Kevin Pacey wrote on Wed, May 22, 2019 10:52 PM UTC:
Today I was looking at the wiki re: the mathemematical concept of Game Complexity, which led to the following sub-link on Game-tree Complexity, that gave me food for thought about CVs that might one day compete in terms of popularity with such well known games as Chess (which arguably is slowly being played out at elite level, in terms of opening theory):
If the mathematically inclined on this CVP website are interested, perhaps there might be a way to evaluate the Game-tree Complexity of various CVs on CVP, and even slowly compile a list of those CVs with very large Game-tree Complexity number estimated for them; thus such CVs, if they ever become popular, might have a longer lifespan than e.g. Chess, and part of popularizing such CVs could be pointing out their great Game-tree Complexity number (as estimated).
Just as an example, here's a link to a 10x10 CV of my own invention:
I'm not mathematically inclined, but I'd guess that the branching factor for Sac Chess (based on the Chess and Sac Chess armies operating at maximum centralized power for each piece in each game's setup) would be 2 to 3 times higher than for Chess on average, and I'd also guess that the average game of Sac Chess (especially for well-played games) would be about 2 to 3 times more than for Chess in terms of number of ply (a piece is traded in Chess about every 10 ply, I've read long ago, so a game of Chess [or possibly Sac Chess?!] would thus be over on average with a total of 32-2x(70/10)=18 units left on the board), and thus Sac Chess' Game-tree Complexity may be ((35 [=avg. # moves in chess] x2.5) to the power of 70 [=avg. # ply in a game of chess] x2.5, if I understand the Game tree Complexity estimate formula right) which may well easily exceed that of e.g. the game of Go - see the chart given further below in the sub-link on Game-tree Complexity that I first gave. Note that in played Sac Chess games I've looked so far, it seems a pair of pieces are traded about every 8 ply (rather than every 10 ply, as in Chess) on average, but this is based only on a small observation.
Today I was looking at the wiki re: the mathemematical concept of Game Complexity, which led to the following sub-link on Game-tree Complexity, that gave me food for thought about CVs that might one day compete in terms of popularity with such well known games as Chess (which arguably is slowly being played out at elite level, in terms of opening theory):
https://en.wikipedia.org/wiki/Game_complexity#Game-tree_complexity
If the mathematically inclined on this CVP website are interested, perhaps there might be a way to evaluate the Game-tree Complexity of various CVs on CVP, and even slowly compile a list of those CVs with very large Game-tree Complexity number estimated for them; thus such CVs, if they ever become popular, might have a longer lifespan than e.g. Chess, and part of popularizing such CVs could be pointing out their great Game-tree Complexity number (as estimated).
Just as an example, here's a link to a 10x10 CV of my own invention:
https://www.chessvariants.com/rules/sac-chess
I'm not mathematically inclined, but I'd guess that the branching factor for Sac Chess (based on the Chess and Sac Chess armies operating at maximum centralized power for each piece in each game's setup) would be 2 to 3 times higher than for Chess on average, and I'd also guess that the average game of Sac Chess (especially for well-played games) would be about 2 to 3 times more than for Chess in terms of number of ply (a piece is traded in Chess about every 10 ply, I've read long ago, so a game of Chess [or possibly Sac Chess?!] would thus be over on average with a total of 32-2x(70/10)=18 units left on the board), and thus Sac Chess' Game-tree Complexity may be ((35 [=avg. # moves in chess] x2.5) to the power of 70 [=avg. # ply in a game of chess] x2.5, if I understand the Game tree Complexity estimate formula right) which may well easily exceed that of e.g. the game of Go - see the chart given further below in the sub-link on Game-tree Complexity that I first gave. Note that in played Sac Chess games I've looked so far, it seems a pair of pieces are traded about every 8 ply (rather than every 10 ply, as in Chess) on average, but this is based only on a small observation.