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Message: <blockquote data-quote="LazarusLong42" data-source="post: 1206321" data-attributes="member: 9620">Ay ay ay.  For any complex network of more than a few rooms, you're no longer talking about a simple statistics problem; you're talking about chaos theory.  However, for some simple networks we should be able to figure out actual formulas.The easiest is a ring of N rooms, connected 0-1-2-3-4-.... with the last room connected back to room 0.  As t approaches infinity:  if N is odd, the probability is 1/N for all rooms; if N is even, the probability is 2/N for odd rooms at odd time increments, 0 for even rooms at odd time increments, and vice versa for even time increments.(This is assuming the N rooms are labeled 0, 1,... , N-1 and that the dragon starts at t=0 in room 0.)The simple case here--that the probability is simply 1/N for each room--would also be the case for any system in which every room was connected to every other--for instance, the room placed on the corners of a tetrahedron with tunnels along the edges, or, assuming tunnels can cross and not create "rooms", a pentagram.The Sigil has already answered for your network.  It's actually pretty easy to set up in Excel and run out for a hundred iterations or so.And now, you have me setting up random ones because, yes, I'm a dork... <img src="https://cdn.jsdelivr.net/joypixels/assets/8.0/png/unicode/64/1f642.png" class="smilie smilie--emoji" loading="lazy" width="64" height="64" alt=":)" title="Smile    :)"  data-smilie="1"data-shortname=":)" /></blockquote>

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