There will be a slight delay...

Not that anyone is reading this, but it's going to take a bit longer to get to the next bit than I hoped.

So now we're getting a handle on this.

I've come up with a pattern that I can use to collect my data.

_	_	_	t	-	-	t	t	-	o
_	_	_	-	m	-	m	-	m	o
_	_	_	-	-	b	-	b	b	o
l	-	-	tl	tc	tr	tml	tmc	tmr
-	c	-	ml	mc	mr	tbl	tbc	tbr
-	-	r	bl	bc	br	mbl	mbc	mbr
l	c	-	tmlc	tmlr	tmcr	tlc	mlc	blc
l	-	r	tblc	tblr	tbcr	tlr	mlr	blr
-	c	r	mblc	mblr	mbcr	tcr	mcr	bcr
o	o	o

There are forty-nine interactions which I can show with this format.  The first -- no influences -- is going to be expressed by the color of the blanks or Xs in the square where we'll show the crowd patterns.  The single influences and double influences within a zone will be shown by the segments in the zones.  I.E., if I'm looking at the effect of the influence "tm" I'll do it by coloring the lettering in the vertical segment that has a "t" and an "m"  - in the horizontal zone.

In this particular example we're looking at the empty crowdsquare.  There are no effects from the crowd, and none from any single influence or pair of influences (in black).  Three influences always produce a pair (in green), and four influences always produce a hit (in blue).  There are no invalid combinations (so nothing in red.)

The ooo's at the end of the zones will be how we'll identify crowdsquares.  I'll explain that plan tomorrow.

Some interactions between crowdedness and influences.

Let's start with one of the simplest sets of interactions.  We'll look at squares with three spaces left and a single influence.

X	X	X		t					t
X	X	X		m					m
				b					b
l	c	r
l	c	r

For each influence, I've color coded the result.

Black is no effect

Green is pair

Blue is deduction

Red is impossible/invalid

So in this first chart we can see that out of six occasions, three have a result and one can never happen in the game.  So 3/5ths or 60% of the time we get at least a pair.

But of course, the "crowd" in the square mighte be in a different configuration.

How about something that looks like this:

X	X	X		t					t
X	X			m					m
X				b					b
l	c	r
l	c	r

Here, our results are different.  There are no invalid interactions, and while two of the interactions have no result, two of them (b) will give us a hit, not just a pair.  If 2/3rds of our interactions give us a result here, that's 66%.  

We can create different charts with three spaces, but are they functionally equivalent to this one?

Nothing to do but test it.

X	X			t					t
X	X			m					m
X		X		b					b
l	c	r
l	c	r

And clearly the answer is no.  We're looking at one result with no influence, but we've raised our pairs to four and reduced our hits to one.  

5/6ths into percentages is more than my brain is up to just now.  But I've got one more chart for us to investigate.

This time, we'll break things up a bit.

X		X		t					t
X	X			m					m
X		X		b					b
l	c	r
l	c	r

And we get a similar result.  One dud, one hit, and four pairs.

What makes this arrangement functionally equivalent to the one above it?

Something to think about.