Thinking Machine 4 is just such a game.
In response to each one of your moves, the Java applet creates a breath-taking display of beauty as the AI maps out future potential moves whilst deciding upon the best one to make. As each move is presented by an arc connecting two squares, yellow for black and green for white, a window into the soul of the machine is opened for all to see. And while the computer contemplates the possibilities, some often several moves ahead, a network of color is formed with the brighter arcs drawn representing moves the AI thinks are better for white. It is fascinating to watch the machine think 'out loud' as it determines each move, and those who are astute might even learn something in the process.
Created by Martin Wattenberg, with Marek Walczak. The authors state that the goal of the piece is not to make an expert chess playing program but to lay bare the complex thinking that underlies all strategic thought.