Is it possible to design a player rotation system for Pair Go where

a) each player makes 1/4 of the moves,

b) each player's moves are preceded equally often by moves made by each one of the opposing players, and

c) each player's moves are followed equally often by moves made by each one of the opposing players?

you probably want to add the condition that no player switches colors.

There is a system. More than one.

Have the players of one team alternate and the other players play each twice before handing the bowl to the partner (alternating at half speed).

If you have A1 and A2 for team A and B1 and B2 for team B it looks like this:
A1 B1 A2 B1 A1 B2 A2 B2 and start over

If you think it unfair (it probably is) that one team has always to alternate while the other only alternates at "half speed", you can change the role of the teams after 8 moves. Players won't be able to tell whether it is their turn or not, though. Might be easier to do it the way it is usually done and play 2 games.

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If something sank it might be a treasure. And 2kyu advice is not necessarily Dan repertoire..

Sure... just have a move pattern of ACADBCBD, where A and B are one team and C and D are the other. You could even follow it with the pattern reversed by side, so that C and D have a chance to play twice in a row (ACBCADBD).

The only theoretical problem with any such pattern is that you don't respect the maxim that a player shouldn't play two moves in a row for their own team.

Realistically, you'll likely have all sorts of move violations as players get confused as to whose turn it is to play.

Thank you, guys. Your suggested 16-move protocol where average alternation speed is the same for both teams (I should have added that condition, too) is exactly what I was looking for. I agree that it's unpractical, though.

FWIW, when I used to play pair go, which we called tandem go (or random go ), each player made 5 moves in a row. To avoid confusion, we took out the 5 stones to play at the start of our turn.

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One way to perhaps minimize the 2-move in a row violation (or its impact?) is to have the weakest player among the four make two moves and everyone else alternate.

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Dave Sigaty
"Short-lived are both the praiser and the praised, and rememberer and the remembered..."
- Marcus Aurelius; Meditations, VIII 21

What do you mean? The weaker player and the stronger player of the same team have the same alternating pattern (if they shall play the same number of moves in a game). They either alternate or they each play n stones in sequence.

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If something sank it might be a treasure. And 2kyu advice is not necessarily Dan repertoire..

Forget my suggestion! I just realized that in my plan I fix the rotation issue but only by unbalancing the number of moves played.

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Dave Sigaty
"Short-lived are both the praiser and the praised, and rememberer and the remembered..."
- Marcus Aurelius; Meditations, VIII 21

One could think about an app that serves both at keeping time (clock), and indicating whose turn it is to play.

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It occurs to me that the standard rotation system can be unfair because the weaker player in one pair who is followed by the stronger player in the opposing pair can play ko threats to make entire stretches of the game effectively a contest between the stronger player in their pair and the weaker player in the opposing pair.

One advantage of playing 5 stones at your turn is that the weaker player is more likely to run out of kikashi plays.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.