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Do bridge paradoxes exist?

Being logically-minded, I'm sure many bridge players are aware of the unusual fact involving three dice:

Die A has sides 2, 2, 4, 4, 9, 9.

Die B has sides 1, 1, 6, 6, 8, 8.

Die C has sides 3, 3, 5, 5, 7, 7.

You pick one die, and then I pick another, and the higher roll wins.

Whichever die you pick, I can beat you 5/9 of the time.

Suppose you have three lines available to you in MP:

1/3 of the time, A>B>C

1/3 of the time, B>C>A

1/3 of the time, C>A>B

Whichever line you choose, there is another line that will average 66% against you. There is therefore no optimal line. (I guess the correct play would be to choose one at random).

This is probably more likely to occur at IMPs rather than MPs, due to the weighting.

So a question - does there exist a bridge hand, in which there is no optimal line? That is, if you informed the other table which line you plan to play, single dummy, you will (in the long run average) always lose?

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