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use strict;
use warnings;
...
    # Rotate last position to second
    splice @players, 1, 0, pop(@players);
}

1) 1-6, 2-5, 3-4
2) 1-5, 4-6, 2-3
3) 1-4, 3-5, 2-6
4) 1-3, 2-4, 5-6
5) 1-2, 3-6, 4-5