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Duplicate bridge was created to "eliminate" the luck factor. That is partnerships are compared only against other partnerships playing the same cards.

Rubber bridge is a different animal. Here, "luck of the draw" is clearly a major factor in the result, at least until you get to a "law of large numbers" point where the luck factors cancel out.

Suppose there are two partnerships, A and B, playing ONE rubber. From their play at duplicate, we "know" that partnership A plays one trick better than the other. Clearly partnership A would have better than a 50-50 chance at rubber as well. But how much better?

Is there any computer software, statistical formula, or mathematical algorithm that could estimate the relative chances of partnerships A and B winning the rubber?

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As Eric Murray famously said in the case of Crown vs St. Clair Bridge Club:

"The game [rubber bridge] is only one of luck when played as the justices of the Ontario Superior Court play it in closed chambers."

That is of course the same Eric Murray of the Canadian partnership Murray & Kehela that was widely ranked the third best in the world during the 1960's and early 1970's.

Ironically, the luck element reduces as the overall quality of the players improves, yet increases in importance because the qualitative differences between the various players is reduced even more.

This question is difficult to address because of the above point. However, consider this advice to the budding "play for money" bridge player:

Choose Chicago against players who are a little bit weaker than you; but choose Rubber against players a lot weaker than you.

The reason is that when your skill advantage is small, you want lots of points in play, so that the luck evens out faster. When your skill advantage is larger, you want more opportunity for the opponent to make foolish decisions. A typical rubber-bridge strategy is to sit on a part-score and collect penalties for several hands before converting the game. Then repeat. even if the opponents get "lucky" and win the rubber, they will often have lost much more in penalties than the rubber bonus was worth.

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