The game that I think is one of the most well balanced games is chess, which is why I think it has stood the test of time and is still very popular today. When you look at it through the lens of “asymetric games,” chess is pretty symmetric with the one exception that is mentioned in the reading, which is that white always goes first. Because of this, if you look at how a chess engine scores the very beginning of a chess game, it will usually say that white is winning by a tiny fraction. However, this slight advantage is soon equalized by good play from black. Chess is also asymetric in the sense that there is completely different opening strategy for black and white. It is plausible that one could be much better trained to play as one color over the other, which can cause imbalance as well. This imbalance can be mitigated simply by spending an equal amount of time training with both colors. Once the game reaches the middlegame/endgame, it usually doesn’t matter anymore which color you are playing.
In terms of balance between strategies, chess is also very balanced. In the opening, there are a number of different good strategies that players can choose from, and there is no particular strategy that is necessarily better than another. This creates challenge because it requires players to learn about a variety of different openings and the potential strategies behind them. After the opening, however, there usually is one optimal strategy that players should follow. However, the optimal strategy is not usually obvious, which is what makes chess challenging. There are many options for suboptimal stragies, so players must learn how to tease out what the optimal strategy is in a given position.
As for balance between game objects, chess has a lot of balance despite having pieces with differing levels of value. For example, a rule of thumb is that pawns are worth one point and queens are worth nine points, making queens nine times as valuable as pawns. However, this doesn’t mean that queens get to just dominate the board and all other pieces become usesless. Because the queen is so valuable, it becomes a quick target, so it is not advantageous to bring your queen out right away. Also, pawns are supposed to be the least valuable pieces, but they have a special ability to turn into whatever piece you want it to be if you can get your pawn to the end of the board.
I think the balance between pieces in chess incorporates both transitive and intransitive relationships. It is transitive in the sense that there is a rule of thumb about how much each piece is worth. For example, if you’re going to give up a knight, which is worth about three points, you would hope that you would get at least something back in return of similar value, whether that be another knight, a bishop, or three pawns. Or you might think that it is advantageous to give up a knight if you will win back a bishop and a pawn, for example. It is also intransitive because these piece values are not solidified and depend on the relationships between pieces. For instance, having two bishops is worth more than two knights because of how powerful two bishops are together.