If two computers using the same programming played each other in a game of chess, would the moves and outcomes always be the same for any given opening move? How does a computer choose it’s opening move if it goes first?
First of all, “with the same programming” doesn’t mean anything at all any more. The best chess computer in the world (and hence, the best chess player, period, in the world), by a significant margin, is a computer that wasn’t programmed to play chess. It was programmed to learn how to play games, and then it played a very large number of chess games against itself to learn how to play chess well. A true comparison would require two computers with both the same programming, and the same learning history.
That right there is enough to prevent duplicate games, because even if you copy over the entire learning history (which is doable), after the first game, the two won’t have the same learning history any more: One will have a history that included winning that game, while the other will have a history that included losing that game.
But even aside from that, almost all chess programs made, even the ones from before machine learning was a thing, included a small amount of randomness: The computer will usually choose whatever it thinks is the best move, but occasionally choose the second or third or whatever best, especially if it considers those moves to be very close in quality.
[Moderating]
Oh, and since this is about a game, let’s move it to the Game Room.