I tried to find a mathematical combinatorial game, and I wanted it to be a Pen-&-Paper game too. This is what I came up with:
https://docs.google.com/document/d/1NY- ... sp=sharing
Here is my initial analysis of the game:
https://boardgamegeek.com/thread/273404 ... hmetic-mul
If you scroll down in that thread you will see that someone has already brute-forced 3x3 for us, and it looks like pie should work nicely. I'm still not sure which player may or may not have an advantage on 4x4, and I'm not sure what the best way to implement pie for a game with second player advantage would be.
Draws should be pretty rare, but they are out there! If my feelings about advantage turn out to be correct, then I suppose it makes sense to award draws to the player who's most likely to be at a disadvantage right?
You can easily test the game for yourselves in “google sheets”:
https://docs.google.com/spreadsheets/d/ ... sp=sharing
https://docs.google.com/document/d/1NY- ... sp=sharing
Here is my initial analysis of the game:
https://boardgamegeek.com/thread/273404 ... hmetic-mul
If you scroll down in that thread you will see that someone has already brute-forced 3x3 for us, and it looks like pie should work nicely. I'm still not sure which player may or may not have an advantage on 4x4, and I'm not sure what the best way to implement pie for a game with second player advantage would be.
Draws should be pretty rare, but they are out there! If my feelings about advantage turn out to be correct, then I suppose it makes sense to award draws to the player who's most likely to be at a disadvantage right?
You can easily test the game for yourselves in “google sheets”:
https://docs.google.com/spreadsheets/d/ ... sp=sharing