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Tandem backgammon

Tandem Chess, more widely known as Bughouse Chess, is an extremely popular (and even more fun) variant of chess played between two 2-players teams, generally at high speed. Here is my go at importing some of the fun of Bughouse Chess into backgammon. It is a modest change from tournament backgammon, using only the scoring system as a link between the two simultaneous games.

It is not easy for me to get three players in order to play that variant over the board, and I have managed to do it only once. So if you play it, by all means tell me about how it went !

Rules of Tandem Backgammon

Main rules
1. Two two-players teams (team A, players A1 and A2, team B, players B1 and B2) play a match to n points on two independent backgammon boards (A1 vs B1, A2 vs B2), each with its own cube and its own clock. Each pair of games is played simultaneously : the clocks are started in the same time. After one of the games is finished, the other one is played until the end.
2. All games count towards the same scoreline. E.g. if in the first pair of games A1 wins a doubled gammon and A2 loses a single game, team A will lead 4-1.
3. The clocks are reset after each pair of games. The recommended time control is 2 minutes per game plus the usual 12-15 seconds of increment.
4. If a team reaches n points by winning the first of the two simultaneous games, the other game is still played until the end. If both teams reach n points in the same pair of games, the match is a draw.

Variant 4'. if the tournament format requires a winner, then as soon as one team reaches n points the match is over, even if the second game is still unfinished.

5. If a player forfeits on time, his opponent scores the maximum number of points which is still possible in the game (generally, three times the cube value).
Fuzzy variant 5'. if the players agree that the forfeiting player can avoid a gammon or a backgammon by minimally competent play, then that player loses only the points of a single game, or respectively of a gammon.
6. ("Crawford" rule) When the opponents are 1 or 2 points away from winning the match at the start of the game, it is allowed to send the cube in only one of the two simultaneous games. That cube can very well be a redouble to 4. The above rule applies to all games played from those scores : there is no post-Crawford.
7. Unrestricted communication is allowed within a team, but not manual interference on the partner's board.

How to play it

Well that is largely for you to discover ! So far I have managed to play only one test match, which confirmed that there was no blatant bug in the game design and that the experience is pretty pleasant. Both teams were constituted of players of unequal strength, which emphasized that the decisions of how much time to spend on coaching / waiting for advice are pretty difficult - indeed one of the "coaches" lost a game on time! We had only one of the "double sits" that are characteristic of Bughouse Chess. Double sits happen when neither A1, neither B2 wants to play first, and the clock decides who will have to move in order to avoid loss on time. While in Bughouse Chess the double sits happen when a player waits for the killing piece, in Tandem Backgammon it can happen when a cube decision is pending and the situation on the other board is very volatile : "if my partner flunks and gets gammoned on a 2-cube, I might as well accept that dangerous cube offer".

And what about the indispensable companion of the match player, the match equity table ? Well, the match dynamics of Tandem Backgammon appear quite complex, and I am in no way competent for computing a real match equity table. Still, in order to give an idea of whether the "Crawford" rule doesn't lead to absurdities, here is a match equity table computed by making the very simplifying assumption that at any score only one of the two games chosen at random is doubled, with a 28% gammon rate and 0% backgammon rate (see below). The assumptions can be expected to consistently underestimate the trailer's equity. The table indicates that while the values from 2-away on are rather regular, the 1-away equities are pretty low for the leader. That would argue for a "real" Crawford rule at 1-away, with no cube at all allowed. However, I prefer my version of allowing only one cube, which has the advantage of providing interesting cube decisions at every score except 1-away, 1-away. So if you are going to play, the fact to take with you is that getting to 1-away, n-away is not a good bargain, and that getting that last point is big.