I'd go with Cleopatra and Joan of Arc, the reason being that'd be a big crowd pleaser.
What inter-era match would you most like to see?

i would like to see paul morphy versus bobby fischer once in morphy's time and the other 1972 iceland with all the cameras.
capablanca versus kasparov...one game in cuba 1960s and the other in the white house during clinton administration.
It would be interesting to see for example Hou Yifan vs Morphy or Lasker just to see how much the level has improved. I think a 2600 player of today would beat Morphy but lose against Lasker.

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Try harder. You're gonna get fired by the boss scammer if he sees this mediocre effort.
If you could pick two people from different eras to have a match, who would you choose and why?