Regarding the game of Go:

"....suggesting a game-tree complexity of 10^360. For the number of theoretically possible games, including games impossible to play in practice, Tromp and Farnebäck give lower and upper bounds of 10^1048 and 10^10^171 respectively. The lower bound was improved to a googolplex by Walraet and Tromp. The most commonly quoted number for the number of possible games, 10^700 is derived from a simple permutation of 361 moves or 361! = 10^768. Another common derivation is to assume N intersections and L longest game for NL total games. For example, 400 moves, as seen in some professional games, would be one out of 361^400 or 1 × 10^1023 possible games." - Wiki