Comments/Ratings for a Single Item

You have failed to define the term "piece", which seems to be pretty
important.  Under your proposed definitions, I think one could make a
reasonable argument that StarCraft or baseball are "board games" (in that
they are entertainments with rules and goals that contain things that could
reasonably be described as "pieces" that move among a predefined set of
possible "locations"), which is probably not what you intended.  Your
definition of "battle game" also seems very overbroad; it includes many
games that most people would say have nothing to do with "battle", such
as Klondike (card solitaire), Pandemic, etc.

You've defined "piece type" as "a group of pieces that are identical to
each other".  That definition seems to imply that it is a set of specific
pieces, whereas I think most people think of a "piece type" as a
taxonomical grouping.  Furthermore, your definition seems to imply that
pieces owned by different players are never the same type, which I think
also conflicts with common usage.

Your count of "over 2,000 documented board games", while technically
accurate, is far short of the true number.  BoardGameGeek's game database
currently contains 61,611 board games, and if your definition of "unique
game" is generous enough to include all the variants on chessvariants.org,
then I'd wager the true number is at least 100 times that.

You say that "at some point everyone will need to pick a game to play." 
If you mean that everyone will need to agree on one game to be the only
game ever played by any person ever again, I think the idea that this is
necessary, desirable, or even feasible is extremely naive.  Conversely, if
you only mean that a single person typically will not want to play 2,000
games SIMULTANEOUSLY, and therefore any specific individual will need to
settle on one game to play on any given lunch break, then the segue to
talking about the "best game" seems unjustified.

Furthermore, your suggested criteria of "originality" seems to directly
undermine the concept that such a thing as a "best game" is possible,
since it implies a yearning for novelty.  No single game will remain novel
forever.

Actually even if you do not necessarily consider different kind of piece just because they belong to the other player, there is a way to consider them different kind of pieces in some cases, such as in Chinese Chess you can say the 象 is restricted to one side of the board and the 相 is restricted to the other side of the board, the 卒 moves one way and 兵 moves in other direction, and so on.

You also CAN consider a white pawn on e3 and a white pawn on d3 to be different kinds of pieces, because one of them is only allowed to move to e4 and the other is only allowed to move to d4.

But it is also POSSIBLE to construct the rules in such a way that all pawns share the same rules, and location and owning player are treated as accidental, rather than essential, properties.

Thank you for your valuable input. As a result, I edited my article right
away. Hopefully, it has less issues then the first draft.

http://www.quangtrungki.com/gametheory.html

Thank you for your valuable input. As a result, I edited my article right
away. Hopefully, it has less issues then the first draft.

http://www.quangtrungki.com/gametheory.html