Arm's Length: an original card game

In most Anglo-American trick-taking games the only rule of trick-taking is that you must follow suit if you can but may otherwise play any card. But there are still some old European games in which you must also seek to win the trick if you can, and may not underplay. That proved to be the only workable mechanism for this one, as you will see.

Cards: 52, ranking AKQJ1098765432 in each suit.
Deal: Deal each player 13 cards, one at a time and face down.
Object: In each round one member of each partnership aims to win as many tricks as possible and the other as few as possible. The difference between the numbers of tricks they win is their 'arm's length'.
Play: After examining their cards two partners agree which of them will take the high road and which the low. The player at dealer's left leads to the first trick. There is no trump suit until someone can't follow suit to the card led. Whatever they then discard to that trick establishes trumps for the rest of the round.

Any card may be led to a trick, but the rules of following are 'forcing'. This means that you must seek to win the trick if you can (even if, as the low player, you don’t want to). Specifically:

You must follow suit if you can and must beat the highest card so far played if you can, unless someone has already beaten it with a trump.

If you can't follow suit you must play a higher trump than any so far played if you can. If you can't play a higher trump you may make any discard.

The trick is taken by the highest card of the suit led or by the highest trump if any are played, and the winner of each trick leads to the next.
Score: At end of play each partnership scores 10 times their arm's length plus the number taken by the high player. For example, if North-South take respectively five and three tricks they score 25 points (5+2x10), while East-West, taking respectively four tricks and one, score 34 points (4+10x3).

If both partners win the same number of tricks then (logically) they just score the number taken by the high player.

If the high player takes fewer tricks than the low they score zero.
Game: A game is four deals, the turn to deal passing regularly to the left. Scores are accumulated as play proceeds and winning side is the one with the highest total.