I must admit I am getting more and more confused with the cups one. I thought I could see and had modeled an answer and then tried to go through every possibility I can see occurring. Which led me to this:

Winner	Pick#1	House	Stick	Pick#2	Win
1	1	2	Y	1	1
1	1	3	Y	1	1
1	2	3	Y	2	0
1	3	2	Y	3	0
2	1	3	Y	1	0
2	2	1	Y	2	1
2	2	3	Y	2	1
2	3	1	Y	3	0
3	1	2	Y	1	0
3	2	1	Y	2	0
3	3	1	Y	3	1
3	3	2	Y	3	1
					6

I have only considered the stick here but the change would be the opposite. This yeilds a 6/12 result - what moves have I missed?

Jon