[Event "Rybka/IBM cluster"]Actually much more than “gazillions” – something in the order of 10^100, which is vastly more than the number of elementary particles in the universe. Obviously we could not go through all of them – nobody and nothing will ever be able to do that. But: you do not have to check every continuation. It’s similar to Alpha-Beta, which looks at a very small subset of possible moves but delivers a result that is identical to what you would get if you looked at every single move, down to the specified depth.
[Site "?"]
[Date "2012.04.01"]
[Round "?"]
[White "King's Gambit solved"]
[Black "?"]
[Result "1/2-1/2"]
[ECO "C33"]
[PlyCount "7"]
1. e4 e5 2. f4 exf4 3. Be2 $1 {The only move that leads to a draw.} (3.
Bc4 Nf6 $1 {and White loses.}) (3. Nf3 {is indeed winning for Black.} d6 $1
{The only winning move - everything else allows White to escape with a draw.}
({For instance the more popular} 3... g5 {allows White to draw after} 4. h4
$1) {In fact , Fischer's main line holds up incredibly well:} 4. Bc4 h6 $1 5.
d4 g5 $1 {(an exclam denotes any move which gives a better theoretical result
than every alternative)}) 3... d5 4. exd5 $1 {and White can hold a draw against
any attack Black can play.} 1/2-1/2