I am quite divided in the arguments I will present for either Chess and Counter-strike.
Every game has a finite amount of possibilities, however these possibilities is not really accounted for. Meaning that a "possibility" is a term not specified, and can therefore vary from person to person's perspective.
I've seen a lot of constructive arguments for both Chess and Counter-Strike.
However I have to personally say Chess in form of logical complexity and Counter-Strike in form of technical complexity. As argued for in other comments a game of chess has 90040 possibilities if 40 moves are played each game, which is a lot.
However Counter-Strike is a three dimensional, vector based game. Meaning that it has a lot more individual possibilities than other games like chess.
Counter-Strike is more complex by the fact that it's equation based.
For example. Chess as a game can move pieces in a 8 x 8 matrix. Meaning that at any point in the game, a piece has to be placed on one of these 64 points. It can't be 63.2 or 16.9. It has to be exactly in a spot.
In counter-Strike the movement of a player is equation based, meaning that a player can move exponentially close to a location, with a finite solution in the end.
All this comes down to that at any point in the game a player can be placed on more points than at chess.
A game of CS consists of 10 players, that can individually, non-linked move between points.
All this can be expressed in computing power. You can more or less calculate a games technical complexity in form of computing power needed to run it. It's a simple rule of thumb. This may vary on the engine whatsoever.
But psychologically I think chess is a more complex game.
In CS you only have a certain focual point. A) Shoot the enemy B) Plant/Defuse bomb, Rescue/deny rescue the hostages.
This all adds up to about 6 focus areas per game. Kill each player (5) and B (1).
Chess lets you have a total of 16 targets and focal points, meaning that you have a broader focal area.
I know this can be argued for setups like an AK vs an AWP isn't equal to a setup with a M4 vs an MP5. However this will technically go under technical complexity.
It's hard to debate, however in terms of technical complexity CS is superior.