Games are mathematical. That's not something you can avoid. If there are rules for moves and goal states, you've already entered mathematics through logic and proof theory. And even for the simplest games, there is a rich mathematical theory studying it's structure and analysing results.

Mathematicians aren't just interested in finding optimal strategy and assigning a solution to a game. They also look to generalise and abstract theories of the gameplay and find ways to evaluate statements in the ontology of the game. Even simple games have rich logical calculi, and there are questions of rule independence and game extensions that can always be asked.

Dynamic Epistemic Logic is one of the general settings in which more advanced theories of game play have been formulated. Whenever two or more people are involved in gameplay, there are important distinctions between belief, knowledge, shared knowledge, and strategy that must be made to fully understand the dynamics. DEL (and a number of related settings) have been used to evaluate many common games, from simple pebble and card games to complicated board games and beyond, as a means to understand the evolution of belief systems and evaluate strategy during the play.

The Dynamic Epistemic Logic of Games

Epistemic Logic and the Foundations of Decision and Game Theory

Selection Monads and the Relation Between Game Theory and Proof Theory

I think the real mathematical answer to your question, then, is every popular game. There's no "most mathematical". Proof theory, models, modal logics, agent calculi and bisimulation lie at the heart of all games.

Games are mathematical. That's not something you can avoid. If there are rules for moves and goal states, you've already entered mathematics through logic and proof theory. And even for the simplest games, there is a rich mathematical theory studying it's structure and analysing results.

Mathematicians aren't just interested in finding optimal strategy and assigning a solution to a game. They also look to generalise and abstract theories of the gameplay and find ways to evaluate statements in the ontology of the game. Even simple games have rich logical calculi, and there are questions of rule independence and game extensions that can always be asked.

Dynamic Epistemic Logic is one of the general settings in which more advanced theories of game play have been formulated. Whenever two or more people are involved in gameplay, there are important distinctions between belief, knowledge, shared knowledge, and strategy that must be made to fully understand the dynamics. DEL (and a number of related settings) have been used to evaluate many common games, from simple pebble and card games to complicated board games and beyond, as a means to understand the evolution of belief systems and evaluate strategy during the play.

The Dynamic Epistemic Logic of Games

Epistemic Logic and the Foundations of Decision and Game Theory

Selection Monads and the Relation Between Game Theory and Proof Theory

I think the real mathematical answer to your question, then, is every popular game. There's no "most mathematical". Proof theory, models, modal logics, agent calculi and bisimulation lie at the heart of all games.

Games are mathematical. That's not something you can avoid. If there are rules for moves and goal states, you've already entered mathematics through logic and proof theory. And even for the simplest games, there is a rich mathematical theory studying it's structure and analysing results.

Mathematicians aren't just interested in finding optimal strategy and assigning a solution to a game. They also look to generalise and abstract theories of the gameplay and find ways to evaluate statements in the ontology of the game. Even simple games have rich logical calculi, and there are questions of rule independence and game extensions that can always be asked.

Dynamic Epistemic Logic is one of the general settings in which more advanced theories of game play have been formulated. Whenever two or more people are involved in gameplay, there are important distinctions between belief, knowledge, shared knowledge, and strategy that must be made to fully understand the dynamics. DEL (and a number of related settings) have been used to evaluate many common games, from simple pebble and card games to complicated board games and beyond, as a means to understand the evolution of belief systems and evaluate strategy during the play.

I think the real mathematical answer to your question, then, is every popular game. There's no "most mathematical". Proof theory, models, modal logics, agent calculi and bisimulation lie at the heart of all games.

Games are mathematical. That's not something you can avoid. If there are rules for moves and goal states, you've already entered mathematics through logic and proof theory. And even for the simplest games, there is a rich mathematical theory studying it's structure and analysing results.

Mathematicians aren't just interested in finding optimal strategy and assigning a solution to a game. They also look to generalise and abstract theories of the gameplay and find ways to evaluate statements in the ontology of the game. Even simple games have rich logical calculi, and there are questions of rule independence and game extensions that can always be asked.

Dynamic Epistemic Logic is one of the general settings in which more advanced theories of game play have been formulated. Whenever two or more people are involved in gameplay, there are important distinctions between belief, knowledge, shared knowledge, and strategy that must be made to fully understand the dynamics. DEL (and a number of related settings) have been used to evaluate many common games, from simple pebble and card games to complicated board games and beyond, as a means to understand the evolution of belief systems and evaluate strategy during the play.

The Dynamic Epistemic Logic of Games

Epistemic Logic and the Foundations of Decision and Game Theory

Selection Monads and the Relation Between Game Theory and Proof Theory

I think the real mathematical answer to your question, then, is every popular game. There's no "most mathematical". Proof theory, models, modal logics, agent calculi and bisimulation lie at the heart of all games.