You may notice parenthetical entries in the running score tally. Those represent the nights when we had exactly five players, and do not contribute to the cumulative player totals.
The equitable system we've devised for playing with five people is a swiftly rotating ostracism. After your turn as declarer, you must sit out a deal. Ideally this happens around a round table, so that no physical shifting is required, but still it's problematic. Partnership lines are continually redrawn: for any given deal, your partner is whichever person of the five is not out and not sitting adjacent to you, though he or she may be facing you at an oblique angle. This also tends to guarantee that whoever does sit adjacent to you is never your partner; often for the whole of the night, since the every-man-for-himself scoring system required prevents proper rubbering, and hence the seating is never rearranged.
It's the scoring that's the main difficulty. Scores are tabulated in five columns, one for each individual, wherein above- and below-the-line points are stacked. Nothing is subtracted, so at the end of the night, everyone's score is positive. Uncomfortably, because of the rotation of partners, you can get into a situation where you're vulnerable and running a 90-point part-score, while your partner of the moment is non-vulnerable with no partial. Your two sets of bidding priorities are necessarily vastly different, and a pusillanimous player will be tempted to falsely underbid in order to make his own game while leaving his partner unfulfilled. This unpleasant nonmutuality goes hand in hand with other trickery, such as trying to make your partner play the contract, especially an ill-fitting contract, so that she and not you will have to sit out the next round.
There are other questions too, like Does a partial get cut off by an opposing game? Even if the holder of the partial is the fifth wheel during that game? and Ought the first column to reach two games receive a rubber bonus? If any math-minded person -- Matos? Anne? -- would like to weigh in on a better way to handle the scoring of these games, please do!
After typing this up, I'm starting to feel that the traditional way might be better, a slowly rotating ostracism, in which the fifth player sits out while four play their whole rubber, then randomizes in. What do you all think? It's a boon for the scorekeeper and for the comity of partnerships. The downside, of course, is just the fifth wheel's boredom during an interminable rubber, and the consequent vicious cycle in which the bored person chats with the players, thereby distracting them and protracting the rubber further, at the fifth wheel's own expense. Certainly we ought to work on our speed, but I for one am going to bring a book next time; perhaps this one.