Number of distinct chess positions and games I was wondering how many total possible chess games/positions are there? I know Shannon calculated an upper bound of about $10^{120}$ legal chess games and $10^{43}$ legal chess positions. Have there been any more recent developments?

Also, will we ever be able to know exactly how many legal chess games/positions are there in total? It will require tons of computing power but by Moore's Law we should eventually have the necessary computing power. Based on current estimates, when will this happen?
To answer the second part of your question, the number of total possible chess positions will eventually be calculated, but the number of chess games is still unimaginably large. THIS - broken link site will have a slice of the answers:

The number of possible chess positions after White’s first ply move is 20 (16 pawn moves and 4 knight moves).  There are 400 possible chess positions after two ply moves (first ply move for White followed by first ply move for Black).

this is because there are $20$ moves for white's move 1, and $20^2$, or $400$ moves at the beginning of move 2. then, the number balloons. the least number of moves to checkmate is 3, called the fool's checkmate. as for the other numbers, look on the site! as for when the numbers will be calculated, i'm not sure---yet.
To answer the second part of your question, the number of total possible chess positions will eventually be calculated, but the number of chess games is still unimaginably large. THIS - broken link site will have a slice of the answers:

The number of possible chess positions after White’s first ply move is 20 (16 pawn moves and 4 knight moves).  There are 400 possible chess positions after two ply moves (first ply move for White followed by first ply move for Black).

this is because there are $20$ moves for white's move 1, and $20^2$, or $400$ moves at the beginning of move 2. then, the number balloons. the least number of moves to checkmate is 3, called the fool's checkmate. as for the other numbers, look on the site! as for when the numbers will be calculated, i'm not sure---yet.