How much did Chess inspire Alice in Wonderland?

A brief Chess history

There is one board game that is known throughout the entire world, a game that can be played by people from all ages and nationalities, but is also one of the hardest to understand. Many people are unable to understand the game; moreover they are incapable to play it. What is it in this simple-looking board game that makes the entire world interested in it? What is it that makes us stay focused for hours, days and even months in the thirty-two little figurines on the checkered board? What is it that makes it one of the most played and adored of them? Why is Chess so powerful?
The story of the Chess board game begins a long time ago; it is possible that it started in ancient times when people haven't even named it. The game that we know of is, however, considered to have its origins from the Indian Shatranj. When in the 1200 the games rules started being modified in Europe, is when today's variation was born.
Chess is a game that connects logics, mathematics, the ability to foresee and visualize, being perceptive of the others ideas and plans. It is a pure challenge that one mind presents to another. The pace can be fast or slow, the moves can be many and also very little, the positions can vary and the number of routes toward the win is almost endless.

Inspiring Alice in Wonderland

It is also the game that may have inspired the story Through the Looking-Glass, and What Alice Found There by Lewis Carroll.
Just like the first story about the young girl Alice, Through the Looking Glass is also based on the idea of a game. Unlike in the first one, the sequel is not based on the game of cards but about Chess and its marvellous and odd passages, movements and understandings of space. One of the main ideas through the story is the battle between the two coloured armies of figurines. In the board game they usually are in black and white, but in Carroll's mind they are white and red. Just like in a real chess game, in the story we witness the abilities of different pieces and get to know a lot of the actual rules of the game.

How the Red Queen Enters

The explanation by the Red Queen to Alice how she can transform from a pawn to a queen, the ability of the first to move backwards in time just like the queen piece can move around, the brooks that divide the story's field into several section, which can easily be related to the actual chess borders between squares (when Alice's pawn moves a square the surroundings change) these are all references to the board game.
The themes of both Carroll's most famous books (Alice's Adventures in Wonderland and Through the Looking Glass) are about widely known games and game pieces (Cards and the Deck of Cards, Chess and the Chessboard), we cannot help ourselves but wonder what would have a possible third book be about? Both Chess and Card games are connected with the ability to provoke the opponent into making a mistake and seeing through them, what were other games that could've inspired the genius of the author?