you what I mean, then I will explain why.  As an example let say you put Z units in resever.  Here is the question, what is the chance that  X units of the Z in reserve will come in on turn Y.

Here the Graphs:

Turn Two:

Turn Three:

 

Turn Four:

 

    See on turn two, if you have four units, the chance that half will come in is 37.5% not 50%, but wait there is more.  If you have 25% chance that three of the four will come in and 6.25% that all four will come in . So if we put all together 37.5+25+6.25 you have a 68.75% chance that at least half your army will come in on turn two.  

So why does this happen, well lets talk about the humble coin, next post.

Flipping Coins

Check out the First Part of this to get to speed.

If we have four coins (and flip them all at once) what are all the ways they can be flipped?

		TTHH
		THTH
	THHH	HTTH	TTTH
	HTHH	THHT	TTHT
	HHTH	HTHT	THTT
HHHH	HHHT	HHTT	HTTT	TTTT

      Ok so that is 16 different outcomes and you can see that six of the sixteen outcomes is half heads and half heads.

		TTHH
		THTH
	THHH	HTTH	TTTH
	HTHH	THHT	TTHT
	HHTH	HTHT	THTT
HHHH	HHHT	HHTT	HTTT	TTTT
1	4	6	4	1

      Well the odds on any one of these out comes is 1/16 =(1/2)(1/2)(1/2)(1/2) so if there are six ways to get to tails then the odds of flipping two tails is 6/16 or 37.5%.

		TTHH
		THTH
	THHH	HTTH	TTTH
	HTHH	THHT	TTHT
	HHTH	HTHT	THTT
HHHH	HHHT	HHTT	HTTT	TTTT
1	4	6	4	1
1/16 = 6.25%	4/16 = 25%	6/16 = 37.5%	4/16 = 25%	1/16 = 6.25%

      Well what if someone hands you four loaded coins, which come up heads 60% of the time.  Let’s look at the last table again this time with the odds of each result coming up.

		TTHH
		THTH
	THHH	HTTH	TTTH
	HTHH	THHT	TTHT
	HHTH	HTHT	THTT
HHHH	HHHT	HHTT	HTTT	TTTT
1	4	6	4	1
12.96% = (.6)(.6)(.6)(.6)	8.64% = (.6)(.6)(.6)(.4)	5.76% = (.6)(.6)(.4)(.4)	3.84% = (.6)(.4)(.4)(.4)	2.56% = (.4)(.4)(.4)(.4)
1 x 12.96%  = 12.96%	4 x 8.64% = 34.56%	6 x 5.76% = 34.56%	4 x 3.84% = 15.36%	1 x 2.56% = 2.56%

     As you can see the odds of the coins coming up head is shifted to the right.  But in WH40K things are not this easy, I often have to roll 20 to 40 dice in one go, and it would take me a large dedicated effort to make a table of all the outcomes to come up with these odds, but have no fear, there a formula (Binomial Theory) for this and that what we will talk about next.

Wow! Hormagaunts are a guradsman worst nightmare!

Working on my next post, but here a sneak preview.

Hormagaunts vs T3 A4+, the chance for any one attack to kill is 21.9%.  Wow!

Does this mean you will kill about 1/5th of the biomass your attacking, not necessarily so, and that the point I am trying to get across in this blog. One: 21.9% takes calculating two re rolls, which takes some thinking ( I show you the scan of my scratch work here at the end.) Two: to scale this up to more attacks you have to use Binomial Theory (and yes a explanation of what this is is coming.)

Other results from my work so far (to kill for one attack):
w/ Toxin Sacs vs.
>T3 A3+ --> 9.7%
T3 A4+   --> 21.9%
T3 A5+   --> 29.2%

w/ out Toxin Sacs vs.
T4 A3+  --> 6.5%
T3 A4+  --> 14.6%
T3 A5+  --> 19.4%

I should note the first time I ran the numbers I was of by double, it was only after I went back and looked at the numbers in context, that a nagging voice said I should double check my work.  But as of now these numbers are correct.

A study in color. (Termagants Gun Color)

I am trying to decide what color to paint the bio weapons on my Termagants, so I painted up some options, tonight, to see what I liked best.  If you have an opinion pleas chime in.

So this is the paint scheme for the army, the orange has not been added to any of the other models presented here.









 Here are the four options I have painted up, after the wash I know which I think stands out the best, but I like to know what you think.  Remember, there will be an orange added on top of the arms and legs.  I want to let the wash dry and go to bed, so I get to it tomorrow.
 

On a side note, after I get back from vacation in August, I putting this army on the shelf and getting my marries back out.  It will be nice to get back to an army were unit size is ten not twenty plus, at least painting wise.