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This Python3 program runs in 83ms.

Solution:The winning players were Colle and Dragon. In the final round Colle played French and Dragon played Bishop.There is only one possible sequence of rounds, but there are three possible outcomes for the matches (distinguished by the numbers in square brackets below):

Round 1: AvF (draw), BvE (draw), CvD (C wins [1, 2], D wins [3])

Round 2: AvB (draw), CvE (C wins [1, 3], E wins [2]), DvF (draw)

Round 3: AvC (A wins [1], C wins [2, 3]), BvF (B wins), DvE (draw)

Round 4: AvD (D wins [1, 2], A wins [3]), BvC (draw), EvF (draw)

Round 5: AvE (E wins [1, 3], A wins[2]), BvD (D wins), CvF (draw)

The final scores are always: C and D, 3 points; B and E 2½ points; A and F, 2 points.