I have seen a lot of debate about who is better between Carlsen and Kasparov.
Could a match between Carlsen and the exact same Deep Blue configuration that beat Kasparov be used to settle this?
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I'd say no. Playing against a human being is a lot different than playing computers. Here is an article (unfortunately, it is in Dutch) about a German player with a rating under 2100 who regularly beat the top chess programs, by playing strange openings and long-term sacrifices. This was a few years after the Kasparov - Deep Blue match.
Deep blue was dismantled soon after playing Kasparov.
So, I guess, we will never know what would have happened. However, if it does happen, then I would favour Carlsen winning against the computer. At the time that the match against Kasparov was played, computers weren't really stronger than humans.
And to be honest, I think, Kasparov lost because of his usually attacking instincts and the fact that he played openings that he never usually played.(This was because, he feared the computer had access to his games and he wanted to take the computer out of theory known at that time.) Even then, Deep Blue barely managed to win when Kasparov fell into a known trap in the last game.
So, I would say if this hypothetical match did happen and Carlsen plays at his best, Carlsen would easily win against Deep Blue.
However, this does not mean that in the current times, humans would beat computers without odds. Deep Blue was far weaker than modern-day engines, say Stockfish or Komodo. If you want to see the strongest human chess player vs strongest engine and who will win, then, engines would reign supreme.
Chess engines and hardware since Kasparov played Deep Blue continue to improve.
Recently (Dec 2016) Stockfish achieved a rating of 3478: http://www.computerchess.org.uk/ccrl/404/
Carlesen fares reasonably well against it (on a reasonably normal computer) though its a strong engine.
Carleson playing against Deep Blue also has a couple of advantages Kasparov didn't have. Carlesen himself can use computers to prepare to play a computer AND Deep Blue has now has games on record so can have its own play analyzed.
So a Carlesen/Deep Blue game would tell us little. More interesting would be a Carlesen game against a modern chess engine with less time restrictions per move on searches, and on optimized hardware beyond what you can get at home.
Even then advantage goes to machine (likely).
I would say no.
In an interview with GM Illescas, who was on the IBM team, I remember that he said Kasparov complained Deep Blue was not designed to beat a GM, it was designed to specifically beat him.
As the question says with the exact same configuration, I would say no because Deep Blue didn't include Carlsen’s games in its database in 1996 for an obvious reason.