Mechanical Complexity vs. Game Depth: Go/Checkers and Rock Paper Scissors

The game of Go is played with two pieces: White and Black on a grid of varying sizes, most commonly 19 by 19. The game of Checkers is played with two pieces: Red and Black on an 8 by 8 grid. In terms of board space, Go has more open space overall.

In Go, the object of the game is to surround your opponents pieces with your own in a full enclosure. Once a piece is placed, it cannot move.  In Checkers, the object of the game is to kill your opponents pieces by hopping over them diagonally, otherwise moving forward.

Go has more straightforward mechanics here: Players alternately place a piece on the board, capturing the appropriate pieces when the enemy is surrounded. In Checkers, you can move a piece forward, capture another piece, chain capture another piece with multiple hops, promote a piece by landing at the end of the board thus allowing you to move in any direction.

Checkers, overall then, has more mechanical complexity. There are more rules to memorize regarding what you can and cannot do. The moves you can make are more complicated and strung together...

...and yet Go is the game with overall more strategic depth. The game of Checkers has been solved by computers, giving you a perfect play by play of how to win (or at least draw) every game of checkers. Part of this is due to the board space disparity. 64 squares cannot compare with 361 tiles in terms of problem space.

Yet, Go is routinely played on smaller boards to practice. However, the game of Go has only been solved up to (at the time of this writing at least) 7 x 7 grid. How can this be?

Mechanical complexity does not directly translate into game depth. Game depth is created by unique interactions between you and your opponent.  Each move has far flung ramifications in Go, although each individual move is simple, eventually, in the end, each individual move will matter.

If you want to take this principle to the extreme, look at Rock/Paper/Scissors/Spock/Lizard. This game is an extension of RPS in that there are many more unique roles involved that have different interactions with the existing roles.  RPSSL also has a greater problem space than RPS, having 5 choices at any given time rather than 3... However, when you play RPSSL, you quickly find that the depth of RPSSL is exactly the same as RPS, despite the fact that there is more rules baggage, memorization and problem space.

However, let us imagine a game tentatively called RPS^3, where you simply perform rock/paper/scissors 3 times in a row until someone wins best 2 out of 3. Suddenly, this game has depth, despite being utterly simplistic. Why is this? Because previous interactions start influencing future interactions.

Let's take this further and consider 'uneven RPS' where winning with scissors scores 5 points, winning with rock scores 3 points and winning with paper scores 1 point. Now each individual interaction has more depth as well somehow, despite the fact that the game hasn't gotten any more mechanically complex simply because the decisions have uneven outcomes (despite all being 'winning' states.)

There are other elements to Game Depth, but before I veer too far off course, these simple examples should illustrate to some faint degree that, despite how complex each individual move can be, it is in large part due to the interactions that you can have with your opponent that Game Depth is mostly created.