Well btickler's statement is an opinion and not supported by any math. It appears he (and others) have confused the complexity of the game (often expressed with the Shannon number) with the amount of work required to solve the game. There is no known connection between these numbers for solving chess (other than to say brute force, which is a naïve analytical method, can't be used).
An example is tic-tac-toe. It has a large amount of games that can be played and almost nobody ever writes all down. But young children learn to play it perfectly without memorizing or writing down all the possible games. They use deductive logic.



"there is always just one option for the moves for one side, the entire range for the other"
This statement is clearly incorrect for positions where there is a forced move (that is to say 'only move' positions) and many other forcing combinations where making a second choice move loses outright to an easily seeable continuation. So, saying that in every chess position there are (insert number over 25) possible moves and then extrapolating from that is nonsense and facile as I said many posts ago.