KanBan Database architecture

Question

I'm trying to implement a kanban agile board like Trello in my application. I'm wondering how to do it the best way. I'm considering these entities:

Board
has many Lists

List
has many Cards

Card
contains some content

However I'm stuck with ordering of Cards. Each Card should have a sort position to sort Cards in particular order in a List. When dragging a Card, I should change it's position and save it in the database. What is the most efficient way of doing this?

Adding a position field to each Card seems redundant since I would have to recalculate positions of all Cards in a List (or two) after I drag a Card to a different position (there will be hundreds of Cards). I was thinking of storing an array of all Card ids in a List and sort Cards by this array. What are pros/cons of this solution? And are there any better solutions?

I'm using Ruby on Rails and PostgreSQL.

UPDATE

Using @cske answer I came up with the following solution:

CREATE OR REPLACE FUNCTION move_buyer_card(
    new_list_id   INT
  , param_id      INT
  , new_position  INT
) RETURNS FLOAT4
LANGUAGE plpgsql SECURITY DEFINER
AS $$
DECLARE
  var_lower_bound FLOAT4;
  var_upper_bound FLOAT4;
  var_new_weight  FLOAT4; /*between 0 and 1*/
BEGIN
  IF new_position < 2 THEN /*first position*/
    var_lower_bound := 0;
    SELECT MIN(weight) FROM Buyers
      WHERE board_list_id = new_list_id
      INTO var_upper_bound;
    IF var_upper_bound IS NULL THEN /*empty list*/
      var_upper_bound := 1;
    END IF;
  ELSE /*not first position*/
    WITH ordered_cards AS (
      SELECT id, RANK() OVER (ORDER BY weight ASC) AS rank, weight
      FROM Buyers WHERE board_list_id = new_list_id
    )
    SELECT cards0.weight, cards1.weight from ordered_cards cards0
      JOIN ordered_cards cards1
        ON cards0.rank = cards1.rank - 1
      WHERE cards1.rank = new_position
      INTO var_lower_bound, var_upper_bound;
    IF NOT FOUND THEN /*only 1 item in list OR last position*/
      SELECT MAX(weight) FROM Buyers WHERE board_list_id = new_list_id
        INTO var_lower_bound;
      IF var_lower_bound IS NULL THEN /*empty list*/
        var_lower_bound := 0;
      END IF;
      var_upper_bound := 1;
    END IF;
  END IF;
  var_new_weight := var_lower_bound + (var_upper_bound - var_lower_bound) / 2;
  UPDATE Buyers
    SET weight = var_new_weight,
      board_list_id = new_list_id
    WHERE id = param_id;
  RETURN var_new_weight;
END;
$$;

Answer 1

Consider this, trick is not storing the position, but a weight so you can insert between any two elements

create table listOfCards (
   listId INTEGER
  ,cardId INTEGER
  ,weigth FLOAT4
  ,PRIMARY KEY (listId,cardId)
);

CREATE OR REPLACE FUNCTION addCard(
    plistId INT
  , pcardId INT
  , ppos    INT
) RETURNS FLOAT4
LANGUAGE plpgsql SECURITY DEFINER
AS $$
DECLARE
  vlb FLOAT4;
  vub FLOAT4;
  vnw FLOAT4;
BEGIN
  IF 2 > ppos THEN
    vlb := 0;
    SELECT min(weigth) FROM listOfCards WHERE listId = plistId INTO vub;
    IF vub IS NULL THEN /*empty list*/
      vub := 2;
    END IF; 
  ELSE
    with corder as (select cardId,RANK() OVER (order by weigth asc) as r,weigth FROM listOfCards WHERE listId=1)
    select c0.weigth,c1.weigth from corder c0 JOIN corder c1 ON c1.r = c0.r + 1 where c1.r = ppos INTO vlb,vub;
    IF NOT FOUND THEN
      SELECT max(weigth) FROM listOfCards WHERE listId = plistId INTO vlb;
      IF vlb IS NULL THEN /*empty list*/
        vlb := 0;
      END IF;
      vub := (vlb+1) * 2;
    END IF;  
  END IF;
  vnw := vlb + (vub-vlb) /2;
  INSERT INTO listOfCards(listId, cardId, weigth) 
       VALUES (plistId,pcardId,vnw )
  ON CONFLICT ON CONSTRAINT listofcards_pkey DO UPDATE SET weigth = vnw ;
  RETURN vnw;
END;
$$;

Usage:

select addCard(1,1,1);
select addCard(1,2,1);
select addCard(1,3,2);
select addCard(1,4,2);
select addCard(1,5,5);
select addCard(1,5,2);

select * from listOfCards ORDER BY weigth;

Result: 1,2,0.5 1,5,0.5625 1,4,0.625 1,3,0.75 1,1,1