Yes, I think you're both right. I'm going to enlist the help on on of my Uni friends - he's a Maths Phd on symmetry and group theory but he's also very much into maths theories on gambling. I have a feeling he'd be interested in this subject and, therefore, think he's my best bet to try and push forward on this. We'll see...
Good idea to enlist the help of some brainy bods... but a pure math bod?
The thing that makes this problem interesting / difficult is that you can change the rules. Doesn't sit so well with group theory IIRC.