There aren't an infinite number of chess positions, moves or even games, so that's not a good example. It's possible to come up with a number game that could have infinite possibilities, but that doesn't mean that the universe could even contain some of the options within our visibility. Our current state of knowledge about the universe strongly suggests that there's a finite limit to the available knowledge (I.e. between the Planck scale and the visible horizon due to the speed of light).
A googolplex looks to be the first number we've found that is too big to be contained in our universe.
A googolplex looks to be the first number we've found that is too big to be contained in our universe.