I have been trying to analyse the game of chompOrdinal Chomp played on a (rules$3 \times 3 \times \omega$ board. The rules can be found onin the https://en.wikipedia.org/wiki/ChompWikipedia article), played on a 3x3xw board.briefly:
- This game is played between two players on the set $3 \times 3 \times \omega$. A move is to pick any remaining $(i,j,k)$ and remove all $(i^\prime,j^\prime,k^\prime)$ where $i^\prime \geq i$, $j^\prime \geq j$ and $k^\prime \geq k$. The player to take $(0,0,0)$ loses.
Unfortunately, the analysis is extremely complicated, so I have been unable to find a winning move for the first player or a proof that none exists. So, my question is:
Is there a winning move in 3x3xw chomp$3 \times 3 \times \omega$ Ordinal Chomp for the first player, and if so, what is it?
