It doesn't matter because they won't live in the same period.
Morphy vs Carlsen?
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These What If scenarios are typically a waste of time.
carlsen wins thats the end
What if there is a cake in 1855 but the cake is eaten and in 2009 there is another cake and then the 2009 cake timetravels to 1855 and then there is two cakes and one cake gets eaten but the other one doesn't and in the end it turns out it was a dinosaur disguised as a cake that timetravelled back to 1855 to eat the other cake and some humans?
If ever that Paul Morphy and Magnus Carlsen both lived at the same time and they have a chess match, who do you think will win??