## Friday, August 12, 2016

### Games@Dal 2016: Craig talks about PenFib Nim

Games@Dal 2016 talk: "Penultimate Nim and Conjoined Games" - Craig Tennenhouse, w/ Kelsey Mihachik

Craig talked about Conjoined Games, another type of "sum" extending the notion of sequential sums.  The sequential sum of G and H works that both players must play as normal on G until the game ends, at which point the next player makes a move on H.  Conjoined Games are special in that the second summand (H) is not defined until G ends; H is based on the state terminal position from G.  The nicest games to play are those where the state of the terminal position is exactly the state of H.  Craig suggested Colobber: Col followed by Clobber.

Craig then described Penultimate Nim (AKA Gale's Nim), which is just like Nim except that there are no moves when there's only one heap.  Pen(ultimate) Nim is solved for all games with 3 or less heaps.  He then showed Fibonacci Nim: a single-heap subtraction game with the following rules:

* For the first turn, the first player may take any number of sticks aside from the entire heap.
* On any subsequent turn, the current player may take any sticks up to twice the amount the previous player took.

Craig then presented PenFib Nim, which is Penultimate Nim followed by Fibonacci Nim.  He's working on trying to categorize the P-positions.